Casio CFX-9970G User Manual Download

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Matrix Inversion

Matrix

Mat A

Mat Z
MatAns

Example

To invert the following matrix :

Matrix A =

(Mat)

!Xw

• Only square matrices (same number of rows and columns) can be inverted.

Trying to invert a matrix that is not square produces an error.

• A matrix with a value of zero cannot be inverted. Trying to invert a matrix with

value of zero produces an error.

• Calculation precision is affected for matrices whose value is near zero.

• A matrix being inverted must satisfy the conditions shown below.

A A

–1

= A

–1

A = E =

• The following shows the formula used to invert Matrix A into inverse matrix

–1

A =

–1

d –b

ad – bc

–c

Note that ad – bc

Matrix Calculations

6 - 4

Summary of Contents for CFX-9970G

Page 1: ...antenna Increase the separation between the equipment and receiver Connect the equipment into an outlet on a circuit different from that to which the receiver is connected Consult the dealer or an experienced radio TV technician for help FCC WARNING Changes or modifications not expressly approved by the party responsible for compliance could void the user s authority to operate the equipment Prope...

Page 2: ... 2 Load the four batteries that come with calculator Make sure that the positive and negative ends of the batteries are facing correctly 3 Remove the insulating sheet at the location marked BACK UP by pulling in the direction indicated by the arrow 4 Replace the back cover making sure that its tabs enter the holes marked 2 in the illustration 5 Press m If the Main Menu shown to the right is not on...

Page 3: ...em lighter uTo adjust the tint 1 Use f and c to move the pointer to the color you want to adjust ORANGE BLUE or GREEN 2 Press e to add more green to the color and d to add more orange 9 To exit display color adjustment press m REMOVING AND REPLACING THE CALCULATOR S COVER To remove the cover Grasp the top of the cover and slide the unit out from the bottom To replace the cover Grasp the top of the...

Page 4: ...green to make data easier to understand Main Menu Display Color Adjustment Graph Function Menu Graph Display Example 1 Graph Display Example 2 Graph To Table Display Dynamic Graph Display Table Graph Numeric Table Recursion Formula Convergence Divergence Graph Example iii ...

Page 5: ... Enter the GRAPH Mode and input the following 3 TYPE 1 Y Specifies rectangular coordinates svwf 45 Stores the expression 2 4 COLR 23456 Press the function key that corresponds to the color you want to use for the graph 1for blue 2 for orange 3 for green 3 2 Orng Specifies the graph color J 6 4 6 DRAW Draws the graph You can also draw multiple graphs of different color on the same screen making eac...

Page 6: ...ter for division not Alpha Lock Normally once you press a and then a key to input an alphabetic character the key board reverts to its primary functions immediately If you press and then a the keyboard locks in alpha input until you press a again ...

Page 7: ...Y TABLE vi Page Page Page Page Page Page 128 Page Page Page Page Page 132 113 47 46 2 47 46 154 144 120 383 4 2 27 28 3 46 46 46 46 45 45 45 45 21 20 36 36 36 36 39 36 45 36 47 36 49 49 47 36 45 45 22 49 ...

Page 8: ...urning Power On And Off Auto Power Off Function Using Modes Basic Calculations Replay Features Fraction Calculations Exponents Graph Functions Dual Graph Box Zoom Dynamic Graph Table Function Quick Start ...

Page 9: ...le we ve indicated it as follows Press fh Whenever necessary we ve included samples of what your screen should look like If you find that your screen doesn t match the sample you can restart from the beginning by pressing the All Clear button o TURNING POWER ON AND OFF To turn power on press o To turn power off press o OFF AUTO POWER OFF FUNCTION Note that the unit automatically turns power off if...

Page 10: ...lude mixed arithmetic operators and parentheses the calcula tor automatically applies true algebraic logic to calculate the result Example 15 3 61 1 Press o to clear the calculator 2 Press bf d gbw Parentheses Calculations Example 15 3 61 1 Press bf d gb w Built In Functions The CFX 9970G includes a number of built in scientific functions including trigonomet ric and logarithmic functions Example ...

Page 11: ...Y FEATURES With the replay feature simply press dor eto recall the last calculation that was performed This recalls the calculation so you can make changes or re execute it as it is Example To change the calculation in the last example from 25 sin 45 to 25 sin 55 1 Press d to display the last calculation 2 Press d twice to move the cursor under the 4 3 Press f 4 Press wto execute the calculation a...

Page 12: ... dh jw Converting a Mixed Fraction to an Improper Fraction While a mixed fraction is shown on the display press d c to convert it to an improper fraction Press d c again to convert back to a mixed fraction Converting a Fraction to Its Decimal Equivalent While a fraction is shown on the display press M to convert it to its decimal equiva lent Press M again to convert back to a fraction Indicates 6 ...

Page 13: ...Quick Start xii EXPONENTS Example 1250 2 065 1 Press o 2 Press bcfa c ag 3 Press M and the indicator appears on the display 4 Press f The 5 on the display indicates that 5 is an exponent 5 Press w ...

Page 14: ...angular coordinates horizontal axis x vertical axis y or polar coordi nates angle distance from origin r Example 1 To graph Y X X 1 X 2 1 Press m 2 Use d e f and c to highlight GRAPH and then press w 3 Input the formula v v b v c w 6 4 Press 6 DRAW or w to draw the graph Example 2 To determine the roots of Y X X 1 X 2 1 Press 5 G Solv 1 ...

Page 15: ... the X 1 root obtained for Y X X 1 X 2 1 Press 5 G Solv 12345 6 2 Press 6 g 123456 3 Press 3 dx 4 Use eto move the pointer to the location where X 1 and then press w Next use e again to move the pointer to the location where X 0 and then press wto input the integration range which becomes shaded on the display ...

Page 16: ...ection Y1 X X 1 X 2 Y2 X 1 2 1 Press Zcc1 Grph to specify Graph for the Dual Screen setting 123456 2 Press J and then input the two functions v v b v c w v b cw 12345 6 3 Press 6 DRAW or w to draw the graphs BOX ZOOM Use the Box Zoom function to specify areas of a graph for enlargement 1 Press 2 Zoom 1 BOX 2 Use d e f and c to move the pointer to one corner of the area you want to specify and then...

Page 17: ...a appears in the inactive right side screen DYNAMIC GRAPH Dynamic Graph lets you see how the shape of a graph is affected as the value assigned to one of the coefficients of its function changes Example To draw graphs as the value of coefficient A in the following function changes from 1 to 3 Y AX2 1 Press m 2 Use d e f and c to highlight DYNA and then press w 3 Input the formula aAvxw 12356 4 ...

Page 18: ...R bw to assign an initial value of 1 to coefficient A 1 23456 5 Press 2 RANG bwdwbw to specify the range and increment of change in coefficient A 6 Press J 7 Press 6 DYNA to start Dynamic Graph drawing The graphs are drawn 10 times ...

Page 19: ...for the following function Y X X 1 X 2 1 Press m 2 Use d e f and c to highlight TABLE and then press w 3 Input the formula v v b v c w 6 4 Press 6 TABL or w to generate the number table After you ve completed this Quick Start section you are well on your way to becoming an expert user of the CASIO CFX 9970G Calculator To learn all about the many powerful features of the CFX 9970G read on and explo...

Page 20: ...he manufacturer and its suppliers be liable to you or any other person for any damages expenses lost profits lost savings or any other damages arising out of loss of data and or formulas arising out of malfunction repairs or battery replacement The user should prepare physical records of data to protect against such data loss Never dispose of batteries the liquid crystal panel or other components ...

Page 21: ...h problems it is a good idea to leave 1 or 2 kbytes of memory free unused at all times In no event shall CASIO Computer Co Ltd be liable to anyone for special collateral incidental or consequential damages in connection with or arising out of the purchase or use of these materials Moreover CASIO Computer Co Ltd shall not be liable for any claim of any kind whatsoever against the use of these mater...

Page 22: ... CFX 9970G ...

Page 23: ...3 2 Differential Calculations 55 3 3 Quadratic Differential Calculations 58 3 4 Integration Calculations 60 3 5 Maximum Minimum Value Calculations 63 3 6 Calculations 65 Chapter 4 Complex Numbers 67 4 1 Before Beginning a Complex Number Calculation 68 4 2 Performing Complex Number Calculations 69 Chapter 5 Binary Octal Decimal and Hexadecimal Calculations 73 5 1 Before Beginning a Binary Octal Dec...

Page 24: ...Sketch Function 153 10 1 Before Using the Sketch Function 154 10 2 Graphing with the Sketch Function 155 Chapter 11 Dual Graph 167 11 1 Before Using Dual Graph 168 11 2 Specifying the Left and Right View Window Parameters 169 11 3 Drawing a Graph in the Active Screen 170 11 4 Displaying a Graph in the Inactive Screen 171 Chapter 12 Graph to Table 175 12 1 Before Using Graph to Table 176 12 2 Using...

Page 25: ...ing Lists 244 17 5 Switching Between List Files 248 Chapter 18 Statistical Graphs and Calculations 249 18 1 Before Performing Statistical Calculations 250 18 2 Paired Variable Statistical Calculation Examples 251 18 3 Calculating and Graphing Single Variable Statistical Data 257 18 4 Calculating and Graphing Paired Variable Statistical Data 261 18 5 Performing Statistical Calculations 269 18 6 Tes...

Page 26: ...ta Inside a Program 378 21 8 Editing File Names and Program Contents 379 21 9 Deleting a Program 382 21 10 Useful Program Commands 383 21 11 Command Reference 385 21 12 Text Display 402 21 13 Using Calculator Functions in Programs 403 Chapter 22 Data Communications 413 22 1 Connecting Two Units 414 22 2 Connecting the Unit with a Personal Computer 415 22 3 Connecting the Unit with a CASIO Label Pr...

Page 27: ...ng the Calculator 444 Appendix B Power Supply 446 Appendix C Error Message Table 450 Appendix D Input Ranges 453 Appendix E Specifications 456 Index 458 Command Index 464 Key Index 465 Program Mode Command List 468 Algebraic Mode Command List 471 ...

Page 28: ...d in the function menu When g is indicated in the function menu for key 6 it means that pressing 6 displays the next page or previous page of menu options uMenu Titles Menu titles in this user s guide include the key operation required to display the menu being explained The key operation for a menu that is displayed by pressing K and then COLR would be shown as OPTN COLR 6 g key operations to cha...

Page 29: ...board are color coded to help you find the one you need quickly and easily Function Key Operation 1 log l 2 10x l 3 B al The following describes the color coding used for key markings Color Key Operation Orange Press and then the key to perform the marked function Red Press aand then the key to perform the marked function ...

Page 30: ...e that is different than the one you thought you selected The following explains the meaning of each icon Icon Mode Name Description RUN Use this mode for arithmetic calculations and function calculations and for calculations involving binary octal decimal and hexadecimal values STATistics Use this mode to perform single variable standard deviation and paired variable regression statistical calcul...

Page 31: ...e to obtain mathematical expression results using natural mathematical display notation LINK Use this mode to transfer memory contents or back up data to another unit SYStem Use this mode to check how much memory is used and remaining to delete data from memory and to initialize reset the calculator It also lets you adjust display contrast Icon Mode Name Description 2 Selecting Icons and Entering ...

Page 32: ...ct decimal hexadecimal binary octal uFunc Type graph function type Y r Parm X c rectangular coordinate polar coordinate parametric coordinate X constant graph Y Y Y Y y f x y f x y f x y f x inequality graph The v key inputs one of three different variable names Which variable name it inputs is determined by the Func Type setting you make uDraw Type graph drawing method Con Plot connected points u...

Page 33: ...t Wind statistical graph view window setting method Auto Man automatic manual uGraph Func function display during graph drawing and trace On Off display on display off uBackground graph display background None PICT no background graph background picture specification uPlot Line plot and line graph color setting Blue Orng Grn blue orange green uResid List residual calculation None LIST no calculati...

Page 34: ...ic Graph Locus Mode On Off locus identified by color locus not drawn uVariable Table Generation and Graph Draw settings Rang LIST use table range use list data u Display value display in recursion table On Off display on display off uSlope display of derivative at current pointer location in implicit function graph On Off display on display off uPayment payment period setting BGN END beginning end...

Page 35: ...ator can display data in three colors orange blue and green The default color for graphs and comment text is blue but you can specify orange or green if you want Orng Grn orange green The above setting affects the color of graphs and comment text Specify the color you want to use before inputting the graph s function or the program comment text k About Menu Item Types This calculator uses certain ...

Page 36: ...d Norm 2 each time you perform the above operation There is no display indicator to show you which exponential display range is currently in effect but you can always check it by seeing what results the following calculation produces Ab caaw Norm 1 Norm 2 All of the examples in this manual show calculation results using Norm 1 uHow to interpret exponential format 1 2E 12 indicates that the result ...

Page 37: ... 12 34 56 78 In addition to the above this calculator also uses other indicators or symbols which are described in each applicable section of this manual as they come up k Calculation Execution Indicator Whenever the calculator is busy drawing a graph or executing a long complex calculation or program a black box k flashes in the upper right corner of the display This black box tells you that the ...

Page 38: ... Press the e cursor key to make the display darker and the d cursor key to make it lighter Holding down either key changes the setting at high speed uTo adjust the color tint 1 Use the cursor f and c keys to move the pointer so it is next to the color ORANGE BLUE GREEN whose tint you want to adjust 2 Press the e cursor key to give the color a greener tint and the d cursor key to give it an orange ...

Page 39: ...Hang Up Should the unit hang up and stop responding to input from the keyboard press the P button on the back of the calculator to reset the memory Note however that this clears all the data in calculator memory k Low Battery Message The low battery message appears whenever you press o to turn power on or m to display the Main Menu while the main battery power is below a certain level o or m About...

Page 40: ...Basic Operation 1 1 Before Starting Calculations 1 2 Memory 1 3 Option OPTN Menu 1 4 Variable Data VARS Menu 1 5 Program PRGM Menu 1 Chapter ...

Page 41: ...ans 400 grads 90 2 radians 100 grads k k k k k Setting the Display Format Display 1 Display the set up screen and use the f and c keys to highlight Display 2 Press the function key for the item you want to set Fix Sci Norm Eng fixed number of decimal places specification number of significant digits specification exponential format display range toggle Engineering Mode 3 Press J to return to the s...

Page 42: ... u To specify the exponential display range Norm 1 Norm 2 Press 3 Norm to switch between Norm 1 and Norm 2 Norm 1 10 2 0 01 x x 1010 Norm 2 10 9 0 000000001 x x 1010 u u u u u To specify the engineering notation display Eng Press 4 Eng to switch between engineering notation and standard notation The indicator E is on the display while engineering notation is in effect The following are the 11 engi...

Page 43: ...Mat Fill Seq SortA SortD Min Max Median Mean Augment Mat List List ALGBR Mode unique commands expand factor tExpand tCollect diff solve tanLine collect combine sequence sumSeq expToTrig trigToExp signum 2 Type A functions With these functions the value is entered and then the function key is pressed x2 x 1 x ENG symbols 3 Power root xy x 4 Fractions ab c 5 Abbreviated multiplication format in fron...

Page 44: ... the above calculation should be input 5 3 2 Compound functions are executed from right to left Anything contained within parentheses receives highest priority Example 2 3 log sin2 2 6 8 22 07101691 angle unit Rad k k k k k Multiplication Operations without a Multiplication Sign You can omit the multiplication sign in any of the following operations Example 2sin30 10log1 2 2 2Pol 5 12 etc 3 Before...

Page 45: ...outine stack Example Calculations are performed according to the priority sequence Once a calculation is executed it is cleared from the stack Storing a complex number takes up two numeric value stack levels Storing a two byte function takes up two command stack levels k k k k k Input Output and Operation Limitations The allowable range for both input and output values is 10 digits for the mantiss...

Page 46: ...en you use a command that requires an argument without providing a valid argument Arg ERROR When an attempt is made to use an illegal dimension during matrix calculations Dim ERROR When no solution exists for an ALGBR Mode operation Undefined When the result of an ALGBR Mode operation exceeds the range of the calculator Overflow ERROR When a value input in the ALGBR Mode is outside the domain of t...

Page 47: ...c Display and Text Display The unit uses both a graphic display and a text display The graphic display is used for graphics while the text display is used for calculations and instructions The contents of each type of display are stored in independent memory areas u u u u uTo switch between the graphic display and text display Press 6 G T You should also note that the key operations used to clear ...

Page 48: ... u u uTo insert a step Example To change 2 362 to sin2 362 c dgx ddddd s When you press the insert location is indicated by the symbol t The next function or value you input is inserted at the location of t To abort the insert operation without inputting anything move the cursor press again or press d e or w ...

Page 49: ... u u uTo assign a value to a variable value a variable name w Example To assign 123 to variable A AbcdaaAw Example To add 456 to variable A and store the result in variable B AaA efgaaBw u u u u uTo display the contents of a variable Example To display the contents of variable A AaAw u u u u uTo clear a variable Example To clear variable A AaaaAw To clear all variables select Memory Usage from the...

Page 50: ...ction list u u u u uTo store a function Example To store the function A B A B as function memory number 1 K6 g 6 g 3 FMEM A aA aB aA aB 1 STO 1 f1 If the function memory number you assign a function to already contains a function the previous function is replaced with the new one u u u u uTo recall a function Example To recall the contents of function memory number 1 K6 g 6 g 3 FMEM A 2 RCL 1 f1 T...

Page 51: ...hing Example To store x3 1 x2 x into function memory and then graph y x3 x2 x 1 Use the following View Window parameters Xmin 4 Ymin 10 Xmax 4 Ymax 10 Xscale 1 Yscale 1 Zc1 Y JK6 g 6 g 3 FMEM AvMd b1 STO 1 f1 stores x3 1 Avx v1 STO 2 f2 stores x2 x A 4 Sketch 1 Cls w 4 Sketch 5 GRPH 1 Y K6 g 6 g 3 FMEM 3 fn 1 f1 2 f2 w For full details about graphing see 8 Graphing k k k k k Memory Status You can ...

Page 52: ...ons and graphs Matrix Matrix memory data List File List data Y Graph functions Draw Memory Graph drawing conditions View Window enlargement reduction factor graph screen Graph Memory Graph memory data View Window View Window memory data Picture Graph screen data Dynamic Graph Dynamic Graph data Table Function Table Graph data Recursion Recursion Table Graph data Equation Equation calculation data ...

Page 53: ...n step 1 allows deletion of specific data 2 Press 1 DEL 3 Press the function key that corresponds to the data you want to delete The above example shows the function menu that appears when you highlight List File in step 1 4 Press 1 YES If the data type you select in step 1 allows deletion of all data only 2 Press 1 DEL 3 Press 1 YES to delete all of the data 1 2 3 4 5 6 1 2 3 4 5 6 This menu appe...

Page 54: ...umeric calculation menu ANGL menu for angle coordinate conversion sexagesimal input conversion ESYM engineering symbol menu PICT graph save recall menu FMEM function memory menu LOGIC logic operator menu Pressing K causes the following function key menu to appear while binary octal decimal or hexadecimal is set as the default number system COLR graph color menu u u u u uOption Menu during numeric ...

Page 55: ...s menu T menu u u u u u R X R Y R T x axis menu y axis menu T menu for right side of Dual Graph The following are the items that appear in the above menus min max scal ptch minimum value maximum value scale pitch k k k k k FACT Recalling enlargement reduction factors Selecting FACT from the VARS menu displays the enlargement reduction factor recall menu Xfct Yfct x axis factor y axis factor k k k ...

Page 56: ...t data recall The following are the items that appear in the above menu n o o o o o x n 1 number of data data mean sample standard deviation n1 n2 number of data 1 data 2 o o o o o1 o o o o o2 mean of data 1 data 2 x1 x2 sample standard deviation of data 1 data 2 xp pooled sample standard deviation F F value Fdf SS MS factor degrees of freedom sum of squares mean of squares Edf SSe MSe error degre...

Page 57: ...ameters to draw the graph Xmin 5 Ymin 5 Xmax 5 Ymax 5 Xscale 1 Yscale 1 4 Sketch 5 GRPH 1 Y J4 GRPH 1 Y cw k k k k k DYNA Recalling Dynamic Graph Set Up Data Selecting DYNA from the VARS menu displays the Dynamic Graph set up data recall menu Strt End Pitch coefficient range start value coefficient range end value coefficient value increment k k k k k TABL Recalling Table Graph Set Up and Content ...

Page 58: ... menu The following are the items that appear in the above menu Strt End table range start value table range end value a0 a1 a2 zero term ao value first term a1 value second term a2 value b0 b1 b2 zero term bo value first term b1 value second term b2 value anSt bnSt origin of an bn recursion formula convergence divergence graph WEB graph u u u u u Reslt matrix of table contents Selecting Reslt dis...

Page 59: ...ns coefficients for linear equations with two through six unknowns P Rlt P Cof matrix of solution coefficients for a quadratic or cubic equation Example 1 To recall the solutions for the following linear equations with two unknowns 2x 3y 8 3x 5y 14 1 S Rlt w Example 2 To recall the coefficients for the following linear equations with three unknowns 4x y 2z 1 x 6y 3z 1 5x 4y z 7 2 S Cof w Example 3...

