Sharp EL-531LH, Mastering Instructions

Page 1: ...S H A R P E L 5 3 1 L H UNIVERSITY OF SOUTHERN QUEENSLAND The Learning Centre Learning and Teaching Support Unit ...

Page 2: ...tiplication and division 7 3 Brackets 9 4 Powers 10 5 Fractions 16 6 Using the x 1 key 18 7 Scientific notation 19 8 Factorial n 21 9 Using memory 22 10 Statistics 24 11 Trigonometric functions 31 12 Exponential and logarithmic functions 33 13 Degrees minutes seconds 35 Review calculator exercises 37 ...

Page 3: ...Calculator solutions 38 Your Notes 40 ...

Page 4: ...sing the Casio fx 82MS Using the Casio fx 82TL Using the Sharp EL 531LH Using the Sharp EL 556L Using the Sharp EL 531RH The instructions in this booklet only explain some of the keys available on your calculator necessary for basic work in data manipulation If you require more assistance please contact The Learning Centre If you would like information about other support services available from T...

Page 5: ...o clear all values press To clear memory press If your calculator has FIX or SCI or ENG on the display press until the letters disappear If your calculator has RAD or GRAD on the display press until the letter DEG appears If all else fails press the RESET button on the back of your calculator e g after replacing batteries to clear all memory content when an abnormal condition occurs and all keys a...

Page 6: ...t is shown on the photograph of the calculator here Example To add 7 and 3 type The display should read 10 Example I want to find the total amount I earned in the past four weeks If I earned 471 575 471 and 528 the key strokes would be The display should read 2045 addition key cancel last number key Backspace key ...

Page 7: ...I typed I can cancel 6 by typing and then typing The display should read 1 046 Each time is used the last digit is cancelled Try practising cancelling with the key until you are comfortable with its use 1 3 The key is used when you want to delete a whole number Example If you typed 471 566 but you wanted 471 576 press the key Note the 566 disappears Press the key again the sign becomes static Now ...

Page 8: ...471 568 but you wanted 576 Press the until the number 8 begins to flash press to undo Press and 8 disappears Now type in 7 and press until the sign stops flashing 1 5 To subtract numbers Find the key it is shown on the photograph of the calculator following Example To subtract 35 from 257 type The display should read 222 plus minus key subtraction key ...

Page 9: ...keystrokes are The display should read 305 Sometimes you may have a sum like this 7 4 You can use the key The key strokes are The display should read 3 You could also use the keystrokes In this case the calculator recognises the as a negative not recommended to do it this way ...

Page 10: ...cation and division 2 1 To multiply numbers Find the key it is shown on the photograph of your calculator here Example To multiply 7 and 3 type The display should read 21 To find 753 492 type The display should read 370 476 key for division key for multiplication ...

Page 11: ...alculator Example To divide 35 by 7 type The display should read 5 To divide 7 905 by 85 type The display should read 93 To divide 60 by 5 and then by 4 type The display should read 3 2 3 Combining multiplication and division Example If the question is then it is really 27 7 4 Try it The display should read 0 964285714 27 7 4 ...

Page 12: ...rackets Example Do the calculation 471 93 11 2 on the calculator The keystrokes required are The display should read 365 Sometimes in calculations you will see other grouping symbols for example called braces called square brackets Try these examples Exercise 1 a 25 7 2 4 b 18 3 7 a multiplication sign is understood 18 3 7 LH bracket key RH bracket key ...

Page 13: ...sets of brackets d Answers 30 180 104 1 4 Powers 4 1 Squaring and higher powers 62 means 6 6 You can use the square key to do this calculation It is shown on the photograph of your calculator here Press the display should read 36 Or you can use the power key on your calculator Find the yx key on your calculator 5 3 2 power key square key square root key ...

Page 14: ...rnt your multiplication tables you will already know the squares of the whole numbers from 1 to 12 and thus be able to complete much of the following table __________________________________________________________________________ Exercise 2 Use your calculator to find the squares of the whole numbers from 13 to 25 and any other squares you are unsure of ___________________________________________...

Page 15: ...939 __________________________________________________________________________ 4 2 Square root Finding the square root of a number undoes or neutralises the squaring of the number and vice versa The symbol for square root is This is called the radical sign The square root of 36 is written as Now because 62 36 Find the square root key on your calculator and type The display will read 6 What do you ...

Page 16: ...he square root neutralises squaring Try this on your calculator Find the square root of 3 squared that is The key strokes required are The display should read 3 Because squaring and taking square roots are inverse operations the order of the operatons can be reversed and the number is unaffected So the square of the square root of 3 should also equal 3 Try it on your calculator The key strokes req...

Page 17: ...ise 5 Complete the following without using the calculator a b c d 10 e 625 f 144 g because 82 h because 121 i because Check your answers on the calculator __________________________________________________________________________ 7 2 7 2 10 2 2 2 2 64 121 225 ...

