MATHEMATICAL COMPUTING USING CASIO CLASSWIZ fx-570/991EX: TIPS AND TRICKS Authors Siti Nurul Hazwani Kamal Azhar Abd Hamid Politeknik Kuching Sarawak KM22, Jalan Matang, 93050, Kuching, Sarawak. Phone No. : 082-845 596 Fax No. : 082-845 023 Website : http://www.poliku.edu.my/ Copyright © 2023 Politeknik Kuching Sarawak e-ISBN: All right reserved. No part of this publication can be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise without prior permission of the copyright owner. Published by: Politeknik Kuching Sarawak
PREFACE Alhamdulillah, in the name of Allah, the Most Gracious and the Most Merciful, this Mathematical Computing using CASIO CLASSWIZ fx-570/991EX: Tips and Tricks eBook was successfully produced. Thank you to all the staff of the Department of Mathematics, Science and Computer for the encouragement, motivation, comments and insights in the production of this eBook. Not to forget, deepest appreciation to those who had contributed directly and indirectly to this production. Hopefully, this eBook will be beneficial to the readers, particularly the students who are undertaking any course related. i
ABSTRACT The Mathematical Computing course is a compulsory course for semester 1 students who undertake the Information Technology Diploma in all Malaysian Polytechnics. This ebook provides guidance to readers on how to use Casio ClassWiz fx570/991EX calculators, especially in Mathematical Computing courses. Four topics are covered in this eBook which are numbering system, equations, complex numbers and matrices. This eBook is user-friendly because readers are provided with images of each step to help them understand better. Some enrichment exercises are provided in each subtopic. With this eBook, it is hopeful that readers are able to master any topics taught in the field of Mathematical Computing. ii
TABLE OF CONTENTS 01 03 02 04 05 iii PREFACE …………. i ABSTRACT …………. ii NUMBERING SYSTEM …………. 1 - 8 1.1 Introduction 1.2 Conversion number 1.3 Binary arithmetic 1.4 Octal arithmetic 1.5 Hexadecimal arithmetic EQUATION …………. 9 – 16 2.1 Introduction 2.2 Simultaneous equations 2.3 Quadratic equation COMPLEX NUMBERS …………. 17 – 24 3.1 Introduction 3.2 Complex numbers arithmetic 3.3 Modulus and argument 3.4 Rectangular form to polar form 3.5 Polar form to rectangular form MATRICES …………. 25 - 38 4.1 Introduction 4.2 Matrices arithmetic 4.3 Determinant 4.4 Inverse ANSWERS …………. 39 - 41
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2 • The numbering system can be calculated using the Base-N mode in the calculator. • Identify the base of the starting number and the target base you want to convert to. • The abbreviations used are as below: o DEC = Decimal o HEX = Hexadecimal o BIN = Binary o OCT = Octal • Fractional values are not allowed. • An error notification will pop up if an invalid value is entered for the number system you are using. • Below is the table of valid numbers for each base: Base Number Decimal – 10 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Hexadecimal – 16 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F Binary – 2 0, 1 Octal – 8 0, 1, 2, 3, 4, 5, 6, 7 1.1 INTRODUCTION
3 GETTING TO KNOW YOUR CALCULATOR A = 10 (hexadecimal) B = 11 (hexadecimal) Decimal Hexadecimal Binary Octal C = 12 (hexadecimal) D = 13 (hexadecimal) E = 14 (hexadecimal) F = 15 (hexadecimal)
4 MODE: NUMBERING SYSTEM Choose MENU SETUP. Use the arrow keys to highlight the ‘3: Base-N’ icon. Then press or press For numbering system, there are four types of base that we can use; decimal, hexadecimal, binary and octal. Example 1: Converting 10010 into hexadecimal, binary and octal. • Choose MENU > 3: Base-N • By default, decimal base will appear • Press number 100 and followed by • To convert into hexadecimal, press • To convert into binary, press • To convert into octal, press = 3 = 1.2 CONVERSION NUMBER ln log