Page 60: ... 6 unknowns cannot be recalled at the same time The following conditions cause an error to be generated When there are no coefficients input for the equation When there are no solutions obtained for the equation k k k k k TVM Recalling Financial Calculation Data Selecting TVM from the VARS menu displays the financial calculation data recall menu n I PV PMT FV payment periods installments interest ...

Page 61: ... menu DISP display command menu REL conditional jump relational operator menu I O input output control command menu multistatement connector The function key menu appears if you press W in the RUN Mode or the PRGM Mode while binary octal decimal or hexadecimal is set as the default number system Prog JUMP REL The functions assigned to the function keys are the same as those in the Comp Mode For de...

Page 62: ...Manual Calculations 2 1 Basic Calculations 2 2 Special Functions 2 3 Function Calculations Chapter 2 ...

Page 63: ... 3 4 5 1 2 3 E2 does not produce the correct result Be sure to enter this calculation as shown 2 Final closed parentheses immediately before operation of the w key may be omitted no matter how many are required 3 A multiplication sign immediately before an open parenthesis may be omitted 4 This is identical to 6 4 5 w k k k k k Number of Decimal Places Number of Significant Digits Exponential Nota...

Page 64: ... 1010 Norm 2 exponential display for values outside the range of 10 9 to 1010 Example 100 6 16 66666666 Condition Operation Display 100 6w 16 66666667 4 decimal places Zccccccccc 1 Fix 5 4 Jw 16 6667 5 significant digits Zccccccccc 2 Sci 6 g 1 5 Jw 1 6667E 01 Cancels specification Zccccccccc 3 Norm Jw 16 66666667 1 Displayed values are rounded off to the place you specify Example 200 7 14 400 Cond...

Page 65: ...38 k k k k k Calculations Using Variables Example Operation Display 193 2aaAw 193 2 193 2 23 8 4 aA 23w 8 4 193 2 28 6 9 aA 28w 6 9 2 1 Basic Calculations ...

Page 66: ...is one with 15 digits for the mantissa and 2 digits for the exponent Answer memory contents are not cleared when you press the A key or when you switch power off Note that answer memory contents are not changed by an operation that assigns values to value memory such as faaAw k k k k k Performing Continuous Calculations The unit lets you use the result of one calculation as one of the arguments in...

Page 67: ...eplay memory until you perform another calculation or change modes The contents of the replay memory are not cleared when you press the A key so you can recall a calculation and execute it even after performing the all clear operation Note however that replay memory contents are cleared whenever you change to another mode or menu After you press A you can press f or c to recall previous calculatio...

Page 68: ...lculations and in programmed calculations There are two different ways that you can use to connect statements to form multistatements Colon Statements that are connected with colons are executed from left to right without stopping Display Result Command When execution reaches the end of a statement followed by a display result command execution stops and the result up to that point appears on the ...

Page 69: ...t of a multistatement is always displayed regardless of whether it ends with a display result command You cannot construct a multistatement in which one statement directly uses the result of the previous statement Example 123 456 5 Invalid Intermediate result at point where is used 2 2 Special Functions ...

Page 70: ...ion Calculations PROB OPTN PROB x press after inputting a value to obtain the factorial of the value nPr nCr permutation combination Ran pseudo random number generation 0 to 1 P Q R probability P t Q t R t t value of normalized variate t x u u u u uNumeric Calculations NUM OPTN NUM Abs select this item and input a value to obtain the absolute value of the value Int Frac select the item and input a...

Page 71: ...ilo 103 mega 106 giga 109 tera 1012 peta 1015 exa 1018 ENG ENG shifts the decimal place of the displayed value three digits to the left right and decreases increases the exponent by three When you are using engineering notation the engineering symbol is also changed accordingly The ENG and ENG menu options appear only when there is a calculation result shown on the display k k k k k Angle Units On...

Page 72: ...ation binary octal decimal hexadecimal mode Example Operation Display sin 63 0 8910065242 Zcccc 1 Deg J s63w 0 8910065242 cos rad 0 5 Zcccc 3 2 Rad J c 7 d w 0 5 tan 35gra 0 6128007881 Zcccc 3 Gra J t 35w 0 6128007881 2 sin 45 cos 65 0 5976724775 Zcccc 1 Deg J 2 s45 c65w 1 0 5976724775 cosec 30 1 2 1 s30w 2 sin30 sin 1 0 5 30 x when sinx 0 5 S0 5 2 w 30 1 can be omitted 2 Input of leading zero is ...

Page 73: ... 81 34 3 3 3 3 81 3M4w 81 1 7 1237 123 1 988647795 7 q123w 1 988647795 2 3 3 4 10 2 3 3 q64 4w 1 10 64 1 xy and x take precedence over multiplication and division k k k k k Hyperbolic and Inverse Hyperbolic Functions Be sure to specify Comp for Calculation binary octal decimal hexadecimal mode Example Operation Display sinh 3 6 18 28545536 K6 g 2 HYP 1 sinh 3 6w 18 28545536 cosh 1 5 sinh 1 5 K6 g ...

Page 74: ...42 49 w 42 36 42 49 Random number generation K6 g 3 PROB pseudo random number 4 Ran w Ex 0 4810497011 between 0 and 1 What is the absolute value of the common logarithm of 3 4 log 3 0 1249387366 K6 g 4 NUM 4 1 Abs l 3 4 w 0 1249387366 What is the integer part of K6 g 4 NUM 3 5 2 Int 3 5w 3 What is the decimal part of K6 g 4 NUM 3 5 3 Frac 3 5w 0 5 What is the nearest integer K6 g 4 NUM not exceedi...

Page 75: ... r and when x 14 and y 20 7 Operation Display Zcccc1 Deg J K6 g 5 ANGL 6 g 1 Pol 14 20 7 w Ans 1 24 989 24 98979792 r 2 55 928 55 92839019 Example To calculate x and y when r 25 and 56 Operation Display Zcccc1 Deg J K6 g 5 ANGL 6 g 2 Rec 25 56 w Ans 1 13 979 13 97982259 x 2 20 725 20 72593931 y k k k k k Permutation and Combination u u u u u Permutation u u u u u Combination Be sure to specify Com...

Page 76: ...exadecimal mode Example Operation Display 2 5 3 1 4w 3 13 20 Conversion to decimal 1 M 3 65 1 2578 1 4572w 6 066202547E 04 2 Norm 1 display format 1 2 5w 0 25 3 1 1 3 1 4 w 4 1 5 7 1 Fractions can be converted to decimal values and vice versa 2 When the total number of characters including integer numerator denominator and delimiter marks exceeds 10 the input fraction is automatically displayed in...

Page 77: ...kilo 999K 1 024M mega 6 g 6 g 1 ESYM 6 g 1 k 251 k w 1 024M 9 10 0 9 900m milli 9 10w 900 m K6 g 6 g 1 ESYM 6 g 6 g 3 ENG 1 0 9 3 ENG 1 0 0009k 2 ENG 2 0 9 2 ENG 2 900 m 1 Converts the displayed value to the next higher engineering unit by shifting the decimal point three places to the right 2 Converts the displayed value to the next lower engineering unit by shifting the decimal point three place...

Page 78: ...binary octal decimal hexadecimal mode Example What is the logical product of A and B when A 3 and B 2 A AND B 1 Operation Display 3aa Aw 2aaBw aAK6 g 6 g 4 LOGIC 1 And aBw 1 Example What is the logical sum of A and B when A 5 and B 1 A OR B 1 Operation Display 5aa Aw 1aaBw aAK6 g 6 g 4 LOGIC 2 Or aBw 1 Example Negate A when A 10 NOT A 0 Operation Display 10aaAw K6 g 6 g 4 LOGIC 3 Not aAw 0 Functio...

Page 79: ...The following table shows all of possible results that can be produced by AND and OR operations Value or Expression A Value or Expression B A AND B A OR B A G 0 B G 0 1 1 A G 0 B 0 0 1 A 0 B G 0 0 1 A 0 B 0 0 0 The following table shows the results produced by the NOT operation Value or Expression A NOT A A G 0 0 A 0 1 ...

Page 80: ...alculations 3 1 Before Performing a Calculation 3 2 Differential Calculations 3 3 Quadratic Differential Calculations 3 4 Integration Calculations 3 5 Maximum Minimum Value Calculations 3 6 Calculations Chapter 3 ...

Page 81: ... Solve calculations The following is the syntax for using the Solve function in a program Solve f x n a b Upper limit Lower limit Initial estimated value There are two different input methods that can be used for Solve calcula tions direct assignment and variable table input With the direct assignment method the one described here you assign values directly to variables This type of input is ident...

Page 82: ...s unit employs central difference to perform differential calculations The following illustrates central difference A A A A A A A The slopes of point a and point a Ax and of point a and point a Ax in function y f x are as follows In the above Ay Ax is called the forward difference while y x is the backward difference To calculate derivatives the unit takes the average between the value of Ay Ax an...

Page 83: ...ease of x bE f w In the function f x only X can be used as a variable in expressions Other variables A through Z r are treated as constants and the value currently assigned to that variable is applied during the calculation Input of Ax and the closing parenthesis can be omitted If you omit Ax the calculator automatically uses a value for Ax that is appropriate for the deriva tive value you are try...

Page 84: ... x a Ax of a differential Note that you cannot use a Solve differential quadratic differential integration maximum minimum value or calculation expression inside a differential calculation term Pressing A during calculation of a differential while the cursor is not shown on the display interrupts the calculation Always use radians Rad Mode as the angle unit when performing trigono metric different...

Page 85: ...tion is finished when the value of f x based on the value of h calculated using the last value of m and the value of f x based on the value of h calculated using the current value of m are identical before the upper n digit is reached Normally you should not input a value for n It is recommended that you only input a value for n when required for calculation precision Inputting a larger value for ...

Page 86: ...a g a f a g a etc The result of a quadratic differential calculation can be used in a subsequent arithmetic or function calculation 2 f a log f a etc Functions can be used within the terms f x a n of a quadratic differential expression Note that you cannot use a Solve differential quadratic differential integration maximum minimum value or calculation expression inside of a quadratic differential ...

Page 87: ...fect calculates the surface area of the shaded area in the illustration If f x 0 where a x b the surface area calculation produces negative values surface area 1 k Changing Integration Calculation Methods This calculator can use either Gauss Kronrod Rule or Simpson s Rule to perform integration calculations To select a method display the set up screen and select either Gaus for Gauss Kronrod Rule ...

Page 88: ...you omit tol the calculator automatically uses a value of 1E 5 In the case of n the calculator automati cally selects the most appropriate value Integration calculations can take a long time to complete k k k k k Application of Integration Calculation Integrals can be used in addition subtraction multiplication and division a b f x dx c d g x dx etc Integration results can be used in addition subt...

Page 89: ... to ensure correct integration values 1 When cyclical functions for integration values become positive or negative for different divisions perform the calculation for single cycles or divide between negative and positive and then add the results together a b f x dx a c f x dx c b f x dx Positive part S Negative part S 2 When minute fluctuations in integration divisions produce large fluctuations i...

Page 90: ... a b n u u u u uMaximum Value 6 g 2 FMax f x a b n u u u u uTo perform maximum minimum value calculations Example 1 To determine the minimum value for the interval defined by start point a 0 and end point b 3 with a precision of n 6 for the function y x2 4x 9 Input f x AK4 CALC 6 g 1 FMin vx ev j Input the interval a 0 b 3 a d Input the precision n 6 g w Precision n 1 to 9 End point of interval St...

Page 91: ...drastic fluctuation can adversely affect precision or even cause an error Note that you cannot use a Solve differential quadratic differential integration maximum minimum value or calculation expression inside of a maximum minimum calculation term Inputting a larger value for n increases the precision of the calculation but it also increases the amount of time required to perform the calculation T...

Page 92: ...ak using the following formula k k k k k Example Calculation Example To calculate the following Use n 1 as the distance between partitions Input sequence ak AK4 CALC 6 g 3 aKx daK f Input variable used by sequence ak aK Input the initial term of sequence ak and last term of sequence ak c g Input n b w Distance between partitions Last term of sequence ak Initial term of sequence ak Variable used by...

Page 93: ...ible operations Sn Tn Sn Tn etc Arithmetic and function operations using calculation results 2 Sn log Sn etc Function operations using calculation terms ak k sink k 1 5 etc Note that you cannot use a Solve differential quadratic differential integration maximum minimum value or calculation expression inside of a calculation term Make sure that the value used as the final term is greater than the v...

Page 94: ...vision Calculation of the reciprocal square root and square of a complex number Calculation of the absolute value and argument of a complex number Calculation of conjugate complex numbers Extraction of the real number part Extraction of the imaginary number part 4 1 Before Beginning a Complex Number Calculation 4 2 Performing Complex Number Calculations Chapter 4 ...

Page 95: ...ion Before beginning a complex number calculation press K3 CPLX to display the complex number calculation menu i imaginary unit i input Abs Arg obtains absolute value argument Conj obtains conjugate ReP ImP real number imaginary number part extraction ...

Page 96: ...ory Example 1 1 2i 2 3i AK3 CPLX b c1 i c d1 i w Example 2 2 i 2 i AK3 CPLX c 1 i c 1 i w k k k k k Reciprocals Square Roots and Squares Example 3 i AK3 CPLX 9 d 1 i w k k k k k Absolute Value and Argument OPTN CPLX Abs Arg The unit regards a complex number in the format Z a bi as a coordinate on a Gaussian plane and calculates absolute value Z and argument arg Example To calculate absolute value ...

Page 97: ...plex number of the format a bi Example To calculate the conjugate complex number for the complex number 2 4i AK3 CPLX 4 Conj c e1 i w k k k k k Extraction of Real and Imaginary Number Parts OPTN CPLX ReP lmP Use the following procedure to extract real part a and imaginary part b from a complex number with the format a bi Example To extract the real and imaginary parts of the complex number 2 5i AK...

Page 98: ... a complex number has more than 21 digits the real number part and imaginary number part are displayed on separate lines When either the real number part or imaginary number part equals zero that part is not displayed 20 bytes of memory are used whenever you assign a complex number to a variable The following functions can be used with complex numbers x2 x 1 Int Frac Rnd Intg Fix Sci ENG ENG a b c...

Page 99: ...operations involving different number systems Number system conversion Arithmetic operations Negative values Logical operations 5 1 Before Beginning a Binary Octal Decimal or Hexadecimal Calculation 5 2 Selecting a Number System 5 3 Arithmetic Operations 5 4 Negative Values and Logical Operations Chapter 5 ...

Page 100: ...cimal part If you attempt to enter a value that is invalid for the number system binary octal decimal hexadecimal you are using the calculator displays an error message The following shows the numerals that can be used in each number system Binary 0 1 Octal 0 1 2 3 4 5 6 7 Decimal 0 1 2 3 4 5 6 7 8 9 Hexadecimal 0 1 2 3 4 5 6 7 8 9 A B C D E F The alphabetic characters used in the hexadecimal numb...

Page 101: ...imal Values Positive 0 x 7FFFFFFF Negative 80000000 x FFFFFFFF u u u u uTo perform a binary octal decimal or hexadecimal calculation 1 In the main menu select RUN 2 Press Z and then specify the defalut number system by pressing 2 Dec 3 Hex 4 Bin or 5 Oct 3 Press J to change to the screen for calculation input This causes a function menu with the following items to appear d o LOG number system spec...

Page 102: ... d ccw Z4 Bin Jw Z5 Oct Jw u u u u uTo specify a number system for an input value You can specify a number system for each individual value you input While binary octal decimal or hexadecimal is set as the default number system press 1 d o to display a menu of number system symbols Press the function key that corresponds to the symbol you want to select and then input the value you want d h b o de...

Page 103: ...tic Operations Example 1 To calculate 101112 110102 Z4 Bin J Ababbb bbabaw Example 2 To input and execute 1238 ABC16 when the default number system is decimal or hexadecimal Z2 Dec J A1 d o 4 o bcd 2 h ABCw Z3 Hex Jw ...

Page 104: ...and or xor xnor NOT AND OR XOR XNOR k k k k k Negative Values Example To determine the negative of 1100102 Z4 Bin J A2 LOG 1 Neg bbaabaw k k k k k Logical Operations Example 1 To input and execute 12016 and AD16 Z3 Hex J Abca2 LOG 3 and ADw Example 2 To display the result of 368 or 11102 as an octal value Z5 Oct JJ Adg2 LOG 4 or J1 d o 3 b bbbaw Example 3 To negate 2FFFED16 Z3 Hex JJ A2 LOG 2 Not ...

Page 105: ...culations Determinant calculations Matrix transposition Matrix inversion Matrix squaring Raising a matrix to a specific power Absolute value integer part extraction fractional part extraction maximum integer calculations Matrix modification using matrix commands 6 1 Before Performing Matrix Calculations 6 2 Matrix Cell Operations 6 3 Modifying Matrices Using Matrix Commands 6 4 Matrix Calculations...

Page 106: ...Matrix Answer Memory Note the following points about Matrix Answer Memory Whenever you perform a matrix calculation the current Matrix Answer Memory contents are replaced by the new result The previous contents are deleted and cannot be recovered Inputting values into a matrix does not affect Matrix Answer Memory contents k k k k k Creating a Matrix To create a matrix you must first define its dim...

Page 107: ...move to the next cell to the right Displayed cell values show positive integers up to six digits and negative integers up to five digits one digit used for the negative sign Exponential values are shown with up to two digits for the exponent Fractional values are not displayed You can see the entire value assigned to a cell by using the cursor keys to move the highlighting to the cell whose value ...

Page 108: ...L 3 Press 1 YES to delete the matrix or 6 NO to abort the operation without deleting anything The indicator None replaces the dimensions of the matrix you delete u u u u uTo delete all matrices 1 While the MATRIX list is on the display press 2 DEL A 2 Press 1 YES to delete all matrices in memory or 6 NO to abort the operation without deleting anything The indicator None is shown for all the matric...

Page 109: ...enu All of the following examples use Matrix A recalled by the above operation k k k k k Row Calculations The following menu appears whenever you press 1 R OP while a recalled matrix is on the display Swap row swap Rw scalar product of specified row Rw addition of scalar product of specified row to another row Rw addition of specified row to another row u u u u uTo swap two rows Example To swap ro...

Page 110: ...e To calculate the scalar product of row 2 of the following matrix multiplying by 4 and add the result to row 3 1 2 Matrix A 3 4 5 6 1 R OP 3 Rw Input multiplier value ew Specify number of row whose scalar product should be calculated cw Specify number of row where result should be added dw u u u u uTo add two rows together Example To add row 2 to row 3 of the following matrix 1 2 Matrix A 3 4 5 6...

Page 111: ...play DEL delete row INS insert row ADD add row u u u u uTo delete a row Example To delete row 2 of the following matrix 1 2 Matrix A 3 4 5 6 2 ROW c 1 DEL u u u u uTo insert a row Example To insert a new row between rows one and two of the following matrix 1 2 Matrix A 3 4 5 6 2 ROW c 2 INS Matrix Cell Operations 6 2 ...

Page 112: ... ADD k k k k k Column Operations The following menu appears whenever you press 3 COL while a recalled matrix is on the display DEL delete column INS insert column ADD add column u u u u uTo delete a column Example To delete column 2 of the following matrix 1 2 Matrix A 3 4 5 6 3 COL e 1 DEL 6 2 Matrix Cell Operations ...

Page 113: ...w column between columns 1 and 2 of the following matrix 1 2 Matrix A 3 4 5 6 3 COL e 2 INS u u u u uTo add a column Example To add a new column to the right of column 2 of the following matrix 1 2 Matrix A 3 4 5 6 3 COL e 3 ADD Matrix Cell Operations 6 2 ...

Page 114: ...ommand assign contents of selected column to list file Aug Augment command link two matrices Iden Identity command identity matrix input Dim Dim command dimension check Fill Fill command identical cell values k k k k k Matrix Data Input Format The following shows the format you should use when inputting data to create a matrix using the matrix operation menu s Mat command a11 a12 a1n a21 a22 a2n a...

Page 115: ...s u u u u uTo check the dimensions of a matrix Use the matrix operation menu s Dim command 2 to check the dimensions of an existing matrix Example 3 To check the dimensions of Matrix A which was input in Example 1 K2 MAT 6 g 2 Dim 6 g 1 Mat aAw The display shows that Matrix A consists of two rows and three columns You can also use Dim to specify the dimensions of the matrix Example 4 To specify di...

Page 116: ...x name A through Z or Ans m row number n column number Example 1 Assign 10 to the cell at row 1 column 2 of the following matrix 1 2 Matrix A 3 4 5 6 baaK2 MAT 1 Mat aA b c w Example 2 Multiply the value in the cell at row 2 column 2 of the above matrix by 5 K2 MAT 1 Mat aA c c fw u u u u uTo fill a matrix with identical values and to combine two matrices into a single matrix Use the matrix operat...

Page 117: ...ile Mat List Mat X m List n X matrix name A through Z or Ans m column number n list number Example To assign the contents of column 2 of the following matrix to list file 1 1 2 Matrix A 3 4 5 6 K2 MAT 2 M L 1 Mat aA c a Column number K1 LIST 1 List bw You can use Matrix Answer Memory to assign the results of the above matrix input and edit operations to a matrix variable To do so use the following...