Page 18: ...LH 15 4 3 Other roots You can also use the root key on the calculator Find the on your calculator To get to this key you must press first Look at the examples below Examples a 9 and the display should read 3 or and the display should read 3 root key ...

Page 19: ... it with the SHIFT key See the key The x stands for the root you want to take so it is typed first From the examples above you may have seen that is called a fractional index 5 Fractions How do you add and Normally you would have to find a common denominator of 252 So Or you can use your calculator to add fractions Find the key 8 1 3 x 8 1 3 8 3 1 3 1 12 4 63 1 12 4 63 21 252 16 252 37 252 a b c ...

Page 20: ...and the represents the fraction part of a mixed number When the number you are typing is a proper or improper fraction the a is zero and there is no need to type a value for it The key storkes required for the calculation are and the display will show 37 252 which is read as fraction key a b c b c 1 12 4 63 37 252 ...

Page 21: ...trokes are and the display will show 8 71 72 which is read as Note if you now press the display will read 647 72 So this key turns a mixed fraction into an improper fraction If you press the key a second time the decimal equivalent is displayed i e 8 9861111 6 Using the x 1 key 8 1 9 63 72 8 71 72 ...

Page 22: ...g The answer should be 0 571428571 This would be the same as if you just typed 4 7 Take another example Type The answer should be 0 051948051 7 Scientific notation Sometimes you may have numbers expressed in scientific notation i e 7 24 103 instead of 7240 When a number is multiplied by 103 you move the decimal point three places to the right You can do this on the calculator by using the key 4 7 ...

Page 23: ...multiply two numbers e g 8 34 10 2 4 28 105 Press and the display will read 35695 2 If you want this answer in scientific notation press both and until sci appears on top of the screen and your display should read 3 56952 1004 If you wish to fix the number of digits displayed press 3 which rounds the number to 3 decimal places Practise using the key on your calculator ...

Page 24: ...he Binomial Distribution This is called the factorial key Use it to find the 3 and 5 Press 3 means 3 2 1 3 6 and 5 5 4 3 2 1 5 120 How many ways would you guess that we could arrange ten people That is how large would you estimate 10 to be Use your calculator to find 10 You should get 3 628 800 10 10 9 8 3 2 1 Thank goodness this can be done on the calculator Use to activate n ...

Page 25: ...g memory To calculate the following it may be useful to use the memory key for each term Example The number of ways of arranging n items in order is known as factorial n which is symbolised as n where n n n 1 n 2 3 2 1 9 16 2 16 23 16 2 16 17 16 2 16 these keys are for memory ...

Page 26: ... above press the following keys this puts the first term 3 0625 into the memory then press this adds the second term 3 0625 into memory then press this adds the third term 0 0625 to memory To find the answer press The answer should be 6 1875 Note For the Sharp EL 531GH just pressing gives you the answer to the above calculation To clear memory press and M will disappear To store a number in memory...

Page 27: ...17438 There are other memory keys in your calculator the X Y keys accessed by using STO and RCL try them yourselves Example and or and 10 Statistics 10 1 Mean and standard deviation single data The formula for the mean is The formulas for the sample standard deviation are Theoretical formula Working formula 18 17 17 17 12 17 x Σx n s Σ xi x 2 n 1 s Σxi 2 Σxi 2 n n 1 ...

Page 28: ...σ and s varies with different calculators On the Sharp EL 531LH σ is denoted by σx and s is denoted by sx The positions of these green keys is shown on the diagram below To find the mean and standard deviation firstly you must access the statistics mode of the calculator by using the keys followed by STAT 0 will appear on the right of the screen Note that once you are in the statistics mode the ke...

Page 29: ...inputted The screen should show n 5 Or press The display should read n 5 Step 3 To display the mean press and the display should read 3 Step 4 Display the standard deviation assume the data set is a sample press and the display should read 5 7008771 __________________________________________________________________________ Example Use your calculator to find the mean standard deviation and varianc...

Page 30: ...read 3 This is the mean and the display will read 13 87443693 This is the sample standard deviation s and the display will read 192 5 This is the variance s2 The mean is 3 the standard deviation is 13 87 and the variance is 192 5 The button accesses a number of extra statistical functions Σx2 Σx In the example below the progressive calculations are shown simply to give you some understanding of th...

Page 31: ... 495 Σx 60 2 61 14 62 8 63 64 5 1 853 s Thus s 1 2 kg and s2 1 4 kg2 Note In calculations like the above you should carry as many decimals as possible until the final result The number of decimals to be retained at the end depends on the accuracy of the data values one rule of thumb is to have one more decimal than in the original data Notice how the frequencies were used in the above calculation ...

Page 32: ... and the display should read 1 4264369 as the variance s2 Thus as expected s 1 2 kg s2 1 4 kg2 and 61 8 kg Exercise 6 Find the mean standard deviation and variance of a The annual rainfall data for the years 1971 1990 Note For the EL 531GH the key strokes are Year 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 Rain mm 1 340 990 1 120 1 736 260 1 100 1 379 1 125 1 430 1 446 Year 1981 1982 1983 1...