5 Example 2: Converting 1010112 into decimal, hexadecimal and octal. • Choose MENU > 3: Base-N • Press button • Press 101011 and followed by • To convert into decimal, press button • To convert into hexadecimal, press button • To convert into octal, press button 1. Convert the following numbering system: a. 1011012 into decimal b. 6010 into octal c. 2578 into hexadecimal d. A416 into binary e. 3038 into binary 2. Complete the following table. Decimal Binary Hexadecimal Octal 787 1001001 8B 612 = SELF-PRACTICE 1.2 ln log
6 Example 3: 111012 + 10012 - 112 • Choose MENU > 3: Base-N • Press button • Press 11101 and followed by • Press 1001 and followed by • Press 11 and followed by Example 4: (10112 x 112 ) - 10112 • Choose MENU > 3: Base-N • Press button • Press (1011 and followed by • Press 11) and followed by • Press 1011 and followed by Calculate the following binary arithmetic. a. 1101012 + 11112 b. 1112 x 1112 c. (10112 - 1112) x 112 d. 1111112 + 10112-100012 e. (1010102 x 1012) - 1011112 1.3 BINARY ARITHMETIC = + ‒ = x ‒ SELF-PRACTICE 1.3 log log
7 Example 5: 468 + 328 • Choose MENU > 3: Base-N • Press button • Press 46 and followed by • Press 32 and followed by Example 6: 10718 - 558 + 248 • Choose MENU > 3: Base-N • Press button • Press 1071 and followed by • Press 55 and followed by • Press 24 and followed by Calculate the following octal arithmetic. a. 778 + 118 b. 2008 - 528 c. 6068 + 638 – 1118 d. (3158 + 468) – 1258 e. (72248 - 41248) + 13328 1.4 OCTAL ARITHMETIC = + = - + SELF-PRACTICE 1.4 ln ln
8 Example 7: 9916 + 2C16 • Choose MENU > 3: Base-N • Press button • Press 99 and followed by • Press 2, press and press Example 8: D1016 – 8E916 + 1516 • Choose MENU > 3: Base-N • Press button • Press 10 and followed by • Press 8 9 and followed by • Press 15 and followed by Calculate the following hexadecimal arithmetic. a. B0716 + 4916 b. 1F316 - 12616 c. 51116 + 5A16 – E216 d. (A2B16 + 3016) – 98816 e. (414D16 - 399916) + 7616 = + = - + SELF-PRACTICE 1.5 1.5 HEXADECIMAL ARITHMETIC sin cos −
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10 • The equation can be calculated using the Equation/Func mode in the calculator. • Use the calculator to find the unknown value of variable in the equation. MODE: EQUATION/FUNC Choose MENU SETUP. Use the arrow keys to highlight ‘A: Equation/Func’ icon. Then press or press • Arrange the variables in order: , and . • Make sure that only constant number is on the right side. • The equal symbol “=“ must be included in the equation. Example 1: Find the value of , and in the following simultaneous equations: + − = − − + − = + − = − • Choose MENU > A: Equation/Func • Press ∗ simultaneous equations involve solving multiple equations with multiple variables simultaneously. ∗ polynomials are algebraic expressions with variables, coefficients, and exponents. • Press ∗ 3 refers to the number of variables (, and ) = 2.1 INTRODUCTION 2.2 SIMULTANEOUS EQUATIONS 1 (−) 3
11 • Press 3 4 - 2 - 4 -6 2 - 3 3 5 8 - 4 - 6 • Press • Press • Press Example 2: Find the value of , and in the following simultaneous equations: − + = − + = + + = − • Choose MENU > A: Equation/Func • Press • Press • Press 1 - 2 4 2 3 - 1 6 2 7 8 2 - 4 = = = = = = = = = = = = = = 1 = = = = = = = = = = = = = 3
12 • Press • Press • Press Example 3: Find the value of , and in the following simultaneous equations: − + = − + − = − + − = • Choose MENU > A: Equation/Func • Press • Press • Press 1 - 1 2 -4 3 1 -4 -6 2 3 -4 4 • Press = = = 1 = = = = = = = = = = = = = 3