Page 118: ...c operations Mat Mat command matrix specification Det Det command determinant command Trn Trn command transpose matrix command Iden Identity command identity matrix input All of the following examples assume that matrix data is already stored in memory k k k k k Matrix Arithmetic Operations Matrix 1 Arithmetic operator key Matrix 2 Mat A Mat A w Mat Z Mat Z MatAns MatAns Example 1 To add the follo...

Page 119: ...command menu s Identity command 1 to input the identity matrix Example 3 To multiply Matrix A from Example 1 by a 2 2 identity matrix 1 Mat aA 6 g 1 Iden cw Number of rows and columns k k k k k Matrix Scalar Product The following is the format for calculating a matrix scalar product which multiplies the value in each cell of the matrix by the same value Scalar value Matrix Mat A k w Mat Z MatAns E...

Page 120: ...ated as shown below A a11 a12 a11a22 a12a21 a21 a22 The determinant of a 3 3 matrix is calculated as shown below a11 a12 a13 A a21 a22 a23 a31 a32 a33 a11a22a33 a12a23a31 a13a21a32 a11a23a32 a12a21a33 a13a22a31 k k k k k Matrix Transposition A matrix is transposed when its rows become columns and its columns become rows The following is the format for matrix transposition Matrix Mat A 4 Trn w Mat ...

Page 121: ... produces an error A matrix with a value of zero cannot be inverted Trying to invert a matrix with value of zero produces an error Calculation precision is affected for matrices whose value is near zero A matrix being inverted must satisfy the conditions shown below A A 1 A 1 A E 1 0 0 1 The following shows the formula used to invert Matrix A into inverse matrix A 1 A a b c d A 1 1 d b ad bc c a N...

Page 122: ...ing a Matrix to a Power Matrix Natural number Mat A M k w Mat Z MatAns Example To raise the following matrix to the third power Matrix A 1 2 3 4 1 Mat aAMdw k k k k k Determining the Absolute Value Integer Part Fraction Part and Maximum Integer of a Matrix Function command Matrix Abs Mat A Frac w Int Mat Z Intg MatAns 6 4 Matrix Calculations ...

Page 123: ...onsiderable time to complete The calculation precision of displayed results for matrix calculations is 1 at the least significant digit If a matrix calculation result is too large to fit into Matrix Answer Memory an error occurs You can use the following operation to transfer Matrix Answer Memory contents to another matrix or when Matrix Answer Memory contains a determinant to a variable MatAns Ma...

Page 124: ...of equations Linear equations with two to six unknowns Quadratic equations Cubic equations 7 1 Before Beginning an Equation Calculation 7 2 Linear Equations with Two to Six Unknowns 7 3 Quadratic and Cubic Equations 7 4 Solve Calculations 7 5 What to Do When an Error Occurs Chapter 7 ...

Page 125: ...s POLY quadratic or cubic equation SOLV solve calculation k k k k k Clearing Equation Memories 1 Enter the equation calculation mode SIML or POLY you want to use and perform the function key operation required for that mode In the case of the SIML Mode 1 use function keys 1 2 through 5 6 to specify the number of unknowns In the case of the POLY Mode 2 use function keys 1 2 or 2 3 to specify the de...

Page 126: ... g1 a2x b2y c2z d2t e2u f2v g2 a3x b3y c3z d3t e3u f3v g3 a4x b4y c4z d4t e4u f4v g4 a5x b5y c5z d5t e5u f5v g5 a6x b6y c6z d6t e6u f6v g6 You can also solve linear equations with three four and five unknowns In each case the format is similar to those shown above k k k k k Specifying the Number of Unknowns While in the Equation Mode press 1 SIML and then specify the number of unknowns 2 3 4 5 6 l...

Page 127: ...wbw cw bw bwgwdwbw fwewbw hw Each time you press w the input value is registered in the highlighted cell Each press of w inputs values in the following sequence coefficient a1 coefficient b1 coefficient c1 coefficient d1 coefficient an coefficient bn coefficient cn coefficient dn n 2 to 6 You can input fractions and value memory contents as coefficients 3 After inputting the coefficients solve the...

Page 128: ...n the coefficients that you use it may take considerable time for the calculation result of simultaneous linear equations to appear on the display Failure of a result to appear immediately does not mean that the unit is not functioning properly k k k k k Changing Coefficients You can change a coefficient either before or after you register it by pressing w u u u u uTo change a coefficient before r...

Page 129: ...atic or Cubic Equation Example To solve the following cubic equation x3 2x2 x 2 0 1 Press 2 3 to enter the Cubic Equation Mode 2 Input each coefficient bw cw bwcw Each time you press w the input value is registered in the highlighted cell Each press of w inputs values in the following sequence coefficient a coefficient b coefficient c coefficient d Input for coefficient d is required only for cubi...

Page 130: ...e root solutions and imaginary number solutions are handled u u u u uTo solve a cubic equation that produces a multiple value solution Example To solve the following cubic equation x3 4x2 5x 2 0 bw ewfw cw 1 SOLV u u u u uTo solve a cubic equation that produces an imaginary number solution Example To solve the following cubic equation x3 x2 x 3 0 bwbwbw dw 1 SOLV It may take considerable time for ...

Page 131: ... then input another one u u u u uTo change a coefficient after registering it with w Use the cursor keys to highlight the cell that contains the coefficient that you want to change Next input the value that you want to change to k k k k k Clearing All the Coefficients While in the Quadratic or Cubic Equation Mode press the 3 CLR function key This operation clears all the coefficients to zero 7 3 Q...

Page 132: ...ut screen appears Input the expression You can input numbers alpha characters and operation symbols If you do not input an equals sign the calculator assumes that the expression is to the left of the equals sign and there is a zero to the right To specify a value other than zero to the right of the equals sign you must input the equals sign and the value u u u u uTo perform solve calculations Exam...

Page 133: ...s based on the assumption that f x can be approximated by a linear expression within a very narrow range First a starting value predicted value xo is given Using this starting value as a base approximate value x1 is obtained and then the left side and right side calculation results are compared Next approximate value x1 is used as the initial value to calculate the next approximate value x2 This p...

Page 134: ...tion again The calculator may be unable to obtain a solution even though a solution exists Due to certain idiosyncrasies of Newton s method solutions for the following types of functions tend to be difficult to calculate Periodic functions i e y sinx a Functions whose graph produce sharp slopes i e y ex y 1 x Inverse proportion expressions and other discontinuous functions Note that the Solve func...

Page 135: ...clear the error and return to the value that was registered for the coefficient before you input the value that generated the error Try inputting a new value again u u u u uError during calculation Press the A key to clear the error and display coefficient a Try inputting values for the coefficients again ...

Page 136: ... Y graphs Polar coordinate r graphs Parametric graphs X constant graphs Inequality graphs Integration graphs in the RUN mode only A selection of graph commands also makes it possible to incor porate graphing into programs 8 1 Before Trying to Draw a Graph 8 2 View Window V Window Settings 8 3 Graph Function Operations 8 4 Graph Memory 8 5 Drawing Graphs Manually 8 6 Other Graphing Functions 8 7 Pi...

Page 137: ... GRAPH Mode When you do the Graph Function menu appears on the display You can use this menu to store edit and recall functions and to draw their graphs SEL draw non draw status DEL function delete TYPE graph type menu COLR graph color GMEM graph memory save recall DRAW graph draw Memory area Use f and c to change selection ...

Page 138: ...D View Window initial settings initial settings using specified angle unit standardized settings STO RCL View Window setting store recall The nearby illustration shows the meaning of each of these parameters 2 Input a value for a parameter and press w The calculator automatically selects the next parameter for input You can also select a parameter using the c and f keys There are actually nine Vie...

Page 139: ... max value causes the axis to be inverted You can input expressions such as 2 as View Window parameters When the View Window setting does not allow display of the axes the scale for the y axis is indicated on either the left or right edge of the display while that for the x axis is indicated on either the top or bottom edge When View Window values are changed the graph display is cleared and the n...

Page 140: ...alization Press 3 V Window 2 TRIG to initialize the View Window to the following settings Deg Mode Xmin 540 Ymin 1 6 Xmax 540 Ymax 1 6 Xscale 90 Yscale 0 5 Rad Mode Xmin 9 4247779 Xmax 9 42477796 Xscale 1 57079632 Gra Mode Xmin 600 Xmax 600 Xscale 100 The settings for Y min Y max Y pitch T min T max and T pitch remain unchanged when you press 2 TRIG u u u u uTo standardize the View Window Press 3 ...

Page 141: ...memories numbered V W1 to V W6 Storing View Window settings in a memory area that already contains settings replaces the existing settings with the new ones u u u u uTo recall View Window settings Pressing 5 RCL 1 V W1 recalls the contents of View Window memory V W1 Recalling View Window settings causes the settings currently on the display to be deleted You can change View Window settings in a pr...

Page 142: ...he graph type you want to specify k k k k k Storing Graph Functions u u u u uTo store a rectangular coordinate function Y Example To store the following expression in memory area Y1 y 2 x2 5 3 TYPE 1 Y Specifies rectangular coordinate expression cvx f Inputs expression w Stores expression You will not be able to store the expression in an area that already contains a parametric function Select ano...

Page 143: ...tant expression or inequality Select another area to store your expression or delete the existing expression first u u u u uTo store an X constant expression Example To store the following expression in memory area X4 X 3 3 TYPE 4 X c Specifies X constant expression d Inputs expression w Stores expression Inputting X Y T r or for the constant in the above procedures causes an error u u u u uTo sto...

Page 144: ...without deleting anything Parametric functions come in pairs Xt and Yt When editing a parametric function clear the graph functions and re input from the beginning k k k k k Drawing a Graph u u u u uTo specify the graph color The default color for graph drawing is blue but you can change the color to orange or green if you want 1 While the Graph Function Menu is on the display press f or c to disp...

Page 145: ...owing View Window parameters Xmin 5 Ymin 5 Xmax 5 Ymax 5 Xscale 1 Yscale 1 cc Select a memory area that contains a function for which you want to specify non draw 1 SEL Specify non draw cc1 SEL c1 SEL 6 DRAW or w Draws graphs Pressing 6 G T or A returns to the Graph Function Menu 1 2 3 4 5 6 1 2 3 4 5 6 8 3 Graph Function Operations Unhighlights ...

Page 146: ... parametric graph will appear coarse if the settings you make in the View Window cause the T pitch value to be too large relative to the differential between the T min and T max settings If the settings you make cause the T pitch value to be too small relative to the differential between the T min and T max settings on the other hand the graph will take a very long time to draw Attempting to draw ...

Page 147: ... uTo store graph functions in graph memory Pressing 5 GMEM 1 STO 1 GM1 stores the selected graph function into graph memory GM1 There are six graph memories numbered GM1 to GM6 Storing a function in a memory area that already contains a function replaces the existing function with the new one If the data exceeds the calculator s remaining memory capacity an error occurs u u u u uTo recall a graph ...

Page 148: ...rdinates Y Sketch GRPH Y You can graph functions that can be expressed in the format y f x Example To graph y 2x2 3x 4 Use the following View Window parameters Xmin 5 Ymin 10 Xmax 5 Ymax 10 Xscale 2 Yscale 5 1 In the set up screen specify Y for Func Type and then press J 2 Input the rectangular coordinate Y expression 4 Sketch 1 Cls w 5 GRPH 1 Y cvx dv e 3 Press w to draw the graph You can draw gr...

Page 149: ... T pitch 36 1 In the set up screen specify r for Func Type 2 Specify Rad as the angle unit and then press J 3 Input the polar coordinate expression r 4 Sketch 1 Cls w 5 GRPH 2 r csdv 4 Press w to draw the graph You can draw graphs of the following built in scientific functions sin cos tan sin 1 cos 1 tan 1 sinh cosh tanh sinh 1 cosh 1 tanh 1 2 log ln 10 e 1 3 View Window settings are made automati...

Page 150: ... 5 T pitch 36 1 In the set up screen specify Parm for Func Type 2 Specify Rad radians as the angle unit and then press J 3 Input the parametric functions 4 Sketch 1 Cls w 5 GRPH 3 Parm hcv ccd fv hsv csd fv 4 Press w to draw the graph u u u u uTo graph X constant Sketch GRPH X c You can graph functions that can be expressed in the format X constant Example To graph X 3 Use the following View Windo...

Page 151: ... expressed in the following four formats y f x y f x y f x y f x Example To graph the inequality y x2 2x 6 Use the following View Window parameters Xmin 6 Ymin 10 Xmax 6 Ymax 10 Xscale 1 Yscale 5 1 In the set up screen specify Y for Func Type and then press J 2 Input the inequality 4 Sketch 1 Cls w 5 GRPH 6 g 1 Y vx cv g 3 Press w to draw the graph 8 5 Drawing Graphs Manually ...

Page 152: ...indow parameters Xmin 4 Ymin 8 Xmax 4 Ymax 12 Xscale 1 Yscale 5 1 In the set up screen specify Y for Func Type and then press J 2 Input the integration graph expression 4 Sketch 1 Cls w 5 GRPH 5 G dx v c v b v d c b bE e 3 Press w to draw the graph Before drawing an integration graph be sure to always press 4 Sketch 1 Cls to clear the screen You can also incorporate an integration graph command in...

Page 153: ...d and connected by lines to create a curve Plot Points are plotted without being connected k k k k k Trace With trace you can move a flashing pointer along a graph with the cursor keys and obtain readouts of coordinates at each point The following shows the different types of coordinate readouts produced by trace Rectangular Coordinate Graph Polar Coordinate Graph Parametric Function Graph X Const...

Page 154: ...ing down either key moves the pointer at high speed 3 Use f and c to move the pointer between the two graphs 4 Use e to move the pointer to the other intersection e e To abort a trace operation press 1 Trace Do not press the A key while performing a trace operation u u u u uTo display the derivative If the Derivative item in the set up screen is set to On the derivative appears on the display alon...

Page 155: ...raphs while tracing You cannot scroll polar coordinate graphs parametric function graphs or X constant graphs The graph on the screen does not scroll when you are tracing while the Dual Screen Mode is set to Graph or G to T Trace can be used only immediately after a graph is drawn It cannot be used after changing the settings of a graph The x and y coordinate values at the bottom of the screen are...

Page 156: ...pecify a range for rectangular coordinate polar coordinate paramet ric and inequality graphs k k k k k Overwrite Using the following syntax to input a graph causes multiple versions of the graph to be drawn using the specified values All versions of the graph appear on the display at the same time function with one variable variable name value value value w Example To graph y Ax2 3 substituting 3 ...

Page 157: ...e and reduce a graph on the display u u u u uBefore using zoom Immediately after drawing a graph press 2 Zoom to display the Zoom Menu BOX graph enlargement using box zoom FACT displays screen for specification of zoom factors IN OUT enlarges reduces graph using zoom factors AUTO automatically sizes the graph so it fills the screen along the y axis ORIG original size SQR adjusts ranges so x range ...

Page 158: ... the function press 2 Zoom 2 Press 1 BOX and then use the cursor keys to move the pointer to the location of one of the corners of the box you want to draw on the screen Press w to specify the location of the corner 3 Use the cursor keys to move the pointer to the location of the corner that is diagonally across from the first corner 4 Press w to specify the location of the second corner When you ...

Page 159: ... move the pointer around the display Example Graph the two functions below and enlarge them five times in order to determine whether or not they are tangential Y1 x 4 x 1 x 3 Y2 3x 22 Use the following View Window parameters Xmin 8 Ymin 30 Xmax 8 Ymax 30 Xscale 5 Yscale 10 1 After graphing the functions press 2 Zoom and the pointer appears on the screen 2 Use the cursor keys to move the pointer to...

Page 160: ...the graph u u u u uTo initialize the zoom factor Press 2 Zoom 2 FACT 1 INIT to initialize the zoom factor to the following settings Xfact 2 Yfact 2 You can use the following syntax to incorporate a factor zoom operation into a program Factor X factor Y factor You can specify only positive value up to 14 digits long for the zoom factors You can use factor zoom for any type of graph k k k k k Auto V...

Page 161: ...2 Press 2 SQR to make the graph a circle k k k k k Coordinate Rounding Function Zoom RND Trace This feature rounds the coordinate values at the pointer location to the optimum number of significant digits Rounding coordinates is useful when using trace and plot Example To round the coordinates at the points of intersection of the two graphs drawn on page 128 Use the same View Window parameters as ...

Page 162: ...unded coordinate values for the pointer position appear on the screen k k k k k Integer Function Zoom INTG This function makes the dot width equal 1 converts axis values to integers and redraws the graph If one x axis dot is Ax and one y axis dot is Ay Ax Xmax Xmin Ay Ymax Ymin 126 62 Other Graphing Functions 8 6 ...

Page 163: ...y of these functions is used in a statement that ends with a display result command to draw a graph these functions affect the graph up to the display result command only Any graphs drawn after the display result command are drawn according to normal graph overwrite rules k k k k k Returning the View Window to Its Previous Settings Zoom PRE The following operation returns View Window parameters to...

Page 164: ...c1 stores the graph drawn on the display in picture memory Pic1 There are six picture memories numbered Pic1 to Pic6 Storing a graph in a memory area that already contains data replaces the existing data with the new data u u u u uTo recall a stored graph In the GRAPH Mode pressing K1 PICT 2 RCL 1 Pic1 recalls the contents of picture memory Pic1 Dual Graph screens or any other type of graph that u...

Page 165: ...n You can use a background in the RUN STAT GRAPH DYNA TABLE RECUR CONICS Modes Example 1 With the circle graph X2 Y2 1 as the background use Dynamic Graph to graph Y X2 A as variable A changes value from 1 to 1 in increments of 1 Recall the background graph X2 Y2 1 Draw the dynamic graph Y X2 1 Y X2 Y X2 1 See 14 Implicit Function Graphs for details on drawing a circle graph and 13 Dynamic Graph f...

Page 166: ... With a statistical histogram as the background graph a normal distribution Recall the backgound graph Histogram Graph the normal distribution See 18 Statistical Graphs and Calculations for details on drawing a statistical graphs P 249 ...

Page 167: ...ion Determination of the maximum and minimum Determination of the y intercept Determination of the intersection of two graphs Determination of the coordinates at any point y for a given x x for a given y Determination of the integral for any range 9 1 Before Using Graph Solve 9 2 Analyzing a Function Graph Chapter 9 ...

Page 168: ...press 5 G Solv to display a function menu that contains the following items ROOT MAX MIN Y ICPT ISCT root maximum minimum y intercept intersections of two graphs Y CAL X CAL dx y coordinate for a given x coordinate x coordinate for a given y coordinate integral for a given range ...

Page 169: ... B Xmin 6 3 Ymin 3 1 Xmax 5 Ymax 5 Xmax 6 3 Ymax 3 1 Xscale 1 Yscale 1 Xscale 1 Yscale 1 k k k k k Determining Roots Example To determine the roots for y x x 2 x 2 View Window B 5 G Solv 1 ROOT This puts the unit into standby waiting for selection of a graph A k cursor appears on the graph that has the lowest memory area number Specify the graph you want to use c Use f and c to move the cursor to ...

Page 170: ...ot selection of the graph is not required Note that the above operation can be performed on rectangular coordinate Y and inequality graphs only k k k k k Determining Maximums and Minimums Example To determine the maximum and minimum for y x x 2 x 2 View Window A 5 G Solv 2 MAX This puts the unit into standby waiting for selection of a graph Specify the graph and determine the maximum cw 9 2 Analyz...

Page 171: ...and inequality graphs only k k k k k Determining y intercepts Example To determine the y intercept for y x 1 View Window B 5 G Solv 4 Y ICPT This puts the unit into standby waiting for selection of a graph Determine the y intercept w y intercepts are the points where the graph intersects the y axis If there is only one graph pressing 4 Y ICPT directly displays the y intercepts selection of the gra...

Page 172: ...fy the second graph Graph Y3 here to determine the points of intersection cw Use f and c to move k on the second graph Intersections are found starting from the left e The next intersection to the right is found If there is no intersection to the right nothing happens when you perform this operation You can use d to move back to the left If there are only two graphs pressing 5 ISCT directly displa...

Page 173: ...Solv 6 g 1 Y CAL Specify a graph cw At this time the unit waits for input of an x coordinate value Input the x coordinate value a f Determine the corresponding y coordinate value w Specify a graph 5 G Solv 6 g 2 X CAL cw At this time the unit waits for input of a y coordinate value Input the y coordinate value d c Determine the corresponding x coordinate value w Analyzing a Function Graph 9 2 ...

Page 174: ... Graph Inequality Graph Note that you can not determine a y coordinate for a given x coordinate with a parametric graph If there is only one graph pressing 1 Y CAL 2 X CAL directly displays the x coordinate y coordinate selection of the graph is not required k k k k k Determining the Integral for Any Range Example 1 5 0 x x 2 x 2 dx View Window A 5 G Solv 6 g 3 dx Graph selection standby Select gr...

Page 175: ...tions Depending on the View Window parameter settings there may be some error in solutions produced by Graph Solve If no solution can be found for any of the above operations the message Not Found appears on the display The following conditions can interfere with calculation precision and may make it impossible to obtain a solution When the solution is a point of tangency to the x axis When the so...

Page 176: ...phs on an existing graph Note that Sketch function operation in the STAT GRAPH TABLE RECUR and CONICS Modes is different from Sketch function operation in the RUN and PRGM Modes 10 1 Before Using the Sketch Function 10 2 Graphing with the Sketch Function Chapter 10 ...

