# Calculator and Casio Essay

CASIO fx-82MS MASTERING THE CALCULATOR USING THE CASIO fx-82MS Learning and Teaching Support Unit (LTSU) The Learning Centre Guide book Wr itten by Linda Galligan Published by University of Southern Queensland Toowoomba Queensland 4350 Australia http://www - **Calculator and Casio Essay** introduction. usq. edu. au © University of Southern Queensland, 2006. 1. Copyrighted materials reproduced herein are used under the provisions of the Copyright Act 1968 as amended, or as a result of application to the copyright owner.

No part of this publication may 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. Produced by the Distance and e-Learning Centre using FrameMaker5. 5. 6 on a Pentium workstation. TABLE OF CONTENTS PAGE Introduction A word about starting out 1. Addition and subtraction 2. Multiplication and division 3. Brackets 4. Powers 5. Fractions 6. Using the x–1 key 7. Scientific notation 8. Factorial x! 9. Using memory 10.

**$13.9/page**

More Essay Examples on Calculator Rubric

Statistics 11. Linear regression 12. Trigonometric functions 1 2 4 8 10 11 17 19 20 22 23 25 31 34 13. Exponential and logarithmic functions 14. Degrees, minutes, seconds Review calculator exercises Calculator solutions Your notes 36 38 41 42 44 Mastering the Calculator using the Casio fx-82MS 1 Introduction This is one in a series of booklets prepared to assist students who are learning to use a calculator. They have been prepared by staff in The Learning Centre from the Learning and Teaching Support Unit (LTSU) at USQ.

The series comprises: Mastering the calculator • • • • • • • • Using the Casio fx-100s (also suitable for Casio fx-570) Using the Casio fx-100AU Using the Casio fx-82LB Using the Casio fx-82TL Using the Casio fx-82MS 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 The Learning Centre, please contact The Learning Centre (TLC) Learning and Teaching Support Unit (LTSU), S-Block The University of Southern Queensland Telephone: 07 4631 2751 Email: [email protected] edu. au Fax: 07 4631 1801 Home page: http://www. usq. edu. au/ltsu Note the booklets are also available online at the above address (follow the prompts). 2 Mastering the Calculator using the Casio fx-82MS A word about starting out • Make sure you are in the correct mode selection and that all previous data is cleared.

• Example: To perform arithmetic operations press • To clear all values press • To clear memory press The screen displays Mcl Mode All Press to clear memory three times • If your calculator has FIX or SCI on the display press appears on the screen press 3, then 2 so you are in Normal mode. • If your calculator has RAD or GRAD on the display press two times appears on the screen press 1 so you are in Degree mode. Mastering the Calculator using the Casio fx-82MS 3 • There is also a mode which gives you a preference for displaying the decimal point as a dot or comma as 34. 26 or 34, 26. Press four times until DISP 1 is displayed. Press

then forward once Press Press for dot end (separates thousands with comma) for comma (separates thousands with dot). 4 Mastering the Calculator using the Casio fx-82MS 1. Addition and subtraction 1. 1 To add numbers DEL key addition key Find the key (it 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. Mastering the Calculator using the Casio fx-82MS 5 1. 2 Sometimes you make an error when typing in a number

If this happens use the and continue. Example If you want to enter 3 + 4 but accidentally type press Now type Example If I want to add 471 and 575 but I typed to cancel the 5. key to cancel the number and then type in the correct number I can cancel 6 by typing The display should read 1 046. and then typing ‘Try practising cancelling with the key until you are comfortable with its use. ’ 1. 3 The Example If you typed: 471 + 546 keys are used when you to delete other data but you wanted 471 + 576 press the key twice. The 4 flashes. Press . The 7 now replaces the 4. Press . The display should read 1 047.

Practice using this key when replacing digits, operation keys (+ – ? ?), or more than one digit (use the DEL key). 6 Mastering the Calculator using the Casio fx-82MS You can also use the insert key Example If you typed 471 + 56 but you wanted 471 + 576, press the display should read 1047. to insert anything you omitted. 1. 4 To subtract numbers Find the Example To subtract 35 from 257, type key (it is shown on the photograph of the calculator following). The display should read 222 negative key subtraction key Mastering the Calculator using the Casio fx-82MS 7 Example 348 – 24 – 19 The keystrokes are The display should read 305.