Page 33: ...ard deviation s 336 4 mm sample standard deviation variance s2 113141 7 mm2 b Snail statistics mean 3 4 cm standard deviation s 0 70 cm variance s2 0 49 cm2 Snail foot length cm 2 2 4 1 3 5 4 5 3 2 3 7 3 0 2 6 3 4 1 6 3 1 3 3 3 8 3 1 4 7 3 7 2 5 4 3 3 4 3 6 2 9 3 3 3 9 3 1 3 3 3 1 3 7 4 4 3 2 4 1 1 9 3 4 4 7 3 8 3 2 2 6 3 9 3 0 4 2 3 5 x x ...

Page 34: ...he correct mode For example if your calculator has RAD or GRAD on the display and you wish to work in degrees press the DRG key until the display shows DEG Example 1 In the right angled triangle below the length of the side opposite the 20 angle needs to be calculated To find the length of the side labelled x cm use 5 cm 20 x cm tan 20 5 5tan 20 x x ...

Page 35: ... length of the hypotenuse needs to be calculated To find the length of the side labelled x cm use The keystrokes on the calculator are The display should read 20 466631 so the length of the hypotenuse is about 20 5 cm Example 3 Given the lengths of two of the sides in the right angled triangle below find the value of the angle θ in degrees In the diagram x cm 20 7 cm 7 sin 20 7 sin 20 x x 2 cm 1 c...

Page 36: ...g brackets Your display should read 60 If it does not check that you are in degree mode 12 Exponential and logarithmic functions There are two log keys on your calculator with their associated exponential keys The latter are accessed by first using the yellow 2ndF key The log key uses base 10 and the ln key uses base e natural logarithm Example 1 Solve equation Taking logs of both sides 2a 20 ...

Page 37: ...hould read 38 370725 Example 3 harder Given find the value of x To find log x the calculator keystrokes are The display should read 0 5187675 Since this is the value of log x you still need to find x where To utilize the answer of 0 5187675 on your display use the stored ANSwer key which is above the key Press log2 log20 log2 log20 log20 log2 a a a 4 32 2 20 log y 1 584 log y 1 584 y 101 584 10x l...

Page 38: ...wer would still be the same Try it 13 Degrees minutes seconds The key involved is This key can be used for problems involving degrees minutes and seconds or hours minutes and seconds Example 1 Suppose that you have a trigonometric problem where the angle involved is given in degrees and minutes e g Find x where The keystrokes involved are x 4 sin 25 36 ...

Page 39: ... minutes and seconds e g 34 88 the keystrokes are The display should read 34 52 48 00 Example 3 To find the sum of 5 hours 52 minutes 30 seconds and 7 hours 45 minutes 49 seconds The keystrokes are The display should now read 13 38 19 00 which is 13 hours 38 minutes and 19 seconds To convert this number on the display into hours minutes and seconds press The display should read 13 638611 hours ...

Page 40: ...viii ix x xi 2 The following data is on growth in m in an economy over a 8 year period 2 5 6 2 2 1 0 04 8 2 7 4 2 1 1 7 Calculate i Σx ii Σx2 iii Σx 2 Explain in words what each of these mean 3 6 8 4 12 8 16 5 3 8 7 0 41 17 4 7 2 2 4 3 4 145 6 17 2 2 5 345 6 17 2 2 5 25 3 27 1 02 30 4 1333 3 000 2 015 0 1366 2 6 0 2000 2 6 100 90 2 90 50 60 2 60 20 30 2 30 ...

Page 41: ... 12 5 8 0 5 3 5 iii 2 5 Either 3 6 8 4 or 3 6 8 4 iv 1 007874 Either 12 8 16 5 3 8 or 16 5 3 8 12 8 v 0 9 Either 4 7 2 or 4 7 2 vi 3 2 Either 2 4 3 4 or 2 4 3 ab c 4 vii 9 296 145 6 17 2x2 5 viii 1 41 345 6 17 2x2 5 ix 39 4985 25 3 27 1 02 30 3 6 8 4 12 8 16 5 3 8 7 0 4 17 4 7 2 2 4 3 4 145 6 17 2 2 5 345 6 17 2 2 5 25 3 27 1 02 30 ...

Page 42: ...1 7 Calculate i Σx ii Σx2 iii Σx 2 Explain in words what each of these mean To do this on the calculator you must be in SD mode Enter the data 2 5 M 6 2 M 2 1 M 0 04 M 8 2 M 7 4 M 2 1 M 1 7 M Display reads n 8 i 22 64 Press the key that says Σx This gives the total growth over the last 8 years ii 178 4016 Press the key that says Σx2 This gives the sum of the squares of the growth in each year iii ...

Page 43: ...40 Mastering the Calculator using the Sharp EL 531LH Your Notes ...