Page 177: ...s appear only when you display the sketch menu while in the GRAPH and TABLE Modes PLOT plot menu LINE line menu Crcl Vert Hztl circle vertical line horizontal line PEN freehand drawing Text comment text RUN PRGM Mode GRPH graph command menu PIXL pixel menu Test tests pixel on off status Other menu items are identical to those in the STAT GRAPH TABLE RECUR CONICS Mode menu P 166 P 155 P 157 P 158 P...

Page 178: ... 2 x 2 The following are the View Window parameters used when drawing the graph Xmin 5 Ymin 5 Xmax 5 Ymax 5 Xscale 1 Yscale 1 k k k k k Tangent Sketch Tang This function lets you draw a line that is tangent to a graph at any point u u u u uTo draw a tangent in the GRAPH or TABLE Mode Example To draw a line that is tangent to point x 2 y 0 of y x x 2 x 2 1 After graphing the function display the sk...

Page 179: ... the tangent line k k k k k Line Normal to a Curve Sketch Norm With this function you can draw a line that is normal to the curve at a specific point A line that is normal to the curve at a given point is one that is perpendicular to the tangent line at that point u u u u uTo draw a line normal to a curve in the GRAPH or TABLE Mode Example To draw a line that is normal to the curve at point x 2 y ...

Page 180: ... in the GRAPH or TABLE Mode Example To graph the inverse of y x x 2 x 2 After graphing the function display the sketch menu and press 4 Inv When graphing an inverse function when there is more than one graph function stored in memory select one of the functions and then press w u u u u uTo graph an inverse function in the RUN or PRGM Mode The following is the syntax for graphing an inverse functio...

Page 181: ...n the graph of y x x 2 x 2 1 After drawing the graph display the sketch menu and press6 g 1 PLOT 1 Plot to display the pointer in the center of the screen 2 Use the cursor keys to move the pointer the locations of the points you want to plot and press w to plot You can plot as many points as you want The current x and y coordinate values are assigned respectively to variables X and Y u u u u uTo p...

Page 182: ...Y k k k k k Turning Plot Points On and Off Sketch PLOT Pl On Pl Off Pl Chg Use the following procedures to turn specific plot points on and off u u u u uTo turn plot points on and off in the STAT GRAPH TABLE RECUR and CONICS Modes To turn a plot point on 1 After drawing the graph display the sketch menu and press 6 g 1 PLOT 2 Pl On to display the pointer in the center of the screen 2 Use the curso...

Page 183: ...menu Line Draw a line between two plotted points F Line Draw a line u u u u uTo connect two plotted points with a line in the STAT GRAPH TABLE RECUR and CONICS Modes Sketch LINE Line Example To draw a line between the two points of inflection on the graph of y x x 2 x 2 Use the same View Window parameters as in the example on page 155 1 After drawing a graph display the sketch menu and then press ...

Page 184: ... display the sketch menu and then press 6 g 2 LINE 2 F Line to display the pointer in the center of the screen 2 Use the cursor keys to move the pointer to one of the points of inflection and press w 3 Use the cursor keys to move the pointer to the other point of inflection and press w to draw the line u u u u uTo draw a line in the RUN or PRGM Mode The following is the syntax for drawing lines in...

Page 185: ...er of the screen 2 Use the cursor keys to move the pointer to the location where you want the center point of the circle to be and press w to plot it 3 Use the cursor keys to move the pointer to a point on the circumference of the circle here to point x 0 and then press w to draw the circle u u u u uTo draw a circle in the RUN or PRGM Mode The following is the syntax for drawing circles in these m...

Page 186: ...e the line left and right and press w to draw the line at the current location To draw a horizontal line simply press 5 Hztl in place of 4 Vert and use the f and c cursor keys to move the horizontal line on the display u u u u uTo draw vertical and horizontal lines in the RUN or PRGM Mode The following is the syntax for drawing vertical and horizontal lines in these modes To draw a vertical line V...

Page 187: ...to quit the freehand draw operation k k k k k Comment Text Sketch Text Use the following procedure to insert text for comments and labels into a graph u u u u uTo insert text in the STAT GRAPH TABLE RECUR and CONICS Modes Example To insert the graph function as comment text into the graph of y x x 2 x 2 1 After drawing a graph display the sketch menu and then press 6 g 6 g 2 Text to display the po...

Page 188: ...omment text insert operation more than once k k k k k Turning Pixels On and Off Sketch PIXL The following procedure lets you turn each individual screen pixel on and off You can specify any pixel from the upper left hand corner 1 1 to the lower right hand corner 63 127 of the screen Line range 1 to 63 Column range 1 to 127 Note that you can turn pixels on and off only in the RUN and PRGM Modes Whe...

Page 189: ...er results in an error Pixel operations are valid only within the allowable line and column ranges k k k k k Clearing Drawn Lines and Points Sketch Cls The following operation clears all drawn lines and points from the screen u u u u uTo clear lines and points in the STAT GRAPH TABLE RECUR and CONICS Modes Lines and points drawn using sketch menu functions are temporary Display the sketch menu and...

Page 190: ...Dual Graph gives you valuable graph analysis capabilities You should be familiar with the contents of 8 3 Graph Function Operations before reading this chapter 11 1 Before Using Dual Graph 11 2 Specifying the Left and Right View Window Parameters 11 3 Drawing a Graph in the Active Screen 11 4 Displaying a Graph in the Inactive Screen Chapter 11 ...

Page 191: ...To execute a function on the right side inactive graph you must first make it active by moving it into the active screen Active Screen Actual graph drawing is done here Inactive Screen Use the inactive screen to make copies of active screen graphs and for the result of Zoom operations Indicators appear to the right of the formulas in the function memory list to tell where graphs are drawn with Dua...

Page 192: ...ndow setting store recall RIGHT LEFT active left inactive right screen View Window setting swap Use the procedures described under View Window V Window Settings to input parameter values Use the following key operations to change to different screens while inputting View Window parameters for the left and right side screens While the View Window parameter setting screen for the active graph is sho...

Page 193: ...hen copy or move the graph to the inactive screen u u u u uDrawing a graph in the active screen Example To draw the graph of y x x 1 x 1 Use the following View Window parameters Xmin 2 Ymin 2 Xmax 2 Ymax 2 Xscale 0 5 Yscale 1 Input the function v v b v b Store the function w Draw the graph 6 DRAW or w ...

Page 194: ... COPY copies active graph to inactive screen SWAP switches active screen and inactive screen PICT picture function k k k k k Copying the Active Graph to the Inactive Screen Example To draw the graph for y x x 1 x 1 on the active screen and the inactive screen Use the following View Window parameters Active Left Screen Inactive Right Screen View Window parameters View Window parameters Xmin 2 Ymin ...

Page 195: ...ed Active Screen y x x 1 x 1 Inactive Screen y 2x2 3 Use the View Window parameters shown below Active Left Screen Inactive Right Screen View Window parameters View Window parameters Xmin 4 Ymin 5 Xmin 2 Ymin 2 Xmax 4 Ymax 5 Xmax 2 Ymax 2 Xscale 1 Yscale 1 Xscale 0 5 Yscale 1 Assume that the functions being graphed are stored in memory areas Y1 and Y2 Select the function for the graph that you wan...

Page 196: ...active left screen A1 SEL Draw the graph 6 DRAW At this point you could perform a copy operation and superimpose the active graph over the inactive graph K1 COPY Pressing 6 G T lets you switch between display of the active and inactive graphs using the entire display for each 6 G T 6 G T 6 G T Displaying a Graph in the Inactive Screen 11 4 ...

Page 197: ...llowing shows some example operations using the zoom function Example 1 To use box zoom to enlarge the graph of y x x 1 x 1 Use the following View Window parameters for the active graph Xmin 2 Ymin 2 Xmax 2 Ymax 2 Xscale 0 5 Yscale 1 Assume that the function is already stored in memory area Y1 Press 6 DRAW or w to draw the graph 2 Zoom 1 BOX Use the cursor keys to move the pointer to one of the co...

Page 198: ...ts current coordinates inside the table whenever you want This function is very useful for summarizing graph analysis results Be sure to read Chapter 8 Graphing and Chapter 9 Graph Solve before trying to perform any of the operations described in this chapter 12 1 Before Using Graph to Table 12 2 Using Graph to Table 12 Chapter ...

Page 199: ...g of the items in the function menu at the bottom of the screen see 8 1 Before Trying to Draw a Graph Whenever the set up screen s Dual Screen item is set to G to T you can only store rectangular coordinate Y polar coordinate r and parametric function graphs in memory You cannot use Graph to Table to display split graph table screens using X constant or inequality graphs of functions stored in the...

Page 200: ... Y2 x 2 Use the following View Window parameters Xmin 5 Ymin 10 Xmax 5 Ymax 10 Xscale 1 Yscale 2 1 Input the two functions 2 Press 6 DRAW or w to draw the graph in the left half of the screen 3 Press 1 Trace and then use e to move the pointer to the first intersection 4 Press w to store the coordinates of the pointer location in the table on the right side of the screen 5 Use e to move the pointer...

Page 201: ...p 6 of the previous example press K The following function menu appears CHNG changes the active screen between left and right LMEM saves table column to list file PICT saves graph data to graph memory 2 Press 2 LMEM 3 Press 1 List1 to store the data in the x coordinate column into List 1 Table data uses the same memory as TABLE menu table data Always be sure to store table data into a list Any of ...

Page 202: ...ing integra tion calculations Graph functions cannot be used while the highlighting is blinking in the table To clear the highlighting and make the graph side the active screen press K 1 CHNG K key operation is disabled whenever a graph and table are both on the screen and there is no numeric data in the table and when the screen is not split i e when either the graph or table only is on the displ...

Page 203: ...at happens to a graph when such changes are made For example you can see the graph change as illustrated here as the value of coefficient A changes in the formula y Ax2 13 1 Before Using Dynamic Graph 13 2 Storing Editing and Selecting Dynamic Graph Functions 13 3 Drawing a Dynamic Graph 13 4 Using Dynamic Graph Memory 13 5 Dynamic Graph Application Examples Chapter 13 ...

Page 204: ... and f to move SEL dynamic Graph draw non draw status DEL function delete TYPE function type specification VAR coefficient menu B IN menu of built in functions RCL recall and execution of Dynamic Graph conditions and screen data The built in function menu contains the following seven functions Y AX B Y A X B 2 C Y AX2 BX C Y AX 3 BX2 CX D Y Asin BX C Y Acos BX C Y Atan BX C P 184 P 190 ...

Page 205: ... are identical to those you use in the GRAPH Mode For details see 8 3 Graph Function Operations Dynamic Graphs can be one of the following three types only rectangular coordinate Y polar coordinate r and parametric You cannot use Dynamic Graph with X constant or inequality graphs of functions stored in the GRAPH or TABLE Mode If you try to use Dynamic Graph with a function that does not contain a ...

Page 206: ...namic coefficient If the range of the dynamic coefficient is already defined from a previous operation you can skip this step 5 Specify the speed of the draw operation If the speed is already defined from a previous operation you can skip this step 6 Draw the Dynamic Graph u u u u uTo set Dynamic Graph conditions Example To use Dynamic Graph to graph y A x 1 2 1 as the value of A changes from 2 to...

Page 207: ...iable If a complex number is assigned to a variable only the integer part appears All variables contained in the currently selected function appear on the display in alphabetical order If there is more than one function that can be drawn using Dynamic Graph the message Too Many Functions appears on the display If the value of the dynamic variable is zero and you press 5 AUTO the dynamic variable a...

Page 208: ...Dynamic Graph draw operation There are four different variations for Dynamic Graphing k k k k k 10 time Continuous Drawing Select Stop as the draw type Dynamic Type to perform 10 time continuous drawing With this drawing style 10 versions of the graph are drawn and then the draw operation stops automatically Example To use 10 time continuous drawing to draw the same graph that you drew in the prev...

Page 209: ...wn on the display with the graph use the graph function set up display to switch Graph Func Off Pressing 5 AUTO draws up to 11 versions of the Dynamic Graph starting from the start Start value of the dynamic coefficient k k k k k Continuous Drawing When the Dynamic Graph draw type Dynamic Type is set to Cont continuous drawing of the Dynamic Graph continues until you press A Example To continuousl...

Page 210: ...ge 184 1 Display the coefficient value specification display and press 3 SPEED 2 Use f and c to select STOP GO tg and press 1 SEL J 3 Start drawing of the Dynamic Graph 6 DYNA w w Pressing A while the Dynamic Graph is being drawn changes to the drawing speed setting display The draw operation is suspended at this time and you can view the graph by pressing 6 G T k k k k k Overwriting By turning On...

Page 211: ...n use the following procedure to adjust the Dynamic Graph speed while the draw operation is taking place 1 While a Dynamic Graph draw operation is being performed press A to change to the speed adjustment menu tg tg tg tg tg Each step of the Dynamic Graph draw operation is performed each time you press w g g g g g h h h h h slow 1 2 speed normal default speed fast double speed STO stores graph con...

Page 212: ...Dynamic Graph draw operation is being performed press A to change to the speed adjustment menu 2 Press 5 STO to store the data If there is already data stored in Dynamic Graph memory the above operation replaces it with the new data u u u u uTo recall data from Dynamic Graph memory 1 Display the Dynamic Graph function list 2 Press 6 RCL to recall all the data stored in Dynamic Graph memory Data re...

Page 213: ... 1 Xmax 42 Ymax 16 Xscale 5 Yscale 2 With the initial velocity defined as V and the angle defined as the parabolas can be obtained using the following expressions X Vcos T Y Vsin T 1 2 gT2 g 9 8 meters per second 1 Input the functions making sure to specify them a Param parametric type 2 Display the coefficient menu and specify the dynamic coefficient 4 VAR daw 3 Display the coefficient range menu...

Page 214: ...ing types of implicit functions using the calculator s built in functions Parabolic graph Circle graph Elliptical graph Hyperbolic graph 14 1 Before Graphing an Implicit Function 14 2 Graphing an Implicit Function 14 3 Implicit Function Graph Analysis Chapter 14 ...

Page 215: ... following built in function menu appears on the screen 2 Use f and c to highlight the built in function you want and then press w The following nine functions are built in Graph Type Function Parabola X A Y K 2 H X AY2 BY C Y A X H 2 K Y AX2 BX C Circle X H 2 Y K 2 R2 AX2 AY2 BX CY D 0 Ellipse X H 2 Y K 2 1 A2 B2 Hyperbola X H 2 Y K 2 1 A2 B2 Y K 2 X H 2 1 A2 B2 ...

Page 216: ...ed to each variable which are general variables used by the calculator If the values include an imaginary part only the real part appears on the display 3 Assign values to each variable bwbwcw You can also use f and c to highlight a variable and then input a value 4 Press 6 DRAW to draw the graph Certain View Window parameters can make a circle graph come out looking like an ellipse When this happ...

Page 217: ...ou want to draw ccccccc 2 Press w and the variable input screen appears 3 Assign values to each variable cwcwdwbw 4 Press 6 DRAW to draw the graph k k k k k Implicit Function Graphing Precautions Assigning the following types of values to variables contained in built in function produces an error 1 Parabola graph A 0 2 Circle graph R 0 for X H 2 Y K 2 R2 A 0 for AX2 AY2 BX CY D 0 3 Ellipse hyperbo...

Page 218: ...ts equidistant from fixed line l and fixed point F not on the line Fixed point F is the focus fixed line l is the directrix the horizontal line that passes through the focus directrix is the axis of symme try the length of a straight line that intersects the parabola passes through the locus and is parallel to fixed line l is the latus rectum and point A where the parabola intersects the axis of s...

Page 219: ... and A where the hyperbola intersects the x axis are the vertexes the x coordinate values of vertexes A and A are called x intercepts the y coordinate values of vertexes A and A are called y intercepts and straight lines l and l which get closer to the hyperbola as they move away from the foci are asymptotes 14 2 Graphing an Implicit Function Vertex A Vertex A Focus F Focus F Asymptote l Asymptote...

Page 220: ...IR draws the axis of symmetry directrix VTX LEN determines the vertex latus rectum Circle Graph Analysis CNTR RADS determines the center radius Ellipse Graph Analysis FOCS X IN Y IN determines the focus x intercept y intercept Hyperbolic Graph Analysis FOCS X IN Y IN VTX determines the focus x intercept y intercept vertex ASYM draws the asymptote The following examples show how to use the above me...

Page 221: ...the first vertex u u u u uTo calculate the latus rectum G Solv LEN Example To determine the latus rectum for the parabola X Y 2 2 3 Use the following View Window parameters Xmin 1 Ymin 5 Xmax 10 Ymax 5 Xscale 1 Yscale 1 5 G Solv 5 LEN Calculates the latus rectum u u u u uTo calculate the center and radius G Solv CNTR RADS Example To determine the center and radius for the circle X2 Y2 2X 2Y 3 0 Us...

Page 222: ... y intercepts for the hyperbola X 1 2 Y 1 2 1 22 22 Use the following View Window parameters Xmin 6 3 Ymin 3 1 Xmax 6 3 Ymax 3 1 Xscale 1 Yscale 1 5 G Solv 2 X IN Calculates the x intercept 5 G Solv 3 Y IN Calculates the y intercept Press e to calculate the second set of x y intercepts Pressing d returns to the first set of intercepts Implicit Function Graph Analysis 14 3 ...

Page 223: ... Ymin 3 1 Xmax 6 3 Ymax 3 1 Xscale 1 Yscale 1 5 G Solv 2 SYM Draws the axis of symmetry 5 G Solv 3 DIR Draws the directrix u u u u uTo draw and analyze the asymptotes G Solv ASYM Example To draw the asymptotes for the hyperbola X 1 2 Y 1 2 1 22 22 Use the following View Window parameters Xmin 6 3 Ymin 5 Xmax 6 3 Ymax 5 Xscale 1 Yscale 1 5 G Solv 5 ASYM Draws the asymptotes 14 3 Implicit Function G...

Page 224: ...ears on the display when graph analysis is unable to produce a result The following can result in inaccurate analysis results or may even make it impossible to obtain a solution at all When the solution is tangent to the x axis When the solution is a point of tangency between two graphs Implicit Function Graph Analysis 14 3 ...

Page 225: ...lues for graphing Because of this Table Graph makes it easy to grasp the nature of numeric tables and recursion formulas 15 1 Before Using Table Graph 15 2 Storing a Function and Generating a Numeric Table 15 3 Editing and Deleting Functions 15 4 Editing Tables and Drawing Graphs 15 5 Copying a Table Column to a List Chapter 15 ...

Page 226: ... appears on the display SEL numeric table generation non generation status DEL function delete TYPE function type specification COLR graph color specification RANG table range specification screen TABL start numeric table generation Note that the RANG item does not appear when a list name is specified for the Variable item in the set up screen ...

Page 227: ...e Table range method With this method you specify the conditions for the change in value of the variable List With this method you substitute the values contained in a previously created list for the value of the variable u u u u uTo generate a table using a table range Example To generate a table as the value of variablex changes from 3 to 3 in increments of 1 5 RANG dwdwbw The numeric table rang...

Page 228: ...tem of the set up screen k k k k k Generating a Table Example To generate a table of values for the functions stored in memory areas Y1 and Y3 of the TABLE Mode function list Use f and c to move the highlighting to the function you want to select for table generation and press 1 SEL to select it The sign of selected functions is highlighted on the screen To deselect a function move the cursor to i...

Page 229: ... setting of set up screen s Derivative item to On causes a numeric table that includes the derivative to be displayed whenever you generate a numeric table An error occurs if a graph for which a range is specified or an overwrite graph is included among the graph expressions k k k k k Specifying the function type You can specify a function as being one of three types Rectangular coordinate Y Polar...

Page 230: ... want to edit Use d and e to move the cursor to the location of the change eeeeef w 6 TABL The Function Link Feature automatically reflects any changes you make to functions in the TABLE Mode list in the GRAPH Mode and DYNA Mode lists u u u u uTo delete a function 1 Use f and c to move the highlighting to the function you want to delete and then press 2 DEL 2 Press 1 YES to delete the function or ...

Page 231: ...delete table ROW display menu of row operations G CON G PLT connected type draw plot type graph draw u u u u uTo change variable values in a table Example To change the value in Column x Row 3 of the table generated on page 208 from 1 to 2 5 cc c fw When you change a variable value in Column x all values in the columns to the right are recalculated and displayed If you try to replace a value with ...

Page 232: ...w Example To delete Row 2 of the table generated on page 208 3 ROW c 1 DEL u u u u uTo insert a row Example To insert a new row between Rows 1 and 2 in the table gener ated on page 208 3 ROW c 2 INS u u u u uTo add a row Example To add a new row below Row 7 in the table generated on page 208 3 ROW cccccc 3 ADD 15 4 Editing Tables and Drawing Graphs 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 ...

Page 233: ...cedure to change the graph color to orange or green 1 Display the function list and then use f and c to highlight the function whose graph color you want to change 2 Press 4 COLR 3 Press the function key that corresponds to the color you want to specify Blue Orng Grn blue orange green u u u u uTo specify the draw non draw status of a formula There are two options for the draw non draw status of a ...

Page 234: ... the functions Example To use the values in the numeric table generated using the Table Range and the View Window parameters from the previous example to graph all functions stored in memory as plot type graphs 6 TABL 6 G PLT Specifies plot type graph After you graph a function you can press 6 G T or A to return to the function s numeric table After graphing a function you can use the trace zoom s...