13 • Press • Press 1. Find the value of , and in the following simultaneous equations: 2 + + 2 = 7 3 + 3 + 4 = 7 + 5 + 5 = −6 2. Find the value of , and in the following simultaneous equations: 5 − − 2 = −6 4 + 2 + = 1 2 + 4 + 3 = 7 3. Find the value of , and in the following simultaneous equations: 3 − + 4 = −2 2 − 2 + 5 = −9 6 + 3 − = 25 4. Find the value of , and in the following simultaneous equations: 2 + 6 = 8 + − 4 = −5 2 + 4 − 3 = −4 SELF-PRACTICE 2.2 = =
14 • Only one unknown variable. • 2 is the highest degree of the unknown variable. • The equals symbol “=“ must be included in the equation. • The value on the right must be 0. • The order of the equation is written as + + = . • Values of , , are generally not written as fractions or decimals but are written as integer values. Example 4: Find the value of in the following quadratic equation. + + = • Choose MENU > A: Equation/Func • Press ∗ simultaneous equations involve solving multiple equations with multiple variables simultaneously. ∗ polynomials are algebraic expressions with variables, coefficients, and exponents. • Press * degree refers to the highest degree in the equation. • For value 2, press 1 and followed by • For value + , press 7 and followed by • For value + 0, press 12 and followed by • Press for value 1 2 2 = = = = 2.3 QUADRATIC EQUATION
15 • Press for value 2 Example 5: Find the value of in the following quadratic equation. + − = • Choose MENU > A: Equation/Func • Press • Press • For value 2, press 3 and followed by • For value + , press 8 and followed by • For value + 0, press -3 and followed by • Press for value 1 • Press for value 2 2 2 = = = = = =
16 Example 6: Find the value of in the following quadratic equation. − = • Choose MENU > A: Equation/Func • Press • Press • For value 2, press 1 and followed by • For value + , press 0 and followed by • For value + 0, press - 64 and followed by • Press for value 1 • Press for value 2 Find the value of in the following quadratic equations. a. 2 + 3 + 2 = 0 b. 22 + 7 − 9 = 0 c. 4 + 2 + 5 = 0 d. 32 − 2 = 5 e. 2 − = 9 − SELF-PRACTICE 2.3 2 2 = = = = =
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18 • The complex numbers can be calculated using the Complex mode in the calculator. • Usually calculators are used for calculating complex numbers that involve +, -, × and ÷ operations. • Besides that, calculators can calculate modulus, arguments and conversion of complex numbers into polar form and vice versa. • Questions involving arithmetic operations of complex numbers will give answers in the form of + . • For the imaginary symbol, press . GETTING TO KNOW YOUR CALCULATOR Option Symbol of angle Imaginary symbol Absolute value Polar form Rectangular form ( + ) 3.1 INTRODUCTION ENG
19 MODE: COMPLEX NUMBERS Choose MENU SETUP. Use the arrow keys to highlight the ‘2: Complex’ icon. Then press or press Example 1: ( − ) – ( − ) • Choose MENU > 2: Complex • Press (3 ‒ 5 ) – ( 2 ‒ 6 ) • Press Example 2: − • Choose MENU > 2: Complex • Press 11 3 ‒ 9 • Press Example 3: ( − ) • Choose MENU > 2: Complex • Press 7 ( 2 ‒ 6 ) • Press Example 4: ( + ) ( − ) • Choose MENU > 2: Complex • Press (4 + ) (1 ‒ 2 ) • Press = 2 3.2 COMPLEX NUMBERS ARITHMETIC = = = = ENG ENG ENG ENG ENG ENG ENG ENG
20 Example 5: − + • Choose MENU > 2: Complex • Press • Press 7 ‒ 2 • Use to insert value denominator • Press 2 + 3 • Press Simplify the following operations into the form of +. a. 8 + 9 − 18 + 4 b. 15 2 − 10 + 6 + 13 5 c. (3 + 2)(2 + ) − 23 d. 14 + 6(2 + 5) − 15 e. 3 − 4 3 + 4 = SELF-PRACTICE 3.2 ENG ENG
