Casio 3950P, Programming Manual

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Page 2: ...l tool that can help students grasp important concepts and stimulate their imagination This manual is a collection of actual problems and exercises including actual operations It is intended as the fi...

Page 3: ...rapezoidal rule 19 13 Definite integrals Simpsons formula 21 14 Finding the area of a triangle 23 15 The angle between two vectors 24 16 Finding the angles in a triangle 25 17 The radius of the Inscri...

Page 4: ...PCL 1 2 3 PRGM MODE MODE MODE 1 S s s A s B s C P 1234 308 Ed i t Pr og PRGM If there is already a program in memory its number appears on the display Remaining capacity bytes 2 000 PRGM Number of byt...

Page 5: ...mbers Let be the remainder after dividing by If set and and return to 2 If 0 then is the greatest common divisor Program 60 STEP Execution Example Find the greatest common divisor of 210 and 60 A B Gr...

Page 6: ...f digits in the repeated pattern e g 3 in the example The recurring sequence of digits e g 345 in the example This program deals only with the case in which the 1st to Ath digits immediately following...

Page 7: ...time second time OUTPUT X Y solutions to the simultaneous equation Execution Example The solution to is AE BD G 0 Ax By C Dx Ey F x EC FB G y AF CD G ON MODE MODE MODE 1 PRGM MODE 1 COMP 1 P1 Ax By C...

Page 8: ...a unique solution In this case please enter a different problem 9 EXE M S A D R P1 P1 P2 P3 P4 G 8 EXE M S A D R P1 P1 P2 P3 P4 G 5 EXE M S A D R P1 P1 P2 P3 P4 G 1 EXE M Disp S A D R P1 P1 P2 P3 P4...

Page 9: ...two complex solutions Program 70 STEP Execution Example i Find solutions to the equation ax 2 bx c 0 x b b 2 4ac 2a b 2 4ac 0 b 2 4ac 0 b 2 4ac 0 ON MODE MODE MODE 1 PRGM MODE 2 CMPLX 1 P1 2x 2 4x 16...

Page 10: ...isplay the imaginary parts x 2 6x 12 0 x 3 3i Prog 1 CMPLX S A D R P1 P1 P2 P3 P4 G 1 EXE 6 EXE 1 2 EXE M CMPLX R I Disp S A D R P1 P1 P2 P3 P4 G SHIHT EXE M CMPLX R I Disp i S A D R P1 P1 P2 P3 P4 G...

Page 11: ...te values of given for the function To continue the calculation press enter some value of X and To end the calculation presss x y y x y x y x 3 2x 2 x 1 y 13 x 3 y 3 x 1 y1 x1 ON MODE MODE MODE 1 PRGM...

Page 12: ...of arithmetical progression Execution Example Calculate the sum up to the 10th term of the arithmetic progression with first term 1 and difference term 3 C A B A k 1 B k 1 C A A B A 2B A C 1 B C 2 2A...

Page 13: ...T sum of arithmetical progression Execution Example The of an arithmetic progression of 10th terms with first term 1 and last term 28 is A A B A C 1 B C terms ON MODE MODE MODE 1 PRGM MODE 1 COMP 1 P1...

Page 14: ...sum of geometric progression Execution Example Calculate the sum up to the 5th term of the geometric progression with first term 1 and ratio term 3 C A B AB k 1 k 1 C A AB AB 2 AB C 1 A 1 B n 1 B ON...

Page 15: ...c progression Execution Example The sum of the geometric progression with first term 1 last term 81 and common ratio 3 is A B C A AC AC 2 B C B A BC 1 C ON MODE MODE MODE 1 PRGM MODE 1 COMP 1 P1 Prog...

Page 16: ...y comparing the signs of and we can half the interval in which we search Repeating this procedure will yield an approximate solution of arbitrary accuracy Program 126 STEP Execution Example Find solut...

Page 17: ...15 To stop program press the key To calculate for other functions alter the program where underlined EXE EXE Disp S A D R P1 P1 P2 P3 P4 G AC...

Page 18: ...on the initial value Program 40 STEP Execution Example Find solutions to the equation Solutions are and To stop program press the key To calculate for other functions enter the apropriate function in...

Page 19: ...al logarithm 2 718281828 For X too large it may not be possible to calculate the exponent and Y may become 1 To stop program press the key To calculate for other functions alter the program where unde...

Page 20: ...X becomes too small a Math Error may occur To stop program press the key To calculate for other functions alter the program where underlined x sin x x 0 lim 1 0 ON MODE MODE MODE 1 PRGM MODE 1 COMP 1...

Page 21: ...with the precise value of the definite integral Program 89 STEP INPUT interval of integration number of trapezoids OUTPUT value of the definite integral Execution Example Calculate the value of the de...

Page 22: ...For large n the calculation may take a considerable amount of time To calculate for other functions alter the program where underlined 1 0 EXE S A D R P1 P1 P2 P3 P4 G 2 0 EXE S A D R P1 P1 P2 P3 P4...

Page 23: ...istent with the true answer In general this method gives good approximations Program 105 STEP INPUT interval of integration number of stripes OUTPUT value of the definite integral Execution Example Ca...

Page 24: ...22 For large n the calculation may take a considerable amount of time To calculate for other functions alter the program where underlined 2 0 EXE M S A D R P1 P1 P2 P3 P4 G...