Page 235: ...th the graph and its table Use the same View Window parameters as in the example on page 214 Display the set up screen and specify T G for Dual Screen Press J 6 TABL Shows the table 6 G PLT Draws plot type graph Pressing 6 G T causes the graph on the left side of the Dual Screen to fill the entire display Note that you cannot use the sketch function while a graph is displayed using 6 G T P 7 1 2 3...

Page 236: ...ts of a numeric table column into a list u u u u uTo copy a table to a list Example To copy the contents of Column x into List 1 K1 LIST 2 LMEM You can select any row of the column you want to copy Press the function key that corresponds the list you want to copy to 1 List1 1 2 3 4 5 6 ...

Page 237: ...eneral term of sequence an made up of an and n Formulas for linear recursion between two terms made up of an 1 an and n Formulas for linear recursion between three terms made up of an 2 an 1 an and n 16 1 Before Using the Recursion Table and Graph Function 16 2 Inputting a Recursion Formula and Generating a Table 16 3 Editing Tables and Drawing Graphs Chapter 16 ...

Page 238: ...specification n an menu for input of variable n and general terms an and bn RANG screen for setting of table range TABL recursion formula table generation u u u u uTo specify the recursion formula type Before inputting a recursion formula you must first specify its type 1 In the Recursion Menu press 3 TYPE In this display an An B is the general term an A n B of an 2 Press the function key for the ...

Page 239: ... formula and the initial term of the numeric value table You should also specify a starting point for the pointer when drawing a convergence diver gence graph WEB graph for a formula for linear recursion between two terms Start Starting value of variable n End Ending value of variable n a0 b0 Value of 0th term a0 b0 a1 b1 Value of 1st term a1 b1 anStr bnStr Pointer starting point for convergence d...

Page 240: ...1 1 Specify the recursion formula type as linear recursion between three terms and then input the formula 3 TYPE 3 an 2 4 n an 3 an 1 2 an 2 Press w and then press 5 RANG to display the table range setting screen which contains the following items a0 a1 setting of value for a0 b0 and a1 b1 a1 b1 and a2 b2 The table range settings specify the conditions that control the value of variable n in the r...

Page 241: ... start value the calculator makes the starting value of variable x the same as the value of a0 b0 or a1 b1 before generating the table If the start value is greater than the end value the calculator swaps the two values before generating the table If the start value is the same as the end value the calculator generates a table using the start value of variable x only If the start value is very lar...

Page 242: ... recursion formula from non generation to generation select the formula and press 1 SEL C 1 SEL u u u u uTo change the contents of a recursion formula Changing the contents of a recursion formula causes the values in the table to be updated using the current table range settings Example To change an 1 2an 1 to an 1 2an 3 e Displays the cursor ee dw Changes the formula contents 6 TABL u u u u uTo d...

Page 243: ... The WEB item is available only when a table generated using a formula for linear recursion between two terms an 1 bn 1 is on the display u u u u uTo delete a recursion table 1 Display the recursion table you want to delete and then press 2 DEL 2 Press 1 YES to delete the table or 6 NO to abort the operation without deleting anything k k k k k Before Drawing a Graph for a Recursion Formula You mus...

Page 244: ...on draw status use same procedure as that for specifying generation non generation status u u u u uTo specify the type of data to be plotted Display On You can specify one of two types of data for plotting an on the vertical axis n on the horizontal axis an on the vertical axis n on the horizontal axis In the function menu that appears while a table is on the display press 5 G CON or 6 G PLT to di...

Page 245: ...ph WEB graph With this feature you can draw a graph of an 1 f an where an 1 and an are the terms of linear recursion between two terms substituted respectively for y and x in the function y f x The resulting graph can then be viewed to determine whether or not the graph is convergent or divergent Example 1 To determine whether or not the recursion formula an 1 3an 2 3an is convergent or divergent ...

Page 246: ...e display w w This graph indicates that recursion formula an 1 3an2 3an is convergent Example 2 To determine whether or not the recursion formula bn 1 3bn 0 2 is convergent or divergent Use the following table range Start 0 End 6 b0 0 02 bn Str 0 02 Use the View Window parameters from Example 1 1 Press 6 TABL 4 WEB to draw the graph 16 3 Editing Tables and Drawing Graphs ...

Page 247: ...start point is always 0 3 Each press of w draws web like lines on the display w w This graph indicates that recursion formula bn 1 3bn 0 2 is divergent Inputting bn or n for the expression an 1 or Inputting an or n for the expression bn 1 for linear recursion between two terms causes an error Editing Tables and Drawing Graphs 16 3 ...

Page 248: ...ical table of values Example To draw the graph of an 1 2an 1 from Example 1 displaying both the graph and its table Display the set up screen and specify T G for Dual Screen Press J 6 TABL Shows the table 6 G PLT Draws plot type graph Pressing 6 G T causes the graph on the left side of the Dual Screen to fill the entire display Note that you cannot use the sketch function while a graph is displaye...

Page 249: ...tistical and matrix calculations and for graphing 17 1 List Operations 17 2 Editing and Rearranging Lists 17 3 Manipulating List Data 17 4 Arithmetic Calculations Using Lists 17 5 Switching Between List Files Element number Display range Cell Row List name Column List 1 List 2 List 3 List 4 List 5 List 6 1 56 1 107 3 5 4 0 2 37 2 75 6 0 0 3 21 4 122 2 1 0 0 4 69 8 87 4 4 2 0 5 40 16 298 3 0 0 6 48...

Page 250: ...generated by GRAPH TO TABLE to a list w List internal operations w Memory transfer Generating a table by defining a list as the variable K 1 LIST 2 LMEM 4 List4 Inside list Copying the column of a specific table to a specific list w Memory transfer Example To send column 1 of Mat A to a list Graph Operation List graphing Y1 List 1X ...

Page 251: ...ntain a value The screen automatically scrolls when the highlighting is located at either edge of the screen The following example procedure is performed starting with the highlighting located at Cell 1 of List 1 1 Input a value and press w to store it in the list dw 2 The highlighting automatically moves down to the next cell for input Note that you can also input the result of an expression in a...

Page 252: ...hould not input a comma after the final value of the set you are inputting Right 34 53 78 Wrong 34 53 78 You can also use list names inside of a mathematical expression to input values into another cell The following example shows how to add the values in each row in List 1 and List 2 and input the result into List 3 1 Use the cursor keys to move the highlighting to the name of the list where you ...

Page 253: ...the above cell delete operation does not affect cells in other lists If the data in the list whose cell you delete is somehow related to the data in neighboring lists deleting a cell can cause related values to become misaligned u u u u uTo delete all cells in a list Use the following procedure to delete all the data in a list 1 Use the cursor key to move the highlighting to any cell of the list w...

Page 254: ... you insert a cell is somehow related to the data in neighboring lists inserting a cell can cause related values to become misaligned k k k k k Sorting List Values You can sort lists into either ascending or descending order The highlighting can be located in any cell of the list u u u u uTo sort a single list Ascending order 1 While the lists are on the screen press 1 SRT A 2 The prompt How Many ...

Page 255: ...er ascending order or descending order while the cells of the linked lists are arranged so that the relative relationship of all the rows is maintained Ascending order 1 While the lists are on the screen press 1 SRT A 2 The prompt How Many Lists H appears to ask how many lists you want to sort Here we will sort one base list linked to one other list so we should input 2 cw 3 In response to the Sel...

Page 256: ...s that you should press 2 SRT D in place of 1 SRT A You can sort up to six lists at one time If you specify a list more than once for a single sort operation an error occurs An error also occurs if lists specified for sorting do not have the same number of values rows 17 2 Editing and Rearranging Lists ...

Page 257: ...ains the following items List L M Dim Fill Seq Min Max Mean Med Sum Prod Cuml A A A A A Note that all closing parentheses at the end of the following operations can be omitted u u u u uTo count the number of values OPTN LIST Dim K1 LIST 3 Dim 1 List list number 1 6 w The number of cells that contain data in a list is called its dimension Example To enter the RUN Mode and count the number of values...

Page 258: ...eate a 2 row 3 column matrix each cell of which contains 0 in Matrix A A c d a K1 LIST 3 Dim J 2 MAT 1 Mat aAw u u u u uTo replace all cell values with the same value OPTN LIST Fill K 1 LIST 4 Fill value 1 List list number 1 6 w Example To replace all values in List 1 with 3 AK1 LIST 4 Fill d 1 List b w The following shows the new contents of List 1 u u u u uTo generate a sequence of numbers OPTN ...

Page 259: ...To find the minimum value in List 1 36 16 58 46 56 AK1 LIST 6 g 1 Min 6 g 6 g 1 List b w u u u u uTo find the maximum value in a list OPTN LIST Max Use the same procedure as when finding the minimum value Min except press 2 Max in place of 1 Min u u u u uTo find which of two lists contains the smallest value OPTN LIST Min K1 LIST 6 g 1 Min 6 g 6 g 1 List list number 1 6 1 List list number 1 6 w Th...

Page 260: ... that contains values and one that contains the number of occurrences of each value The frequency of the data in Cell 1 of the first list is indicated by the value in Cell 1 of the second list etc The two lists must contain the same number of values If they don t an error occurs K1 LIST 6 g 3 Mean 6 g 6 g 1 List list number 1 6 data 1 List list number 1 6 frequency w Example To calculate the mean ...

Page 261: ... whose frequency is indicated by List 2 75 89 98 72 67 AK1 LIST 6 g 4 Med 6 g 6 g 1 List b 1 List c w u u u u uTo calculate the sum of values in a list OPTN LIST Sum K1 LIST 6 g 6 g 1 Sum 6 g 1 List list number 1 6 w Example To calculate the sum of values in List 1 36 16 58 46 56 AK1 LIST 6 g 6 g 1 Sum 6 g 1 List bw u u u u uTo calculate the sum of products OPTN LIST Prod K1 LIST 6 g 6 g 2 Prod 6 ...

Page 262: ...n ListAns Memory Example To calculate the percentage represented by each value in List 1 2 3 6 5 4 AK1 LIST 6 g 6 g 4 6 g 1 List bw u u u u uTo calculate the differences between neighboring data inside a list OPTN LIST A A A A A K1 LIST 6 g 6 g 5 A 6 g list number 1 6 w The result of this operation is stored in ListAns memory Example To calculate the difference between the values in List 1 1 3 8 5...

Page 263: ...e number of cells in the original list Note that an error occurs if you execute A List for a list that has no data or only one data item u u u u uTo transfer list contents to Matrix Answer Memory OPTN LIST L M K1 LIST 2 L M 1 List list number 1 6 1 List list number 1 6 w You can input the following as many times as necessary to specify more than one list in the above operation list number 1 6 Exam...

Page 264: ...ent dimensions An error occurs whenever an operation involving any two cells generates a mathematical error k k k k k Inputting a List into a Calculation There are two methods you can use to input a list into a calculation u u u u uTo input a specific list by name Example To input List 6 1 Press K to display the first Operation Menu This is the function key menu that appears in the RUN Mode when y...

Page 265: ... e b gf cc Example 2 To assign the list in ListAns Memory to List 1 K1 LIST 1 List Ka1 List bw u u u u uTo input a single list cell value into a calculation You can extract the value in a specific cell of a list and use it in a calculation Specify the cell number by enclosing it between square brackets using the and keys Example To calculate the sine of the value stored in Cell 3 of List 2 sK1 LIS...

Page 266: ...h as Y1 List1 X If List 1 contains the values 1 2 3 this function will produces three graphs Y X Y 2X Y 3X P 111 There are certain limitations on using lists with graphing functions k k k k k Inputting Scientific Calculations into a List You can use the numeric table generation functions in the Table Graph Menu to input values that result from certain scientific function calculations into a list T...

Page 267: ...t d operation in the above procedure you could input eb gf cc 1 4 Example 2 To use List 1 2 and List 2 5 to perform List 1List 2 3 6 List1MList2w This creates a list with the results of 14 25 36 1 The resulting list 32 is stored in ListAns Memory 729 Arithmetic Calculations Using Lists 17 4 ...

Page 268: ...st files u u u u uTo switch between list files In the Main Menu select the LIST icon and enter the LIST Mode Press Z to display the LIST Mode set up screen Press the function key to select the file you want Example To select File 3 3 File3 J All subsequent list operations are applied to the lists contained in the file you select List File3 in the above example ...

Page 269: ...18 3 Calculating and Graphing Single Variable Statistical Data 18 4 Calculating and Graphing Paired Variable Statistical Data 18 5 Performing Statistical Calculations 18 6 Tests 18 7 Confidence Interval 18 8 Distribution Important This chapter contains a number of graph screen shots In each case new data values were input in order to highlight the particular characteristics of the graph being draw...

Page 270: ...the highlighting around the lists P 251 GRPH graph menu P 269 CALC statistical calculation menu P 276 TEST test menu P 293 INTR confidence interval menu P 303 DIST distribution menu P 234 SRT A SRT D ascending descending sort P 233 DEL DEL A deletes highlighted data all data P 234 INS inserts new cell at highlighted cell The procedures you should use for data editing are identical to those you use...

Page 271: ...t values can be up to 10 digits long You can use the f c d and e keys to move the highlighting to any cell in the lists for data input k k k k k Plotting a Scatter Diagram Use the data input above to plot a scatter diagram 1 GRPH 1 GPH1 To return to the statistical data list press J or Q View Window parameters are normally set automatically for statistical graphing If you want to set View Window p...

Page 272: ... is on the display press 1 GRPH to display the graph menu which contains the following items GPH1 GPH2 GPH3 only one graph 1 2 3 drawing The initial default graph type setting for all the graphs Graph 1 through Graph 3 is scatter diagram but you can change to one of a number of other graph types P 252 SEL simultaneous graph GPH1 GPH2 GPH3 selection P 254 SET graph settings graph type list assignme...

Page 273: ...iety of other statistical graph types for each graph List The initial default statistical data is List 1 for single variable data and List 1 and List 2 for paired variable data You can specify which statistical data list you want to use for x data and y data Frequency Normally each data item or data pair in the statistical data list is represented on a graph as a point When you are working with a ...

Page 274: ...X Med X 2 X 3 X 4 linear regression graph Med Med graph quadratic regression graph cubic regression graph quartic regression graph Log Exp Pwr Sin logarithmic regression graph exponential regression graph power regression graph sine regression graph u u u u uXList x axis data list List1 List2 List3 List4 List5 List6 List 1 List 2 List 3 List 4 List 5 List 6 u u u u uYList y axis data list List1 Li...

Page 275: ...bution and plots the result The expected NPP values of the normal distribution are used as the vertical axis while the observed values of the variable being tested are on the horizontal axis Press J or Q to return to the statistical data list k k k k k Selecting the Regression Type After you graph paired variable statistical data you can use the function menu at the bottom of the display to select...

Page 276: ...ression parameter calculation results while a scatter diagram is on the display 6 g 1 Log k k k k k Graphing Statistical Calculation Results You can use the parameter calculation result menu to graph the displayed regression formula P 267 COPY stores the displayed regression formula as a graph function DRAW graphs the displayed regression formula Example To graph a logarithmic regression While log...

Page 277: ...eady be input in the statistical data list see Inputting Data into Lists Draw the graph using the procedure described under Changing Graph Parameters 6 DRAW The display screen appears as shown above before the graph is drawn At this point you can change the Start and pitch values k k k k k Med box Graph Med Box This type of graph lets you see how a large number of data items are grouped within spe...

Page 278: ...u press 6 SET and then change the graph type of the graph you want to use GPH1 GPH2 GPH3 to mean box graph k k k k k Normal Distribution Curve P 254 The normal distribution curve is graphed using the following normal distribution Graph Type function N Dis y 1 2 x n e 2x n 2 x x 2 The distribution of characteristics of items manufactured according to some fixed standard such as component length fal...

Page 279: ...e before the graph is drawn At this point you can change the Start and pitch values k k k k k Displaying Single Variable Statistical Results Single variable statistics can be expressed as both graphs and parameter values When these graphs are displayed the menu at the bottom of the screen appears as below 1VAR single variable calculation result menu Pressing 1 1VAR displays the following screen Us...

Page 280: ...rtile _ x x n data mean population standard deviation _ x x n data mean population standard deviation maxX maximum Mod mode Press 6 DRAW to return to the original single variable statistical graph 18 3 Calculating and Graphing Single Variable Statistical Data ...

Page 281: ...ic representation of this relationship is a linear regression graph Graph Type Q1 GRPH 6 SET c Scatter 1 Scat GPH1 Q1 GRPH 1 GPH1 X 1 X 1 2 3 4 5 6 6 DRAW a regression coefficient slope b regression constant term intercept r correlation coefficient r2 coefficient of determination k k k k k Med Med Graph P 254 When it is suspected that there are a number of extreme values a Med Med graph can be use...

Page 282: ... regression Ex Quadratic regression 3 X 2 1 2 3 4 5 6 6 DRAW Quadratic regression a regression second coefficient b regression first coefficient c regression constant term intercept Cubic regression a regression third coefficient b regression second coefficient c regression first coefficient d regression constant term intercept Quartic regression a regression fourth coefficient b regression third ...

Page 283: ...m intercept b regression coefficient slope r correlation coefficient r2 coefficient of determination k k k k k Exponential Regression Graph P 254 Exponential regression expresses y as a proportion of the exponential function of x The standard exponential regression formula is y a ebx so if we take the logarithms of both sides we get Iny Ina bx Next if we say Y Iny and a Ina the formula corresponds...

Page 284: ...ssion coefficient b regression power r correlation coefficient r2 coefficient of determination k k k k k Sine Regression Graph Sine regression expresses the relationship between specific pair of data vari ables as a trigonometric function Residual mean square partial differentiation is expressed in the form of a matrix and the iteration method is used to determine the coefficient that minimizes th...

Page 285: ...8 39 40 41 42 43 44 45 46 47 48 List 2 Gas Usage Meter Reading 130 171 159 144 66 46 40 32 32 39 44 112 116 152 157 109 130 59 40 42 33 32 40 71 138 203 162 154 136 39 32 35 32 31 35 80 134 184 219 87 38 36 33 40 30 36 55 94 Input the above data and plot a scatter diagram 1 GRPH 1 GPH1 Since this example involves monthly billing we will assume a period of 12 You can also estimate the period by usi...

Page 286: ...egression model will be stored Plots that are higher than the regression model are positive while those that are lower are negative Residual calculation can be performed and saved for all regression models Any data already existing in the selected list is cleared The residual of each plot is stored in the same precedence as the data used as the model k k k k k Displaying Paired Variable Statistica...

Page 287: ...imum of yList data k k k k k Copying a Regression Graph Formula to the Graph Mode After you perform a regression calculation you can copy its formula to the GRAPH Mode The following are the functions that are available in the function menu at the bottom of the display while regression calculation results are on the screen COPY stores the displayed regression formula to the GRAPH Mode DRAW graphs t...

Page 288: ...ession calculations 6 DRAW P 254 1 X The text at the top of the screen indicates the currently selected graph StatGraph1 Graph 1 StatGraph2 Graph 2 StatGraph3 Graph 3 1 Use f and c to change the currently selected graph The graph name at the top of the screen changes when you do c 2 When graph you want to use is selected press w P 259 Now you can use the procedures under Displaying Single Variable...

Page 289: ... where single variable frequency values Frequency are located 2Var XList specifies list where paired variable statistic x values XList are located 2Var YList specifies list where paired variable statistic y values YList are located 2Var Freq specifies list where paired variable frequency values Frequency are located Calculations in this section are performed based on the above specifications k k k...

Page 290: ... see Displaying Paired Variable Statistical Results k k k k k Regression Calculation In the explanations from Linear Regression Graph to Sine Regression Graph regression calculation results were displayed after the graph was drawn Here the regression line and regression curve is represented by mathematical expressions You can directly determine the same expression from the data input screen Pressi...

Page 291: ...he nearby data and estimate the values of and when xi 40 and yi 1000 1 In the Main Menu select the STAT icon and enter the STAT Mode 2 Input data into the list and draw the power regression graph 3 In the Main Menu select the RUN icon and enter the RUN Mode 4 Press the keys as follows ea value of xi K5 STAT 2 w The estimated value is displayed for xi 40 baaa value of yi 1 w The estimated value is ...

Page 292: ...e t obtains normalized variate t x value Probability P t Q t and R t and normalized variate t x are calculated using the following formulas P t Q t R t Example The following table shows the results of measurements of the height of 20 college students Determine what percentage of the students fall in the range 160 5 cm to 175 5 cm Also in what percentile does the 175 5 cm tall student fall Class no...

Page 293: ...3 PROB 6 g You obtain the normalized variate immediately after performing single variable statistical calculations only 4 t bga f w Normalized variate t for 160 5cm Result 1 633855948 1 634 4 t bhf f w Normalized variate t for 175 5cm Result 0 4963343361 0 496 1 P a ejg 1 P b gde w Percentage of total Result 0 638921 63 9 of total 3 R a ejg w Percentile Result 0 30995 31 0 percentile Performing St...

Page 294: ...n the Sketch Mode Example To graph probability P 0 5 Perform the following operation in the RUN Mode 4 Sketch 1 Cls w 5 GRPH 1 Y K6 g 3 PROB 6 g 1 P a f w The following shows the View Window settings for the graph Ymin Ymax 0 1 0 45 Xmin Xmax 3 2 3 2 18 5 Performing Statistical Calculations ...