21 ( Example 6: Find the modulus for + • Choose MENU > 2: Complex • Press SHIFT • Press 5 + 2 • Press • Press to convert value into decimal Example 7: Find the modulus for − • Choose MENU > 2: Complex • Press SHIFT • Press 7 - 3 • Press • Press to convert value into decimal Example 8: Find the argument for + • Choose MENU > 2: Complex • Press • Press • Press 5 + 2 ) • Press ∗ the value of the argument depends on where is the quadrant. If the answer is negative, add 360 from that value to get the positive value. 3.3 MODULUS AND ARGUMENT = = 1 OPTN S⟺D ENG ENG = S⟺D ENG (
22 Example 9: Find the argument for − • Choose MENU > 2: Complex • Press • Press • Press 7 - 3 ) • Press ∗ the value of the argument depends on where is the quadrant. If the answer is negative, add 360 from that value to get the positive value. Find the modulus and argument for the following equations. a. 4 + 7 b. − 2 c. 3( + 3) d. 5 − 5 − 2 + 11 e. 8 − 13 SELF-PRACTICE 3.3 = 1 OPTN ENG
23 Example 10: Convert + into polar form • Choose MENU > 2: Complex • Press 5 + 2 • Press • Use • Press • Press • Press to convert value into decimal 1. Convert 4 − 7 into polar form. 2. Convert 6 + 13 into polar form. 3. Convert 21 + 13 into polar form. 4. Convert 2(5 + 7) into polar form. 5. Convert 3 3 − 2 2into polar form 3.4 RECTANGULAR FORM TO POLAR FORM = 1 OPTN ENG S⟺D SELF-PRACTICE 3.4
24 Example 11: Convert . ∠ . ° into polar form • Choose MENU > 2: Complex • Press 5.39 SHIFT 21.80 • Press • Use • Press • Press • Use to view full answer 1. Convert 20 ∠ 63° into rectangular form. 2. Convert 15.6 ∠ 219° into rectangular form. 3. Convert 66 ∠ 188° into rectangular form. 4. Given || = 37.80 and = 72.28°, convert them into rectangular form. 5. Given || = 125 and = 92.35° , convert them into rectangular form. = 2 3.5 POLAR FORM TO RECTANGULAR FORM SELF-PRACTICE 3.5 OPTN ENG
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26 • Matrices can be calculated using the Matrix mode in the calculator. • Usually calculators are used for calculating matrices numbers that involve +, -, × and ÷ operations. • Besides that, calculators can calculate determinant and inverse. • Matrices can't be calculated directly. It needs to be declared as a variable (such as Matrix A, Matrix B) before data is entered and the operation is executed. MODE: MATRIX Choose MENU SETUP. Use the arrow keys to highlight the ‘4: Matrix’ icon. Then press or press Example 1: � − � + � − − � ∗ Assume � − � as matrix A and � − − � as matrix B • Choose MENU > 4: Matrix • Press to declare matrix A • Press to determine number of rows Row � − � • Press to determine number of columns column � − � = 4 4.2 MATRICES ARITHMETIC 1 2 2 4.1 INTRODUCTION
27 • Press 4 -9 2 7 • Press • Next, define matrix B by pressing • Press • Press • Press to determine number of rows Row � − − � • Press to determine number of columns Column • Press -8 6 -3 1 • Press • For addition arithmetic, press • Press • Press • Press • Press • Press to view the answer. = = = = 2 1 2 = = = = 2 3 OPTN AC OPTN + OPTN 4 = � − − � AC
28 Example 2: � − � × [ ] ∗ Assume � − � as matrix A and [ ] as matrix B • Choose MENU > 4: Matrix • Press • Press • Press • Press to determine number of rows Row � − � • Press to determine number of columns Column � − � • Press 5 3 -2 • Press • Next, define matrix B by pressing • Press • Press 1 3 1 = = = 2 1 OPTN OPTN 1 AC
29 • Press to determine number of rows Row [ ] • Press to determine number of columns Column [ ] • Press 4 0 6 • Press • For multiplication arithmetic, press • Press • Press • Press • Press • Press 3 = = = 1 3 OPTN AC × OPTN 4 =
30 Example 3: � − � • Choose MENU > 4: Matrix • Press • Press • Press • Press to determine number of rows Row � − � • Press to determine number of columns Column � − � • Press 5 3 -2 • Press • Press 2 • Press • Use to find determinant • Press 1 3 1 = = = 1 OPTN 3 OPTN AC