Page 25: ...llowing formula Let the lengths of the three sides be and and set The area is calculated Program 47 STEP OUTPUT the area of a triangle Execution Example Find the area of the right angled triangle with...

Page 26: ...ctors Execution Example Find the angle between the vectors 0 0 1 and 2 3 4 To obtain the answer in radians press before executing the program a b a b 1 cos a b a b a a1 a2 a3 b b1 b2 b3 ON MODE MODE M...

Page 27: ...33 STEP Execution Example Find the angle in a triangle with sides of length 3 4 and 5 To obtain the answer in radians press before executing the program a 2 b 2 c 2 2bc cos a b c 1 cos b 2 c 2 a 2 2b...

Page 28: ...f the length of the three sides whereby the radius of the circle is Program 49 STEP OUTPUT the radius of the inscribed circle Execution Example For a triangle with sides of length 3 4 and 5 the radius...

Page 29: ...three sides of the triangle Program 41 STEP OUTPUT the radius of the circumscribed circle Execution Example For a triangle with sides if length 3 4 and 5 the radius of the circumscribed circle is 2 5...

Page 30: ...f mass is given Program 67 STEP INPUT X Y first time A X Y X Y second time B X Y X Y third time C X Y OUTPUT X Y center of mass P X Y Execution Example The center of mass for a triangle with corners A...

Page 31: ...he point A X Y A gradient B y intercept OUTPUT the distance between the line y Ax B and the point A X Y Execution Example Calculate the distance between the point 3 4 and the straight line A x y y ax...

Page 32: ...ective components For example for The inner product is defined Program 111 STEP INPUT first time second time OUTPUT first time sum of two vectors second time difference of two vectors inner product Ex...

Page 33: ...EXE 3 EXE M Disp S A D R P1 P1 P2 P3 P4 G EXE M Disp S A D R P1 P1 P2 P3 P4 G EXE M Disp S A D R P1 P1 P2 P3 P4 G EXE M Disp S A D R P1 P1 P2 P3 P4 G EXE M Disp S A D R P1 P1 P2 P3 P4 G EXE M Disp S A...

Page 34: ...le Find the location of the point 1 0 after rotation through an angle of To obtain the answer in radians press before executing the program x y x y x y x y cos sin sin cos x y ON MODE MODE MODE 1 PRGM...

Page 35: ...he distance from the origin Y the angle from the real line Execution Example when written in polar coordinates is To obtain the answer in degrees press before executing the program a bi r cos i sin a...

Page 36: ...rse of matrix Execution Example The inverse matrix of is For the inverse does not exist and the values and must be re entered a b c d 1 ad bc d b c a 1 ad bc d b c a a b c d 1 0 0 1 ad bc 0 a b c d a...

Page 37: ...mber of cards showing A B and C respectively OUTPUT Y the number of combinations Execution Example How many combinations are possible for 3 s 2 s and 2 s A A B B C C A B C C C C B B B A A A A A A C a...

Page 38: ...n will land times with heads up is Program C 34 STEP C INPUT throws probability of heads number of heads Execution Example For a coin with probability of landing heads find the probability of getting...

Page 39: ...Program 39 STEP INPUT Population variance OUTPUT 95 confidence interval Execution Example Calculate 95 confidence intervals Data 1 4 1 5 1 3 1 4 1 7 1 5 1 3 Population variance The interval of 95 cer...

Page 40: ...4 M DT SD S A D R P1 P1 P2 P3 P4 G 1 7 M DT SD S A D R P1 P1 P2 P3 P4 G 1 5 M DT SD S A D R P1 P1 P2 P3 P4 G 1 3 M DT SD S A D R P1 P1 P2 P3 P4 G Prog 1 SD S A D R P1 P1 P1 P1 P2 P3 P4 G 0 0 2 EXE SD...

Page 41: ...pothesis for the significance level For different significance levels the confidence limits are given below Program 24 STEP INPUT given value population variance OUTPUT value of Z Execution Example Te...

Page 42: ...1 4428571 1 2111 0 02 7 1 442857143 1 2 Z 1 96 0 05 MODE MODE 1 SD S A D R P1 P1 P2 P3 P4 G 1 4 M DT SD S A D R P1 P1 P2 P3 P4 G 1 3 M DT SD S A D R P1 P1 P2 P3 P4 G Prog 1 SD S A D R P1 P1 P1 P1 P2...

Page 43: ...possible to find the answer within 11 attempts Program 68 STEP Running the Program Enter a random number and press If the answer is smaller than the number you entered A will be displayed If the answe...

Page 44: ...42 30 Various areas and volumes Area OUTPUT areas Triangle Base Height Square Length of sides Rectangle Height Width Trapezium Top length A Bottom length B Height C Circle Radius A B A B C A 0 A B A A...

Page 45: ...43 Volume OUTPUT volumes Cube Length of sides Rectangular prism Depth Width Height Triangular Quadrangular pyramid Base Area A Height C Cone Radius Height Sphere Radius A B C A C A C A A A A...

Page 46: ...MEMO MEMO MEMO MEMO...

Page 47: ...Authors Dr Yuichi Takeda Research and Development Initiative Chuo University...

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