Page 295: ...determination is made whether the null hypothesis or alternative hypothesis will be adopted When the sample shows a trend the probability of the trend and to what extent it applies to the population is tested based on the sample size and variance size Inversely expressions related to the t test are also used to calculate the sample size required to improve probability The t test can be used even w...

Page 296: ...rinciples and terminology can be found in any standard general statistics textbook While the statistical data list is on the display press 3 TEST to display the test menu which contains the following items Z t CHI F Z t 2 F test ANOV analysis of variance ANOVA About data type specification For some types of tests you can select data type using the following menu List Var specifies list data parame...

Page 297: ...ation or draws a graph The following shows the meaning of parameter data specification items that are different from list data specification o sample mean n sample size positive integer Example To perform a 1 Sample Z Test for one list of data For this example we will perform a µ µ0 test for the data List1 11 2 10 9 12 5 11 3 11 7 when µ0 11 5 and 3 1 List c2 c bb fw dw 1 List1 c1 1 c 1 CALC µ 11 ...

Page 298: ... size Perform the following key operation from the statistical data list 3 TEST 1 Z 2 2 S The following shows the meaning of each item in the case of list data specification Data data type µ1 population mean value test conditions G µ2 specifies two tail test µ2 specifies one tail test where sample 1 is smaller than sample 2 µ2 specifies one tail test where sample 1 is greater than sample 2 1 popul...

Page 299: ... are input For this example we will perform a µ1 µ2 test for the data List1 11 2 10 9 12 5 11 3 11 7 and List2 0 84 0 9 0 14 0 75 0 95 when 1 15 5 and 2 13 5 1 List c 2 c bf fw bd fw 1 List1 c2 List2 c 1 1 c1 1 c 1 CALC µ1 µ2 direction of test z Z score p p value o1 sample 1 mean o2 sample 2 mean x1 n 1 sample 1 standard deviation x2 n 1 sample 2 standard deviation n1 sample 1 size n2 sample 2 siz...

Page 300: ...statistical data list 3 TEST 1 Z 3 1 P Prop sample proportion test conditions G p0 specifies two tail test p0 specifies lower one tail test p0 specifies upper one tail test p0 expected sample proportion 0 p0 1 x sample value x 0 integer n sample size positive integer Execute executes a calculation or draws a graph Example To perform a 1 Prop Z Test for specific expected sample proportion data valu...

Page 301: ...sample 2 size p estimated sample proportion Perform the following key operation from the statistical data list 3 TEST 1 Z 4 2 P p1 sample proportion test conditions G p2 specifies two tail test p2 specifies one tail test where sample 1 is less than sample 2 p2 specifies upper one tail test where sample 1 is greater than sample 2 x1 sample 1 data value x1 0 integer n1 sample 1 size positive integer...

Page 302: ... You can use the following menu to select a t test type 1 S 2 S REG 1 Sample 2 Sample LinearReg t Test u u u u u1 Sample t Test This test uses the sample size and population mean value to test the hypothesis that the sample is taken from the population The 1 Sample t Test is applied to standard normal distribution t o 0 µ x n 1 n o sample mean µ0 assumed population mean x n 1 sample standard devia...

Page 303: ...ning of parameter data specification items that are different from list data specification o sample mean x n 1 sample standard deviation x n 1 0 n sample size positive integer Example To perform a 1 Sample t Test for one list of data For this example we will perform a µ G G G G G µ0 test for the data List1 11 2 10 9 12 5 11 3 11 7 when µ0 11 3 1 List c 1 G c bb dw 1 List1 c1 1 c 1 CALC µ G 11 3 as...

Page 304: ... deviation x2 n 1 sample 2 standard deviation n1 sample 1 size n2 sample 2 size This formula is applicable when the sample is not pooled and the denominator is different when the sample is pooled Degrees of freedom df and xp n 1 differs according to whether or not pooling is in effect The following applies when pooling is in effect df n1 n2 2 xp n 1 n1 n2 2 n1 1 x1 n 1 2 n2 1 x2 n 1 2 The followin...

Page 305: ...2 frequency of sample 2 positive integer Pooled pooling On or Off Execute executes a calculation or draws a graph The following shows the meaning of parameter data specification items that are different from list data specification o1 sample 1 mean x1 n 1 sample 1 standard deviation x1 n 1 0 n1 sample 1 size positive integer o2 sample 2 mean x2 n 1 sample 2 standard deviation x2 n 1 0 n2 sample 2 ...

Page 306: ...wn when Pooled On xp n 1 pooled sample standard deviation u u u u uLinearReg t Test LinearReg t Test treats paired variable data sets as x y pairs and plots all data on a graph Next a straight line y a bx is drawn through the area where the greatest number of plots are located and the degree to which a relationship exists is calculated b x o y p i 1 n x o 2 i 1 n a p bo t r n 2 1 r2 a intercept b ...

Page 307: ...s a calculation Example To perform a LinearReg t Test when two lists of data are input For this example we will perform a LinearReg t Test for x axis data 0 5 1 2 2 4 4 5 2 and y axis data 2 1 0 3 1 5 5 2 4 1 G c 1 List1 c 2 List2 c 1 1 c 1 CALC G 0 G 0 direction of test t t value p p value df degrees of freedom a constant term b coefficient s standard error r correlation coefficient r2 coefficien...

Page 308: ...AT Mode Perform the following key operation from the statistical data list 3 TEST 3 CHI Next specify the matrix that contains the data The following shows the meaning of the above item Observed name of matrix A to Z that contains observed counts all cells positive integers Execute executes a calculation or draws a graph The matrix must be at least two lines by two columns An error occurs if the ma...

Page 309: ... 1 2 x2 n 1 2 Perform the following key operation from the statistical data list 3 TEST 4 F The following is the meaning of each item in the case of list data specification Data data type 1 population standard deviation test conditions G 2 specifies two tail test 2 specifies one tail test where sample 1 is smaller than sample 2 2 specifies one tail test where sample 1 is greater than sample 2 List...

Page 310: ... perform a 2 Sample F Test when two lists of data are input For this example we will perform a 2 Sample F Test for the data List1 0 5 1 2 2 4 4 5 2 and List2 2 1 0 3 1 5 5 2 4 1 List c1 G c 1 List1 c2 List2 c 1 1 c1 1 c 1 CALC 1G 2 direction of test F F value p p value x1 n 1 sample 1 standard deviation x2 n 1 sample 2 standard deviation o1 sample 1 mean o2 sample 2 mean n1 sample 1 size n2 sample...

Page 311: ...How Many number of samples List1 list whose contents you want to use as sample 1 data List2 list whose contents you want to use as sample 2 data Execute executes a calculation A value from 2 through 6 can be specified in the How Many line so up to six samples can be used Example To perform one way ANOVA analysis of variance when three lists of data are input For this example we will perform analys...

Page 312: ...1 CALC F F value p p value xp n 1 pooled sample standard deviation Fdf numerator degrees of freedom SS factor sum of squares MS factor mean squares Edf denominator degrees of freedom SSe error sum of squares MSe error mean squares 18 6 Tests ...

Page 313: ...onfidence interval width and confidence level The confidence level changes in accordance with the application 1 Sample Z Interval calculates the confidence interval when standard deviation is known 2 Sample Z Interval calculates the confidence interval when the standard deviations of two samples are known 1 Prop Z Interval uses the number of data to calculate the confidence interval when the propo...

Page 314: ...nfidence level is 95 for example inputting 0 95 produces 1 0 95 0 05 Perform the following key operation from the statistical data list 4 INTR 1 Z 1 1 S The following shows the meaning of each item in the case of list data specifica tion Data data type C Level confidence level 0 C Level 1 population standard deviation 0 List list whose contents you want to use as sample data Freq sample frequency ...

Page 315: ...ample Z Interval 2 Sample Z Interval calculates the confidence interval when the standard deviations of two samples are known Left o1 o2 Z 2 Right o1 o2 Z 2 n1 1 2 n2 2 2 n1 1 2 n2 2 2 o1 sample 1 mean o2 sample 2 mean 1 population standard deviation of sample 1 2 population standard deviation of sample 2 n1 sample 1 size n2 sample 2 size Perform the following key operation from the statistical da...

Page 316: ...ample 1 size positive integer o2 sample 2 mean n2 sample 2 size positive integer Example To calculate the 2 Sample Z Interval when two lists of data are input For this example we will obtain the 2 Sample Z Interval for the data 1 55 54 51 55 53 53 54 53 and data 2 55 5 52 3 51 8 57 2 56 5 when C Level 0 95 95 confidence level 1 15 5 and 2 13 5 1 List c a jfw bf fw bd fw 1 List1 c2 List2 c1 1 c 1 1...

Page 317: ...istical data list 4 INTR 1 Z 3 1 P Data is specified using parameter specification The following shows the meaning of each item C Level confidence level 0 C Level 1 x data 0 or positive integer n sample size positive integer Execute executes a calculation Example To calculate the 1 Prop Z Interval using parameter value specification For this example we will obtain the 1 Prop Z Interval when C Leve...

Page 318: ...atistical data list 4 INTR 1 Z 4 2 P Data is specified using parameter specification The following shows the meaning of each item C Level confidence level 0 C Level 1 x1 sample 1 data value x1 0 n1 sample 1 size positive integer x2 sample 2 data value x2 0 n2 sample 2 size positive integer Execute Executes a calculation Example To calculate the 2 Prop Z Interval using parameter value specification...

Page 319: ...he confidence interval Left o tn 1 2 Right o tn 1 2 x n 1 n x n 1 n Perform the following key operation from the statistical data list 4 INTR 2 t 1 1 S The following shows the meaning of each item in the case of list data specifica tion Data data type C Level confidence level 0 C Level 1 List list whose contents you want to use as sample data Freq sample frequency Execute execute a calculation The...

Page 320: ...e t Interval 2 Sample t Interval calculates the confidence interval when the difference between the means of two samples is known The t Interval is applied to t distribution The following confidence interval applies when pooling is in effect Left o1 o2 t 2 Right o1 o2 t 2 n1 n2 2 n1 1 n2 1 xp n 1 2 n1 n2 2 n1 1 n2 1 xp n 1 2 The following confidence interval applies when pooling is not in effect L...

Page 321: ...t whose contents you want to use as sample 2 data Freq1 frequency of sample 1 Freq2 frequency of sample 2 Pooled pooling On or Off Execute executes a calculation The following shows the meaning of parameter data specification items that are different from list data specification o1 sample 1 mean x1 n 1 sample 1 standard deviation x1 n 1 0 n1 sample 1 size positive integer o2 sample 2 mean x2 n 1 s...

Page 322: ...g when C Level 0 95 1 List c a jfw 1 List1 c2 List2 c1 1 c 1 1 c2 Off c1 CALC Left interval lower limit left edge Right interval upper limit right edge df degrees of freedom o1 sample 1 mean o2 sample 2 mean x1 n 1 sample 1 standard deviation x2 n 1 sample 2 standard deviation n1 sample 1 size n2 sample 2 size The following item is also shown when Pooled On xp n 1 pooled sample standard deviation ...

Page 323: ... used to estimate the proportion of the products will reach this value Normal probability density calculates the probability that data taken from a normal distribution is less than a specific value Normal distribution probability calculates the probability of normal distribution data falling between two specific values Inverse cumulative normal distribution calculates a value that represents the l...

Page 324: ...d to standard normal distribution 2 f x 1 e 2 2 x µ 2 µ 0 Perform the following key operation from the statistical data list 5 DIST 1 NORM 1 Npd Data is specified using parameter specification The following shows the meaning of each item x data population standard deviation 0 µ population mean Execute executes a calculation or draws a graph Specifying 1 and µ 0 specifies standard normal distributi...

Page 325: ...tistical data list 5 DIST 1 NORM 2 Ncd Data is specified using parameter specification The following shows the meaning of each item Lower lower boundary Upper upper boundary population standard deviation 0 µ population mean Execute executes a calculation Example To calculate the normal distribution probability for a specific parameter value For this example we will calculate the normal distributio...

Page 326: ... operation from the statistical data list 5 DIST 1 NORM 3 InvN Data is specified using parameter specification The following shows the meaning of each item Area probability value 0 Area 1 population standard deviation 0 µ population mean Execute executes a calculation Example To calculate inverse cumulative normal distribution for a specific parameter value For this example we will determine inver...

Page 327: ...pecific value f x df df 1 2 2 df 2 df 1 df 1 x2 Perform the following key operation from the statistical data list 5 DIST 2 t 1 tpd Data is specified using parameter specification The following shows the meaning of each item x data df degrees of freedom df 1 Execute executes a calculation or draws a graph Example To calculate Student t probability density for a specific parameter value For this ex...

Page 328: ...tion from the statistical data list 5 DIST 2 t 2 tcd Data is specified using parameter specification The following shows the meaning of each item Lower lower boundary Upper upper boundary df degrees of freedom df 1 Execute executes a calculation Example To calculate Student t distribution probability for a specific parameter value For this example we will calculate Student t distribution probabili...

Page 329: ...e f x 1 2 df df 2 x e 2 1 df 2 1 x 2 x 0 Perform the following key operation from the statistical data list 5 DIST 3 CHI 1 Cpd Data is specified using parameter specification The following shows the meaning of each item x data df degrees of freedom positive integer Execute executes a calculation or draws a graph Example To calculate 2 probability density for a specific parameter value For this exa...

Page 330: ...rom the statistical data list 5 DIST 3 CHI 2 Ccd Data is specified using parameter specification The following shows the meaning of each item Lower lower boundary Upper upper boundary df degrees of freedom positive integer Execute executes a calculation Example To calculate 2 distribution probability for a specific parameter value For this example we will calculate 2 distribution probability when ...

Page 331: ...eration from the statistical data list 5 DIST 4 F 1 Fpd Data is specified using parameter specification The following shows the meaning of each item x data n df numerator degrees of freedom positive integer d df denominator degrees of freedom positive integer Execute executes a calculation or draws a graph Example To calculate F probability density for a specific parameter value For this example w...

Page 332: ...dary Upper upper boundary n df numerator degrees of freedom positive integer d df denominator degrees of freedom positive integer Execute executes a calculation Example To calculate F distribution probability for a specific parameter value For this example we will calculate F distribution probability when lower boundary 0 upper boundary 1 9824 n df 19 and d df 16 aw b jicew bjw bgw 1 CALC prob F d...

Page 333: ... List list whose contents you want to use as sample data Numtrial number of trials positive integer p success probability 0 p 1 Execute executes a calculation The following shows the meaning of parameter data specification items that are different from list data specification x integer from 0 to n Example To calculate binomial probability for one list of data For this example we will calculate bin...

Page 334: ...ber of trials positive integer p success probability 0 p 1 Execute executes a calculation The following shows the meaning of parameter data specification item that is different from list data specification x integer from 0 to n Example To calculate binomial cumulative density for one list of data For this example we will calculate binomial cumulative density for data 10 11 12 13 14 when Numtrial 1...

Page 335: ...from the statistical data list 5 DIST 6 g 1 POISN 1 Ppd The following shows the meaning of each item when data is specified using list specification Data data type List list whose contents you want to use as sample data µ population mean µ 0 Execute executes a calculation The following shows the meaning of parameter data specification item that is different from list data specification x value Exa...

Page 336: ... Execute executes a calculation The following shows the meaning of parameter data specification item that is different from list data specification x value Example To calculate Poisson cumulative density for one list of data For this example we will calculate Poisson cumulative density for data 2 3 4 when µ 6 1 List c 1 List1 c gw 1 CALC cumulative density when x 2 cumulative density when x 3 cumu...

Page 337: ...contents you want to use as sample data p success probability 0 p 1 Execute executes a calculation The following shows the meaning of parameter data specification item that is different from list data specification x value Positive integer number is calculated whether list data Data List or x value Data variable is specified Example To calculate geometric probability for one list of data For this ...

Page 338: ... use as sample data p success probability 0 p 1 Execute executes a calculation The following shows the meaning of parameter data specification item that is different from list data specification x value Positive integer number is calculated whether list data Data List or x value Data variable is specified Example To calculate geometric cumulative density for one list of data For this example we wi...

Page 339: ...ions 19 2 Simple Interest Calculations 19 3 Compound Interest Calculations 19 4 Investment Appraisal 19 5 Amortization of a Loan 19 6 Conversion between Percentage Interest Rate and Effective Interest Rate 19 7 Cost Selling Price Margin Calculations 19 8 Day Date Calculations ...

Page 340: ...ing d displays the same values in reverse sequence Zoom Scroll Sketch and G Solve cannot be used in the Financial Mode In the Financial Mode horizontal lines are blue and vertical lines are red These colors are fixed and cannot be changed The present value is positive when it represents receipt of money and a negative value when it represents a payment Note that calculation results produced in thi...

Page 341: ...whenever you enter the Financial Mode which cancels a Sci number of significant digits or Eng engineering notation setting made in another mode k k k k k Entering the Financial Mode On the Main Menu select the TVM icon to enter the Financial Mode When you do the Financial 1 screen appears on the display Financial 1 screen Financial 2 screen SMPL CMPD CASH AMT CNVT COST DAYS simple interest compoun...

Page 342: ...n to display the following input screen for simple interest calculation n number of simple interest periods days I annual interest rate PV present value SI SFV calculates simple interest simple future value Example What would the interest amount and principal plus interest be for a loan of 1 500 borrowed for 90 days at an annual rate of 7 25 Use the 360 day mode and two decimal places In the set u...

Page 343: ...also press 6 GRPH to draw a cash flow graph 6 GRPH The left side is PV while the right side is SI and SFV The upper part of the graph is positive while the bottom part is negative V Window values vary in accordance with simple interest conditions Press J or 6 G T to return to the input screen Press J again to return to the Financial 1 screen Simple Interest Calculations 19 2 ...

Page 344: ...PMT PV FV u n log log 1 i 1 i S PMT PVi 1 i S PMT FVi i 1 i n 1 iu S 1 i n 1 1 i n 1 F i Formula I 1 iS n 1 i n 1 S 1 1 i n FV n 1 i n 1 i i PMT 1 iS 1 1 i n F i u u u u uFormula II I 0 PV PMT n FV 0 Here PV PMT u n FV FV PMT u n PV PV present value FV future value PMT payment n number of compound periods I annual interest rate i is calculated using Newton s Method S 0 assumed for beginning of ter...

Page 345: ... Y compounding periods per year When calculating n PV PMT FV The following calculation is performed after conversion from the nominal interest rate to the effective interest rate and the result is used for all subsequent calculations i I 100 When calculating I After I is obtained the following calculation is performed to convert to I I I 1 1 C Y P Y 100 C Y 100 P Y installment periods per year C Y...

Page 346: ...ed by various calculation conditions Because of this interest calculation results produced by this calculator should be used keeping the above limitation in mind or the results should be verified k k k k k Compound Interest Examples This section shows how compound interest calculations can be used in a variety of applications u u u u uSavings standard compound interest Input Condition Future value...

Page 347: ...xample Calculate the interest rate required to have a 2 500 balance in an installment savings account in two years when 100 is deposited each month and interest is compounded semiannu ally Perform the following key operation from the input screen c bcw Input n 2 12 c aw PV 0 baaw PMT 100 cfaaw FV 2 500 bcw Monthly installment cw Compounding every six months 2 I u u u u uLoans Input Condition Total...

Page 348: ...nt Formula Representation of Input Condition PV PMT FV do not equal zero PV FV n PMT when FV PV PV FV n PMT when FV PV Example Calculate the interest rate required to repay a 2 500 balance on a loan in two years 24 installments paying back 100 per month and a final 200 installment when interest is com pounded monthly Perform the following key operation from the input screen c bcw Input n 2 12 c cf...

Page 349: ... Example Calculate the principal required at 5 5 compounded monthly to produce a total of 20 000 in a year Perform the following key operation from the input screen b bcw Input n 1 12 f fw I 5 5 c aw PMT 0 caaaaw FV 20 000 bw bcw Monthly compounding 3 PV u u u u uCompound interest rate Example Calculate the interest required compounded monthly to produce a total of 10 000 in 10 years on an initial...

Page 350: ...ayment and then press J Perform the following key operation from the input screen c ew I 4 faaaw PV 5 000 aw PMT 0 baaaaw FV 10 000 bw bcw Monthly compounding 1 n u u u u uInstallment savings Example Calculate to two decimal places the principal plus interest for 250 monthly installments for five years at 6 annual interest compounded monthly Calculate amounts for when installments are made at the ...

Page 351: ... u u u uInstallment amount Example Calculate the amount required for each installment to accumulate a total of 10 000 in 5 years at an annual interest rate of 6 compounded semiannually In the set up screen specify End for Payment Norm1 for Display and then press J Perform the following key operation from the input screen f bcw Input n 5 12 gw I 6 0 aw PV 0 c baaaaw FV 10 000 bcw Monthly installmen...

Page 352: ...late a total of 10 000 in 10 years with 60 monthly installments In the set up screen specify End for Payment and then press J Perform the following key operation from the input screen ba bcw Input n 10 12 c aw PV 0 gaw PMT 60 baaaaw FV 10 000 bcw Monthly installments bw Annual compounding 2 I u u u u uPrincipal plus interest with initial deposit Example Calculate the principal plus interest after ...