31 • Press • Press • Press • Press 1. � 1 −1 3 2 5 4 � − � −3 7 9 11 2 −5 � 2. � −3 4 2 −1 � × 3 � −4 0 � 3. � 2 −8 2 3 0 7 −1 4 1 �� 5 −2 −3 4 6 1 0 2 −5 � 4. 2[9 4 5] + �[−1 0]� 5 4 −2 −3 2 1 �� 5. � −4 3 8 8 2 11 � T − 5 � 0 3 −1 −2 2 4 � 3 = OPTN ) SELF-PRACTICE 4.2
32 Example 4: Find determinant of matrix � 9 11 −3 −4 � • Choose MENU > 4: Matrix • Press • Press • Press • Press to determine number of rows Row � 9 11 −3 −4 � • Press to determine number of columns Column � 9 11 −3 −4 � • Press 9 11 -3 -4 • Press • Press • Use to find determinant • Press 4.3 DETERMINANT 1 2 2 = = = 1 OPTN = AC OPTN 2
33 • Press • Press • Press • Press Example 5: Find determinant of matrix � 3 −1 2 4 −2 2 2 −4 1 � • Choose MENU > 4: Matrix • Press • Press • Press • Press to determine number of rows Row � 3 −1 2 4 −2 2 2 −4 1 � • Press to determine number of columns Column � 3 −1 2 4 −2 2 2 −4 1 � OPTN 3 ) = 1 3 3 1 OPTN
34 • Press 3 -1 2 4 -2 2 2 -4 1 • Press • Press • Use to find determinant • Press • Press • Press • Press • Press = = = = = = = = = AC OPTN 2 OPTN 3 ) =
35 Find determinant of the following matrix: a. � 2 5 4 8 � b. � 13 −6 5 −1 � c. � 1 2 1 3 3 4 5 5 6 � d. � 6 1 5 −4 3 −4 1 5 2 � e. � 8 1 −3 4 2 −1 3 6 0 � SELF-PRACTICE 4.3
36 Example 6: Find inverse of matrix � 9 11 −3 −4 � • Choose MENU > 4: Matrix • Press • Press • Press • Press to determine number of rows Row � 9 11 −3 −4 � • Press to determine number of columns Column � 9 11 −3 −4 � • Press 9 11 -3 -4 • Press • Press • Press • Press • Press • Use to view the whole value ∗ Your answer must be in fraction value. 4.4 INVERSE 1 2 2 = = = 1 OPTN = AC OPTN 3 − =
37 Example 7: Find determinant of matrix � 3 −1 2 4 −2 2 2 −4 1 � • Choose MENU > 4: Matrix • Press • Press • Press • Press to determine number of rows Row � 3 −1 2 4 −2 2 2 −4 1 � • Press to determine number of columns Column � 3 −1 2 4 −2 2 2 −4 1 � • Press 3 -1 2 4 -2 2 2 -4 1 • Press • Press • Press • Press • Press • Use to view the whole value ∗ Your answer must be in fraction value. 1 3 3 = = = 1 OPTN = = = = = = AC OPTN 3 − =
38 Find inverse of each matrix below: a. � 2 5 4 8 � b. � 13 −6 5 −1 � c. � 1 2 1 3 3 4 5 5 6 � d. � 6 1 5 −4 3 −4 1 5 2 � e. � 8 1 −3 4 2 −1 3 6 0 � SELF-PRACTICE 4.4
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40 SELF-PRACTICE 1.2 1. a. 4510 b. 748 c. AF16 d. 101001002 e. 110000112 2. SELF-PRACTICE 1.3 a. 10001002 b. 1100012 c. 11002 d. 1110012 e. 101000112 SELF-PRACTICE 1.4 a. 1108 b. 1268 c. 5608 d. 2368 e. 44328 SELF-PRACTICE 1.5 a. B5016 b. CD16 c. 48916 d. D316 e. 82A16 SELF-PRACTICE 2.2 1. = 4, = −3, = 1 2. = −1, = 3, = −1 3. = 2, = 4, = −1 4. = 5, = −2, = 2 SELF-PRACTICE 2.3 a. 1 = −1, 2 = −2 b. 1 = 1, 2 = − 9 2 c. 1 = −1, 2 = −4 d. 1 = 5 3, 2 = −1 e. 1 = 3, 2 = −3 SELF-PRACTICE 3.2 a. 13 − 10 b. −9 + 3 c. 1 − 15 d. −16 − 3 e. −7 25 − 24 25 SELF-PRACTICE 3.3 a. || = 8.06, = 60.26° b. || = 2.24, = 153.43° c. || = 9.49, = 108.43° d. || = 6.71, = 63.43° e. || = 15.26, = 301.61° SELF-PRACTICE 3.4 1. 8.06 ∠ 299.74° 2. 14.32 ∠ 24.78° 3. 24.70 ∠ 31.76° 4. 17.20 ∠ 54.46° 5. 3.61 ∠ 303.69° Decimal Binary Hexadecimal Octal 787 1100010011 313 1423 73 1001001 49 111 139 10001011 8B 213 394 110001010 18A 612
41 SELF-PRACTICE 3.5 1. 9.08 + 17.82 2. −12.12 − 9.82 3. −65.36 − 9.19 4. 11.51 + 36.01 5. −5.13 + 124.89 SELF-PRACTICE 4.2 1. � 4 −8 −6 −9 3 9 � 2. � 36 −24� 3. �−22 −48 −24 15 8 −44 11 28 2 � 4. [13 4 12] 5. �−4 −7 7 13 −2 −9� SELF-PRACTICE 4.3 a. -4 b. 17 c. 2 d. 45 e. -9 SELF-PRACTICE 4.4 a. �−2 54 1 −12 � b. � −1 17 6 17 −5 17 13 17� c. ⎣⎢⎢⎢⎡−1 −72 52 1 12 −12 0 52 −32 ⎦⎥⎥⎥⎤ d. ⎣⎢⎢⎢⎡ 26 45 23 45 −19 45 4 45 7 45 4 45 −23 45 −29 45 22 45 ⎦⎥⎥⎥⎤ e. ⎣⎢⎢⎢⎡ −23 2 −59 13 −1 49 −2 5 −43 ⎦⎥⎥⎥⎤