Page 353: ...then press J Perform the following key operation from the input screen bf bcw Input n 15 12 h fw c efaw PMT 450 aw FV 0 bcw Monthly installments Monthly compounding 3 PV u u u u uLoan installments Example Calculate the size of the monthly installment for a 25 year 300 000 home loan made at 6 2 compounded semiannually In the set up screen specify End for Payment and then press J Perform the followi...

Page 354: ...0 aw FV 0 bcw Monthly installments Monthly compounding 1 n u u u u uEffective interest rate Example Calculate to two decimal places the effective interest rate compounded monthly on a 25 year 65 000 loan repaid with 460 monthly installments In the set up screen specify End for Payment Fix2 for Display and then press J Perform the following key operation from the input screen cf bcw Input n 25 12 c...

Page 355: ...resented by CF0 The cash flow one year later is shown by CF1 two years later by CF2 and so on Investment appraisal can be used to clearly determine whether an investment is realizing profits that were originally targeted uNPV NPV CF0 1 i CF1 1 i 2 CF2 1 i 3 CF3 1 i n CFn i 100 I n natural number up to 254 uNFV NFV NPV 1 i N uIRR 0 CF0 1 i CF1 1 i 2 CF2 1 i 3 CF3 1 i n CFn In this formula NPV 0 and...

Page 356: ...le below all revenues realized at the end of the fiscal year What is the net profit or loss of this investment if the useful service life of the machine is six years the resale value after six years is 14 000 and the capital cost is 11 Year Revenues 1 5 000 2 42 000 3 31 000 4 24 000 5 23 000 6 12 000 14 000 On the Main Menu select the LIST icon to enter the LIST Mode and perform the following key...

Page 357: ...to look up the following values 6 G T 4 NFV 1 REPT 3 PBP Example An investment of 10 000 in machinery projects the annual revenues shown in the table below all revenues realized at the end of the fiscal year What is the internal rate of return of this investment if the useful service life of the machinery is five years and the resale value after five years is 7 000 Year Revenues 1 2 000 2 2 400 3 ...

Page 358: ...wing key operation ee List 3 baaaaw caaaw ceaaw ccaaw caaaw biaa daaaw Return to the Main Menu by pressing m Select the TVM icon to enter the Financial Mode and then press 3 CASH Perform the following key operation from the input screen c 6 List 3 List 3 2 IRR Now you can press 6 to draw a cash flow graph 6 GRPH ...

Page 359: ...erest from installment PM1 to payment of installment PM2 INT a b one repayment PMT a INTPM1 I BALPM1 1 i I PMT sign b PRNPM1 PMT BALPM1 1 i c BALPM2 BALPM2 1 PRNPM2 d PRN PRNPM1 PRNPM1 1 PRNPM2 e INT INTPM1 INTPM1 1 INTPM2 PM2 PM1 PM2 PM1 BAL0 PV INT1 0 and PRN1 PMT at beginning of installment term u u u u uConverting between the nominal interest rate and effective interest rate The nominal intere...

Page 360: ...ent FV future value P Y installments per year C Y compoundings per year BAL balance of principal after installment PM2 INT PRN interest principal portion of installment PM1 INT PRN total principal total interest from installment PM1 to payment of installment PM2 Example Calculate the monthly installment due on a 140 000 15 year home mortgage at an annual rate of 6 5 compounded semiannually Also ca...

Page 361: ...rom the input screen bf bcw Input n 15 12 g fw beaaaaw PV 140 000 c aw FV 0 bcw Monthly installments cw Semiannual compounding 4 PMT Pressing 4 AMT displays the amortization input screen Input 24 for PM1 and 49 for PM2 cewejw Calculate PRN 3 PRN 1 REPT 2 INT 1 REPT 1 BAL ...

Page 362: ...t 24 to 49 1 REPT 4 INT Calculate PRN 1 REPT 5 PRN Now you can press 6 to draw a cash flow graph 6 GRPH Trace can be activated following the calculation Pressing e displays INT and PRN when n 1 Each subsequent press of e displays INT and PRN for n 2 n 3 and so on ...

Page 363: ...version k k k k k Converting the Annual Percentage Rate APR to the Effective Interest Rate EFF EFF n APR 100 1 1 100 n Example Calculate to two decimal places the effective interest rate for an account paying an interest rate of 12 compounded quarterly In the set up screen specify Fix2 for Display and then press J Perform the following key operation from the input screen ew n 4 bcw I 12 1 EFF The ...

Page 364: ...e of 12 55 compounded quarterly In the set up screen specify Norm1 for Display and then press J Perform the following key operation from the input screen ew n 4 bc ffw I 12 55 2 APR The obtained value is assigned to I P 6 19 6 Conversion between Percentage Interest Rate and Effective Interest Rate ...

Page 365: ...MAR SEL CST 1 100 Press 1 COST from the initial screen 2 to display the following input screen Cst cost Sel selling price Mrg margin COST SEL MRG calculates cost selling price margin k k k k k Cost Example Calculate the cost for a selling price of 2 000 and a margin of 15 Perform the following key operation from the input screen c caaaw Sel 2 000 bfw Mrg 15 1 COST ...

Page 366: ... following key operation from the input screen bcaaw Cst 1 200 c efw Mrg 45 2 SEL k k k k k Margin Example Calculate the margin for a selling price of 2 500 and a cost of 1 250 Perform the following key operation from the input screen bcfaw Cst 1 250 cfaaw Sel 2 500 3 MRG 19 7 Cost Selling Price Margin Calculations ...

Page 367: ...ulations Day date calculations are also performed in accordance with the current setting for number of days in the year but the following calculations cannot be performed when the 360 day year is set Attempting to do so causes an error Date Number of Days Date Number of Days The allowable calculation range is January 1 1901 to December 31 2099 The format for inputting a date is month day year Two ...

Page 368: ... following key operation from the input screen g abbjjhw d1 June 1 1997 c d2 Any date baaaw 2 d1 D d D future date calculation Example To determine the date that is 1 000 days before January 1 2001 usig a 365 day year Note that the attempting to perform the following calculation while the 360 day year is in effect causes an error Perform the following key operation from the input screen b abcaabw ...

Page 369: ...ferential and integration calculation results are displayed as mathematical expressions instead of decimal values 20 1 Before Using the Algebraic Mode 20 2 Inputting and Executing Calculations 20 3 ALGBR Mode Commands 20 4 Signum Function 20 5 Natural Display Notation 20 6 ALGBR Mode Error Messages 20 7 ALGBR Mode Precautions Chapter 20 ...

Page 370: ...n transformation using the addition theorem tColl product to sum transformation using the addition theorem comb combination PTS function for line passing through specific points CPLX complex function transformation appr convert to numeric value collc collection tanL tangent expression The following table shows the keys that can be used in the ALGBR Mode The M key performs its screen shot send func...

Page 371: ...the screen Inputting more data while there is data in the input area and solution area causes the previous data to be cleared from two areas automatically If you clear the display by pressing A you can recall the previous operation by pressing d or e Replay Function The Angle item of the set up screen can be set to either Deg or Rad for ALGBR Mode operations The Display item of the set up screen c...

Page 372: ...ession is X 1 variable This item indicates a variable input by you The actual variable you should input depends on the type of operation you are performing One example of a variable is A Anything enclosed within square brackets is optional which means you can skip it if you want Note the following expand expression The above example means that the final closed parenthesis to the right of expressio...

Page 373: ... theorems to transform an expression Syntax tExpand expression Example To transform sin A B using addition theorems 6 g 1 tExp s aA aBw cos B sin A sin B cos A u u u u uProduct to Sum Transformation tColl This command uses addition theorems to perform product to sum transformation Syntax tCollect expression Example To perform product to sum transformation on sin A cos B using addition theorems 6 g...

Page 374: ...rmed Example To integrate the expression X2 for variable X 4 vx vw A default value of 0 is automatically assumed for the integration constant Inputting a symbol name such as C for the integration constant produces a result in a form that is the same as the indefinite integral u u u u uDifferential diff This command can be used to determine the derivative or calculate the value of the derivative fo...

Page 375: ...s the tangent expression of another expression Syntax tanLine expression variable contact point contact point The contact point is specified using the variable name Example To calculate the tangent expression when X 2 for the expression X3 6 g 6 g 3 tanL vMd v cw 12X 16 u u u u uSolve solve This command calculate solutions for an expression Solutions are displayed as mathematical expressions Synta...

Page 376: ...mmand or the signum function into the approx command causes an error Example approx approx 2 Causes an error k k k k k Difference Between approx and Standard Calculations approx differs from standard calculations calculations that do not use natural display notation in the number of display digits and handling of variables With standard calculations calculation results are displayed without using ...

Page 377: ...shows the calculation when A 0 Example 6 g g g g g 6 g g g g g 1 appr f aA dw 3 u u u u uCollection collc This command arranges the terms of an expression focusing on a particular variable Syntax collect expression variable A default variable of X is used when specification of a variable is skipped Example To arrange the terms of the expression X2 AX BX focusing on the variable X 6 g 6 g 2 collc v...

Page 378: ...ame result can be obtained by inputting the following sequence List 1 N Syntax 2 sequence value value value value variable The values input with this syntax are handled as lists with the first value of the first list paired with the first value of the second list the second value with the second value and so on This syntax creates a function using this relationship Example To obtain an expression ...

Page 379: ...igonometric Transformation expTo This command transforms an exponential function whose exponent includes an imaginary number to a trigonometric function Syntax expToTrig expression Example To transform the following function to a trigonometric function eiX 6 g 5 CPLX 1 expTo e 3 i v w cos X i sin X u u u u uComplex Trigonometric to Exponential Transformation trgTo This command transforms a trigono...

Page 380: ... in the ALGBR Mode Syntax signum expression A solution can be obtained only when expression is a numeric value Definition 1 real number A 0 Undefined A 0 1 real number A 0 A signum A A imaginary number A Example To solve signum 3 1 K5 sign d bw 1 Example To solve signum 4 K5 sign ew 1 ...

Page 381: ...d for powers in place of standard mathematical notation Expressions in the ALGBR Mode are displayed using natural display notation which uses standard mathematical notation as shown below Absolute Values A Powers X4 5 Fractions __ 3 Square Roots 2 2 Roots 3 X Integration sin cos X dx dn Differentials ___ X3 dxn ...

Page 382: ...999 99999 uDomain ERROR Input value is outside the domain of the operation being performed Example 4 uNon Real ERROR Only real numbers have been input and the result is a complex number while the set up screen s Answer Type item is specified as Real Example 1 1 2 uNo Solution No solution can be obtained using the Solve Function Example solve X 2 1 X when Answer Type Real uMa ERROR Attempt to use a...

Page 383: ... of different formats that can be used to express a result Because of this even if the format of a result may displayed by the calculator does not match the format that you need for your purposes it does not necessarily mean that the result is wrong Regardless of whether intervals are continuous or discontinuous this calculator performs definite integral calculations by first obtaining an indefini...

Page 384: ...r of Bytes Used by a Program 21 5 Secret Function 21 6 Searching for a File 21 7 Searching for Data Inside a Program 21 8 Editing File Names and Program Contents 21 9 Deleting a Program 21 10 Useful Program Commands 21 11 Command Reference 21 12 Text Display 21 13 Using Calculator Functions in Programs Chapter 21 ...

Page 385: ...Mode When you do a program list appears on the display Selected memory area use f and c to move EXE EDIT program execute edit NEW new program P 382 DEL DEL A specific program all program delete P 376 SRC REN file name search change If there are not programs stored in memory when you enter the PRGM Mode the message No Programs appears on the display and only the NEW item 3 is shown in the function ...

Page 386: ...ter the file name and then input the actual program u u u u uTo register a file name Example To register the file name OCTA Note that a file name can be up to eight characters long 1 Display the program list menu and press 3 NEW to display a menu which contains the following items RUN BASE general calculation number base program input P 374 Q Q Q Q Q password registration SYBL symbol menu 2 Input ...

Page 387: ... registering a file name press J When you register the name of a program that contains binary octal decimal or hexadecimal calculations the indicator B is appended to the right of the file name u u u u uTo input a program The following items are included in the function menu of the program input screen which is used for program input P 379 TOP BTM top bottom of program P 378 SRC search MENU mode m...

Page 388: ...rea S c 9d value of A xw Volume V 9c d value of A Mdw You could also perform this calculation by assigning the value for the length of one side to variable A Length of One Side A value of A aaAw Surface Area S c 9d aAxw Volume V 9c d aAMdw If you simply input the manual calculations shown above however the calculator would execute them from beginning to end without stopping The following commands ...

Page 389: ... f and c to highlight the name of the program you want to run 2 Press 1 EXE or w to run the program Let s try running the program we input above Length of One Side A Surface Area S Volume V 7 cm 169 7409791 cm2 161 6917506 cm3 10 cm 346 4101615 cm2 471 4045208 cm3 15 cm 779 4228634 cm2 1590 990258 cm3 1 EXE or w hw Value of A Intermediate result produced by ww baw 21 2 Programming Examples ...

Page 390: ...inal result is on the display re executes the program P 392 You can also run a program while in the RUN Mode by inputting Prog file name w An error occurs if the program specified by Prog file name cannot be found Programming Examples 21 2 ...

Page 391: ...n below appears whenever something illegal occurs during program execution When such a message appears press d or e to display the location where the P 450 error was generated along with the cursor Check the Error Message Table for steps you should take to correct the situation P 374 Note that pressing d or e will not display the location of the error if the program is password protected u u u u u...

Page 392: ...mands and 2 byte commands Examples of 1 byte commands sin cos tan log A B C 1 2 etc Examples of 2 byte commands Lbl 1 Goto 2 etc While the cursor is located inside of a program each press of d or e causes the cursor to move one byte You can check how much memory has been used and how much remains at any time by selecting the SYS Mode and entering the memory status screen See Memory Status for deta...

Page 393: ... CASIO P 367 The password input procedure is identical to that used for file name input 3 Press w to register the file name and password Now you can input the contents of the program file Registration of a password uses 16 bytes of memory Pressing w without inputting a password registers the file name only without a password 4 After inputting the program press Q to exit the program file and return...

Page 394: ...375 2 Press 2 EDIT 3 Input the password and press w to recall the program The message Mismatch appears if you input the wrong password Secret Function 21 5 ...

Page 395: ...e search Example To use file name search to recall the program named OCTA 1 While the program list is on the display press 3 NEW and input the name of the file you want to find P 374 If the file you are looking for is password protected you should also input the password 3 NEW OCTA 2 Press w to recall the program If there is no program whose file name matches the one you input a new file is create...

Page 396: ...there is no program whose file name starts with the characters you input the message Not Found appears on the display If this happens press J to clear the error message 3 Use f and c to highlight the file name of the program you want to recall and then press 2 EDIT to recall it Searching for a File 21 6 ...

Page 397: ...o match inside the program for the data you specified the contents of the program appear with the cursor located at the point from which you started your search Once the contents of the program are on the screen you can use the cursor keys to move the cursor to another location before searching for the next instance of the data Only the part of the program starting from the current cursor location...

Page 398: ...llowing two operations to correct the situation Press e or d to clear the error and return to the file name input screen Press A to clear the new file name and input a new one u u u u uTo edit program contents 1 Find the file name of the program you want in the program list 2 Recall the program The procedures you use for editing program contents are identical to those P 20 used for editing manual ...

Page 399: ...a S 9d aAx6 g 5 Volume V 9c bc aAMd Compare this with the program for calculating the surface area and volume of a regular octahedron Length of One Side A W4 aaA6 g 5 Surface Area S c 9d aAx6 g 5 Volume V 9c d aAMd As you can see you can produce the TETRA program by making the following changes in the OCTA program Deleting c underlined using a wavy line above Changing d to b c underlined using a s...

Page 400: ...gram Length of One Side A Surface Area S Volume V 7 cm 84 87048957 cm2 40 42293766 cm3 10 cm 173 2050808 cm2 117 8511302 cm3 15 cm 389 7114317 cm2 397 7475644 cm3 1 EXE or w hw Value of A ww baw w Editing File Names and Program Contents 21 8 ...

Page 401: ...gram you want to delete 2 Press 4 DEL 3 Press 1 YES to delete the selected program or 6 NO to abort the operation without deleting anything u u u u uTo delete all programs 1 While the program list is on the display press 5 DEL A 2 Press 1 YES to delete all the programs in the list or 6 NO to abort the operation without deleting anything P 26 You can also delete all programs using the SYS Mode See ...

Page 402: ...on menu items If Then Else I End For To Step Next Whle WEnd Do Lp W If Then Else IfEnd For To Step Next While WhileEnd Do LpWhile command k k k k k CTL program control command menu Selecting CTL from the program menu displays the following function menu items Prog Rtrn Brk Stop Prog Return Break Stop command k k k k k JUMP jump command menu Selecting JUMP from the program menu displays the followi...

Page 403: ...Tabl Web an Cn a Cn an Pl a Pl DispR Tbl DrawWeb DrawR Con DrawR Con DrawR Plt DrawR Plt command k k k k k REL conditional jump relational operator commands Selecting REL from the program menu displays the following function menu items G G G G G G relational operators k k k k k I O input output commands Selecting I O from the program menu displays the following function menu items Lcte Gtky Send R...

Page 404: ...398 DrawR Con DrawR Plt 398 DrawStat 398 DrawWeb 398 Dsz 394 For To Next 389 For To Step Next 390 Getkey 399 Goto Lbl 394 If Then 387 If Then Else 388 If Then Else IfEnd 389 If Then IfEnd 388 Isz 395 Locate 399 Prog 392 Receive 400 Return 393 Send 401 Stop 393 While WhileEnd 391 Input Command 386 Output Command 386 Multi statement Command 387 _ Carriage Return 387 Jump Code 395 G G G G G Relationa...

Page 405: ...uch as AB k k k k k Basic Operation Commands Input Command Function Prompts for input of values for assignment to variables during program execution Syntax variable name Example A _ Description 1 This command momentarily interrupts program execution and prompts for input of a value or expression for assignment to a variable When the input com mand is executed to appears on the display and the calc...

Page 406: ...Description 1 Operation of the carriage return is identical to that of the multi statement command 2 Using a carriage return in place of the multi statement command makes the displayed program easier to read k k k k k Program Commands COM If Then Function The Then statement is executed only when the If condition is true non zero Syntax Parameters condition numeric expression Description 1 The Then...

Page 407: ... whether the If condition is true non zero or false 0 Example If A 0 _ Then A 0 _ IfEnd _ END If Then Else Function The Then statement is executed only when the If condition is true non zero The Else statement is executed when the If condition is false 0 Syntax Parameters condition numeric expression Description 1 The Then statement is executed when the If conditions is true non zero 2 The Else st...

Page 408: ...cuted regardless of whether the If condition is true non zero or false 0 Example A _ If A 0 _ Then TRUE _ Else FALSE _ IfEnd_ END For To Next Function This command repeats everything between the For statement and the Next statement The starting value is assigned to the control variable with the first execution and the value of the control variable is incremented by one with each execution Executio...

Page 409: ...For 1 A To 10_ A 3 B_ B Next For To Step Next Function This command repeats everything between the For statement and the Next statement The starting value is assigned to the control variable with the first execution and the value of the control variable is changed according to the step value with each execution Execution continues until the value of the control variable exceeds the ending value Sy...

Page 410: ... commands contained in the loop as long as its condition is true non zero When the condition becomes false 0 execution proceeds from the statement following the LpWhile statement 2 Since the condition comes after the LpWhile statement the condition is tested checked after all of the commands inside the loop are executed Example Do_ A_ A 2 B_ B LpWhile B 10 While WhileEnd Function This command repe...

Page 411: ...ement Do statement and While statement Example While A 0_ If A 2_ Then Break_ IfEnd_ WhileEnd_ A Executed after Break Prog Function This command specifies execution of another program as a subroutine In the RUN Mode this command executes a new program Syntax Prog file name _ Example Prog ABC _ Description 1 Even when this command is located inside of a loop its execution immediately breaks the loo...

Page 412: ... specified by the Prog command does not exist an error occurs 7 In the RUN Mode inputting the Prog command and pressing w launches the program specified by the command Return Function This command returns from a subroutine Syntax Return _ Description Execution of the Return command inside a main routine causes execution of the program to stop Example Prog A Prog B 1 A_ For A B To 10_ Prog B _ B 1 ...

Page 413: ...ement If the current value is zero execution jumps to the statement following the multi statement command display command or carriage return _ Example 10 A 0 C Lbl 1 B B C C Dsz A Goto 1 C 10 This program prompts for input of 10 values and then calculates the average of the input values Goto Lbl Function This command performs an unconditional jump to a specified location Syntax Goto value or varia...

Page 414: ...le by 1 and then jumps if the current value of the variable is zero Syntax Parameters Variable Name A to Z r Example Isz A Increments the value assigned to variable A by 1 Description This command increments the value of a control variable by 1 and then tests checks it If the current value is non zero execution continues with the next statement If the current value is zero execution jumps to the s...

Page 415: ...age return _ Example Lbl 1 A A 0 A Goto 1 With this program inputting a value of zero or greater calculates and displays the square root of the input value Inputting a value less than zero returns to the input prompt without calculating anything k k k k k Clear Commands CLR ClrGraph Function This command clears the graph screen Syntax ClrGraph_ Description This command clears the graph screen duri...

Page 416: ...ation Syntax DrawDyna_ Description This command performs a Dynamic Graph draw operation during program execution in accordance with the drawing conditions defined within the program DrawFTG Con DrawFTG Plt Function These commands graph functions Syntax DrawFTG Con_ DrawFTG Plt_ Description 1 These commands graph functions in accordance with conditions defined within the program 2 DrawFTG Con produ...

Page 417: ...vertical axis and n as the horizontal axis Syntax DrawR Con_ DrawR Plt_ Description 1 These commands graph recursion expressions with an bn as the vertical axis and n as the horizontal axis in accordance with conditions defined within the program 2 DrawR Con produces a connect type graph while DrawR Plt produces a plot type graph DrawStat Function This draws a statistical graph Syntax DrawStat_ De...

Page 418: ...ed Syntax Getkey_ Description 1 This command returns the code that corresponds to the last key pressed 79 69 59 49 39 29 78 68 58 48 28 38 27 37 77 67 57 47 76 66 56 46 36 26 75 65 55 45 35 25 74 64 54 44 73 63 53 43 33 72 62 52 42 32 71 61 51 41 31 2 A value of zero is returned if no key was pressed previous to executing this command 3 This command can be used inside of a loop Locate Function Thi...

Page 419: ... by a value from 1 to 7 which the column is designed by a value from 1 to 21 1 1 21 1 1 7 21 7 Example Cls_ Locate 7 1 CASIO CFX This program displays the text CASIO CFX in the center of the screen In some cases the ClrText command should be executed before running the above program Receive Function This command receives data from an external device Syntax Receive data Description 1 This command r...

Page 420: ... side right side variable A to Z r numeric constant variable expression such as A 2 relational operator G G G G G Description 1 The following six relational operators can be used in the conditional jump command left side right side true when left side equals right side left side G G G G G right side true when left side does not equal right side left side right side true when left side is greater t...

Page 421: ...ution which means you can add labels to input prompts and results Program Display X X X X If the text is followed by a calculation formula be sure to insert a display command between the text and calculation Inputting more than 21 characters causes the text to move down to the next line The screen scrolls automatically if the text causes the screen to become full ...

Page 422: ...of two rows Swap Example 1 To swap the values of Row 2 and Row 3 in the following matrix 1 2 Matrix A 3 4 5 6 The following is the syntax to use for this program Swap A 2 3 Matrix name Executing this program produces the following result MAT Mode u u u u uTo calculate a scalar product Row Example 2 To calculate the scalar product of Row 2 of the matrix in Example 1 multiplying by 4 The following i...

Page 423: ... following is the syntax to use for this program Row A 2 3 Matrix name Executing this program produces the following result MAT Mode k k k k k Using Graph Functions in a Program P 112 You can incorporate graph functions into a program to draw complex graphs and to overlay graphs on top of each other The following shows various types of syntax you need to use when programming with graph functions V...

Page 424: ...82 Using Dynamic Graph functions in a program makes it possible to perform repeat Dynamic Graph operations The following shows how to specify the Dynamic Graph range inside a program Dynamic Graph range 1 D Start_ 5 D End_ 1 D pitch_ Example Program ClrGraph_ View Window 5 5 1 5 5 1_ Y Type_ AX 1 Y1_ 1 J41JJ 1 2 D SelOn 1_ 2 451 3 D Var A_ 3 3 1 4 D Start_ 4 J51 5 5 D End_ 5 2 1 6 D pitch_ 6 3 7 D...

Page 425: ...e range setting 1 F Start_ 5 F End_ 1 F pitch_ Numeric table generation DispF Tbl_ Graph draw operation Connect type DrawFTG Con_ Plot type DrawFTG Plt_ Example Program ClrGraph_ ClrText_ View Window 0 6 1 2 106 2_ Y Type_ 3X2 2 Y1_ 1 T SelOn 1_ 1 4611 0 2 F Start_ 2 J611 6 3 F End_ 3 2 1 4 F pitch_ 4 3 5 DispF Tbl 5 W6241 6 DrawFTG Con 6 W6242 Executing this program produces the results shown her...

Page 426: ...ut an 1 Type_ Specifies recursion type 3an 2 an 1_ 4bn 6 bn 1_ Table range setting 1 R Start_ 5 R End_ 1 a0_ 2 b0_ 1 an Start_ 3 bn Start_ Numeric table generation DispR Tbl_ Graph draw operation Connect type DrawR Con_ DrawR Con_ Plot type DrawR Plt_ DrawR Plt_ Statistical convergence divergence graph WEB graph DrawWeb an 1 10_ Example Program ClrGraph_ View Window 0 1 1 0 1 1_ 1 an 1 Type_ 1 462...

Page 427: ...ncorporate a solve calculation function into a program The following is the syntax for using the Solve function in a program Solve f x n a b Upper limit Lower limit Initial estimated value Example Program 1 Solve 2X2 7X 9 1 0 1 1 K41 In the function f x only X can be used as a variable in expressions Other variables A through Z r are treated as constants and the value currently assigned to that va...

Page 428: ...ends on the graph type See Changing Graph Parameters The following is a typical graph condition specification for a scatter diagram or xyLine graph S Gph1 DrawOn Scatter List1 List2 1 Square Blue _ In the case of an xy line graph replace Scatter in the above specification with xyLine The following is a typical graph condition specification for a normal probability plot S Gph1 DrawOn NPPlot List1 S...

Page 429: ... Med Med Med Quadratic Regression Quad Cubic Regression Cubic Quartic Regression Quart Logarithmic Regression Log Exponential Regression Exp Power Regression Power The following is a typical graph condition specification for a sine regression graph S Gph1 DrawOn Sinusoidal List1 List2 Blue _ 1 Z6631 2 K11 3 1JJ 4 4121J 5 11J 6 24J 7 J41 8 J51 9 W621 Example Program ClrGraph_ 1 S Wind Auto_ 2 1 2 3...

Page 430: ... Regression statistical calculation 1 LinearReg List 1 List 2 List 3 Calculation Frequency data Frequency type y axis data YList x axis data XList 1 41661 Any one of the following can be specified as the calculation type LinearReg linear regression Med MedLine Med Med calculation QuadReg quadratic regression CubicReg cubic regression QuartReg quartic regression LogReg logarithmic regression ExpReg...

Page 431: ...the separately available CASIO FA 122 Interface Unit This chapter also contains information on how to use the optional SB 62 cable to connect to a CASIO Label Printer to transfer screen data for printing 22 1 Connecting Two Units 22 2 Connecting the Unit with a Personal Computer 22 3 Connecting the Unit with a CASIO Label Printer 22 4 Before Performing a Data Communication Operation 22 5 Performin...

Page 432: ...u u uTo connect two units 1 Check to make sure that the power of both units is off 2 Remove the covers from the connectors of the two units Be sure you keep the connector covers in a safe place so you can replace them after you finish your data communications 3 Connect the two units using the SB 62 cable SB 62 cable Keep the connectors covered when you are not using them ...

Page 433: ... u uTo connect the unit with a personal computer 1 Check to make sure that the power of the unit and the personal computer is off 2 Connect the personal computer to the FA 122 Interface Unit 3 Remove the cover from the connector of the unit Be sure you keep the connector cover in a safe place so you can replace it after you finish your data communications 4 Connect the unit to the FA 122 Interface...

Page 434: ...7 u u u u uTo connect the unit with a Label Printer 1 Check to make sure that the power of the unit and the Label Printer is off 2 Connect the optional SB 62 cable to the Label Printer 3 Remove the cover from the connector of the unit Be sure you keep the connector cover in a safe place so you can replace it after you finish your data communications 4 Connect the other end of the SB 62 cable to th...

Page 435: ...graphic image send features Off Graphic images not sent Monochrome Pressing M sends graphic images in monochrome Color Pressing M sends graphic images in color Do not select Color for Image Set to send data to a Label Printer TRAN RECV menu of send settings receive settings IMGE menu of graphic image transfer settings Communications parameters are fixed at the following settings Speed BPS 9600 bit...

Page 436: ...eive starts as soon as data is sent from the sending unit Sending unit To set up the calculator to send data press 1 TRAN while the data communi cation main menu is displayed Press the function key that corresponds to the type of data you want to send SEL selects data items and sends them CRNT selects data items from among previously selected data items and sends them BACK all memory contents incl...

Page 437: ...eck 2 Program Program contents Yes Yes Mat n Matrix memory A to Z contents Yes List n List memory 1 to 6 contents Yes File n List file memory 1 to 6 contents Yes Y Data Graph expressions graph write non write status View Window No contents zoom factors G Mem n Graph memory 1 to 6 contents Yes V Win n View Window memory contents No Picture n Picture graph memory 1 to 6 data No DynaMem Dynamic Graph...

Page 438: ...put of the password Name of password protected file Password input field 1 2 3 4 5 SYBL symbol input After inputting the password press w u u u u uTo execute a send operation After selecting the data items to send press 6 TRAN A message appears to confirm that you want to execute the send operation YES sends data NO returns to data selection screen Press 1 YES to send the data You can interrupt a ...

Page 439: ... and the back up send menu shown below appears Press 6 TRAN to start the send operation The following shows what the displays of the sending and receiving units look like after the data communication operation is complete Sending Unit Receiving Unit Press A to return to the data communication main menu Data can become corrupted necessitating a RESET of the receiving unit should the connecting cabl...

Page 440: ...data to be sent to any CASIO Label Printer equipped with data communications capabilities Selecting Color allows data to be sent to Color Label Printer models only You cannot send the following types of screens to a computer The screen that appears while a data communication operation is in progress A screen that appears while a calculation is in progress The screen that appears following the rese...

Page 441: ...cable becomes disconnected if the parameters of the two units do not match or if any other communications problem occurs When this happens pressA to clear the error and correct the problem before trying data communications again If data communications are interrupted by A key operation or an error any data successfully received up the interruption will be in the memory of the receiving unit An err...

Page 442: ...ttempting to perform any programming This Program Library is divided into two sections a numeric calculation section and a graphics section Programs in the numeric calculation section produce results only while graphics programs use the entire display area for graphing Also note that calculations within graphics programs do not use the multiplication sign wherever it can be dropped i e in front of...

Page 443: ...program Overview m is divided by 2 and by all successive odd numbers d 3 5 7 9 11 13 to check for divisibility Where d is a prime factor mi mi 1 d is assumed and division is repeated until mi 1 d Example 1 119 7 17 2 440730 2 3 3 5 59 83 3 262701 3 3 17 17 101 Preparation and operation Store the program written on the next page Execute the program as shown below Step Key operation Display Step Key...

Page 444: ...l Lbl Lbl Lbl Lbl R 0 1 2 3 4 6 5 6 7 8 9 M 2 Frac B B A B A F M A I E A A A C 2 B A N C 1 D T 2 2 Goto B B B A Goto A A Goto A C 8 Goto 0 Frac 4 0 2 A 0 Goto Goto A 3 1 1 Goto B 7 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z mi d mi 1 Goto 3 9 Goto B 0 5 No 1 Line Program File name Memory Contents ...

Page 445: ...values are taken as 1010 Overview n0 max a b n1 min a b nk 2 nk nk 2 nk 1 nk 1 k 2 3 If nk 0 then the greatest common measure c will be nk 1 Example 1 2 3 When a 238 a 23345 a 522952 b 374 b 9135 b 3208137866 c 34 c 1015 c 998 Preparation and operation Store the program written on the next page Execute the program as shown below Step Key operation Display Step Key operation Display No 2 ...

Page 446: ...21 22 23 24 25 26 27 C Lbl Abs B A Lbl C B Lbl M 1 A 2 3 N A C 0 A A B F A Goto B Goto C A Abs 2 lnt 3 Goto C B A B 1 T A B 2 A B C Goto B B B A A B C D E F G H I J K L M N O P Q R S T U V W X Y Z a n0 b n1 nk B C No 2 Line Program File name Memory Contents ...

Page 447: ...ata 55 54 51 55 53 53 54 52 is 53 Perform a t test with a level of significance of 5 Preparation and operation Store the program written on the next page Execute the program as shown below No 3 Step Key operation Display Step Key operation Display The above operation produces a t test value of t 53 0 7533708035 According to the t distribution table in the next page a level of significance of 5 and...

Page 448: ... 014 2 009 2 000 1 990 1 980 1 970 1 960 63 657 9 925 5 841 4 604 4 032 3 707 3 499 3 355 3 250 3 169 2 947 2 845 2 787 2 750 2 724 2 704 2 690 2 678 2 660 2 639 2 617 2 596 2 576 0 05 0 01 1 2 3 4 5 6 7 T 5 l Var Lbl Goto 5 4 List 0 x T 0 T 5 1 E 5 M S 5 2 1 M T 4 _ T 5 List x n 1 _ _ 1 1 M 5 n 5 5 T 3 _ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z m t 5 3 P Probability Degree of Freedom N...

Page 449: ...t the points of tangency and factor zoom is used to enlarge the graph Example To determine m and b for the following values r 1 x 3 y 2 Notes The point plotted for A cannot be moved Even if it is moved on the graph the calculation is performed using the original value An error occurs when r x Be sure to always perform a trace operation whenever you select trace and the message TRACE is on the disp...

Page 450: ...2 6 M M B 0 T E O 2 N M B 5 T E O 1 T Factor N W x2 C X P _ _ R S S 0 _ A _ R S S 0 _ R N G I I B A X A 0 B X A 0 A E N Y R Y x2 A C 1 Z Goto C 1 Z Goto C N N D x2 R C A B A M B E _ 2 A N B E _ 3 E T O _ L _ _ B B 1 P 1 W R E _ x2 M _ Goto N _ Goto _ _ R x2 _ 1 _ R _ 1 _ F x2 R B A Z Goto 0 B A Z Goto 5 x2 A x2 P _ x 1 _ _ x2 Factor A F x2 _ x 1 M _ N _ No 4 Line Program File name ...

Page 451: ...h Y Goto Lbl Graph Y Prog Lbl W 1 C Graph Y Graph Y N 3 9 M Goto 3 E I I C 2 _ _ W 6 _ N N 6 1 R I X X I _ D D C R R Graph Y N O 3 L x2 R C M A A D W E x2 L O 6 X E X W x2 X A _ B B 3 x2 S Prog 1 1 B C _ I 3 Goto R 9 C 1 _ L E 3 No 4 Line Program File name File name ...

Page 452: ...435 1 2 3 4 5 Program for Circle and Tangents No 4 Step Key Operation Display ...

Page 453: ...436 Program for Circle and Tangents No 4 Step Key Operation Display 6 7 8 9 10 ...

Page 454: ...437 11 12 13 14 15 Program for Circle and Tangents No 4 Step Key Operation Display ...

Page 455: ...438 16 17 18 Program for Circle and Tangents No 4 Step Key Operation Display ...

Page 456: ... cursor keys to move the pointer around the display To interrupt program execution press A while the graphic screen is on the display The triangle cannot be drawn if the result of the coordinate transformation operation exceeds View Window parameters Preparation and operation Store the program written on the next page Execute the program as shown below A B C D E F G x1 y1 x2 y2 x3 y3 x 1 y 1 x 2 y...

Page 457: ...ot Plot Cls O 4 1 Y A 2 Y C 3 Y E 1 A cos sin G cos sin I cos sin K G T 0 X 1 A X 2 C X 3 E _ Plot N Q Q Q Q Q Q Plot A 1 1 B 2 D 3 F A G H J L H C T 4 Y Y Y L B B _ D D F F E Deg Y Y Y B E sin cos sin cos Line sin cos Line Line D 1 _ 1 A B 2 C D 3 E F Q Q Q Q _ Q Q _ 2 _ B _ _ D _ _ F _ Line Deg Plot 2 Plot _ _ _ _ _ _ _ _ _ _ _ _ G H I J K L E C 1 Q D _ 0 Line F View Window Goto 1 8 5 ...

Page 458: ...441 1 2 3 4 5 Program for Rotating a Figure No 5 Step Key Operation Display ...

Page 459: ...442 6 7 8 9 10 Program for Rotating a Figure No 5 Step Key Operation Display Locate the pointer at X 5 Continue repeating from step 8 ...

Page 460: ...Appendix Appendix A Resetting the Calculator Appendix B Power Supply Appendix C Error Message Table Appendix D Input Ranges Appendix E Specifications ...

Page 461: ... sure to write it down somewhere before performing the RESET operation u u u u uTo reset the calculator F 1 Highlight the SYS icon on the main menu and then press w or press t 2 Use c to move the highlighting down to Reset and then press w 1 2 3 4 5 6 3 Press 1 YES to reset the calculator or 6 NO to abort the operation without resetting anything 4 Press m P 11 If the display appears to dark or dim...

Page 462: ... the P button on the back of the calculator This should make the RESET screen appear on the display Perform the procedure to complete the RESET operation Pressing the P button while an internal calculation is being performed will cause all data in memory to be deleted Resetting the Calculator Appendix A P P ...

Page 463: ...l memory contents will be erased If you do remove both batteries correctly reload them and then perform the reset operation k k k k k Replacing Batteries Precautions Incorrectly using batteries can cause them to burst or leak possibly damaging the interior of the unit Note the following precautions Be sure that the positive and negative poles of each battery are facing in the proper directions Nev...

Page 464: ...operation to resume normal operation Be sure to replace all four batteries with new ones 1 Press O to turn the calculator off Warning Be sure to turn the unit off before replacing batteries Replacing batteries with power on will cause data in memory to be deleted 2 Making sure that you do not accidently press the o key slide the case onto the calculator and then turn the calculator over 3 Slide th...

Page 465: ...wer supply battery Never remove the main power supply and the memory back up batteries from the unit at the same time Be sure to replace the back up power supply battery at least once 2 years regardless of how much you use the unit during that time Failure to do so can cause data in memory to be deleted 1 Press O to turn the calculator off Warning Be sure to turn the unit off before replacing batt...

Page 466: ...nstall the memory protection battery cover onto the calculator and secure it in place with the screw Next replace the back cover 8 Turn the calculator front side up and slide off its case Next press o to turn on power k k k k k About the Auto Power Off Function The calculator turns power off automatically if you do not perform any key operation for about 6 minutes To restore power press o ...

Page 467: ...and correct it 2 Use d or e to display the point where the error was generated and then correct the program 1234 Check the input numeric value and correct it When using memories check that the numeric values stored in memories are correct 5 Try using a smaller value for Ax x increment decrement 6 Try changing the tolerance tol when using Gauss Kronrod Rule or the number of divisions n when using S...

Page 468: ...during program data communications Problem with cable connection or parameter setting during data communications Problem with cable connection or parameter setting during data communications Memory of receiving unit became full during program data communications Message Stk ERROR Mem ERROR Arg ERROR Dim ERROR Com ERROR Transmit ERROR Receive ERROR Memory Full Countermeasure Simplify the formulas t...

Page 469: ... the result is a complex number while the set up screen s Answer Type item is specified as Real No solution can be obtained in the ALGBR Mode using the Solve function Countermeasure Change the input expression Change the input expression Change the input expression 1 Change the setting of Answer Type to Cplx 2 Change the input expression 1 Change the setting of Answer Type to Cplx 2 Change the inp...

Page 470: ...100 2n 1 GRA For sinh and tanh when x 0 errors are cumulative and accu racy is affected at a certain point Input ranges DEG x 9 109 RAD x 5 107 rad GRA x 1 1010 grad x 1 x 1 10100 x 230 2585092 x 1 10100 x 5 1099 1 x 5 1099 x 1 1 10 99 x 1 10100 1 10100 x 100 1 10100 x 230 2585092 0 x 1 10100 x 1 1050 x 1 10100 x G G G G G 0 x 1 10100 0 x 69 x is an integer Result 1 10100 n r n and r are integers ...

Page 471: ...00 ylogx 100 x 0 y 0 x 0 1 y n n is an integer 2n 1 or a fraction However 1 1 10100 log x 100 y y 0 x G G G G G 0 1 1 10100 logy 100 x y 0 x 0 1 y 0 x 2n 1 n n G G G G G 0 n is an integer or a fraction However 1 1 10100 log y 100 x Total of integer numerator and denominator must be within 10 digits includes division marks x 1 1050 y 1 1050 n 1 10100 x n y n x y a b c d e r n G G G G G 0 x n 1 y n ...

Page 472: ...83647 BIN 1000000000000000 x 1111111111111111 negative 0 x 0111111111111111 0 positive OCT 20000000000 x 37777777777 negative 0 x 17777777777 0 positive HEX 80000000 x FFFFFFFF negative 0 x 7FFFFFFF 0 positive Errors may be cumulative with internal continuous calculations such as xy x y x 3 x some times affecting accuracy Input Ranges Appendix D ...

Page 473: ...ely 2 years power off R03 UM 4 Approximately 140 hours continuous display of main menu Approximately 2 years power off The ALGBR Mode requires more electrical power than other modes so extensive use of the ALGBR Mode shortens battery life Back up Approximately 2 years Auto power off Power is automatically turned off approximately six minutes after last operation except when drawing dynamic graphs ...

Page 474: ...ory data list data variable data Table Graph data graph functions equation calculation coefficients Method Start stop asynchronous half duplex Transmission speed BPS 9600 bits second Parity none Bit length 8 bits Stop bit Send 3 bits Receive 2 bits X ON X OFF Control None Specifications Appendix E ...

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