Sometimes you may have a sum like this: -7 + 4 You can use the The key strokes are key. 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). 8 Mastering the Calculator using the Casio fx-82MS 2. Find the Multiplication and division key (it is shown on the photograph of your calculator here). 2. 1 To multiply numbers key for multiplication key for division Example To multiply 7 and 3, type The display should read 21 To find 753 ? 492, type The display should read 370 476 Mastering the Calculator using the Casio fx-82MS 9

2. 2 To divide numbers Find the Example To divide 35 by 7, type key (it is shown here on the photograph of the calculator) The display should read 5 To divide 7 905 by 85, type The display should read 93 To divide 56 by 23947 type The display should read 0. 002338497 If it reads 2. 3385? 10 or something similar, then your calculator is in SCI (Scientific mode). See page 2 to change to NORM (normal mode). -03 2. 3 Combining multiplication and division Example If the question is 27 ———– then 7? 4 it is really 27 ? 7 ? 4. Try it. The display should read 0. 964285714 10 Mastering the Calculator using the Casio fx-82MS

3. Brackets Find the set of bracket keys on your calculator. The fx-100AU allows you to use many sets of brackets. LH bracket key RH bracket key Example Do the calculation 471 – (93 + 11 + 2) on the calculator. (Make sure your calculation is in ordinary comp. mode – ) 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). Mastering the Calculator using the Casio fx-82MS 11 Try these examples: Exercise 1 (a) 25 + (7 + 2 – 4) (b) 18 (3 + 7) [a multiplication sign is understood 18 ?

(3 + 7)] but you don’t need to press the ? key (c) 4 + 5 [2 (3 + 7)] [to use two sets of brackets just press the same button] 5 (d) —————(3 + 2) 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. ) power key square root key square key 12 Mastering the Calculator using the Casio fx-82MS Press the display should read 36. Or you can use the power key on your calculator. Find the ^ key on your calculator (similar to the key on your computer keyboard). Example To square 6, that is, find 62, type

The display should read 36 To find 273 the required key strokes are and the display should read 19683. If you have learnt 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. 12 = 1 22 = 4 32 = 9 42 = 52 = 62 = 72 = 82 = 92 = 102 112 = 122 = 132 = 142 = 152 = 162 = 172 = 182 = 192 = 202 212 = 222 = 232 = 529 242 = 576 252 = 625

__________________________________________________________________________ Mastering the Calculator using the Casio fx-82MS 13 Exercise 3 You can use this key for other powers as well. Try these examples (a) 74 (b) 810 (c) (0. 4)6 (you do not have to type the brackets in) (d) (–7)6 (you need to type the brackets in) (e) 50. 4 (f) 5–4 __________________________________________________________________________ Answers: (a) 2401 (b) 1073741824 (c) 4. 096 ? 10–3 or 0. 004096 (you move the decimal 3 places to the left) (d) (e) 1. 903653939 (f) 0.

0016 [Just press 1 —- so you could press 4 5 5–4 is the same as 117649 to get the same answer] __________________________________________________________________________ 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, 36 = 6 . 36 Find the square root key on your calculator and type 14 Mastering the Calculator using the Casio fx-82MS The display will read 6. What do you think 81 is? 81 =

__________________________________________________________________________ You should have said 9 because 92 = 81 (Check your calculator) __________________________________________________________________________ What do you think – 49 will be? You should have said ‘you can’t find the square root of a negative’ since you can’t find a number that squares to give a positive. Your calculator will say Math ERROR. Exercise 4 Try these by looking at the table of squares you completed on the previous page and then check your answers on your calculator (a) (b) (c) (d) 16 144 100 441 = = = = (e) (f) (g) (h) 49 169 121 361 = = = =

__________________________________________________________________________ The answers are 4, 12, 10, 21, 7, 13, 11, 19. Let’s now check that taking the square root neutralises squaring. Try this on your calculator. Find the square root of 3 squared that is, The key strokes required are 3 2 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 required are

__________________________________________________________________________ Mastering the Calculator using the Casio fx-82MS 15 Exercise 5 Complete the following without using the calculator (a) (b) (c) (d) (e) (f) (g) (h) (i) 64 121 225 7 7 2 2 2 2 2 2 = = = = = = = = = 10 625 144 , , , because 82 because because = = = 121 10 Check your answers on the calculator. __________________________________________________________________________ 4. 3 Other roots You can also use the root key on the calculator. Find the key you must press shift first. on your calculator. To get to this shift key root key 16

Mastering the Calculator using the Casio fx-82MS Look at the examples below. Examples (a) 9? and the display should read 3. or and the display should read 3. (b) 8 1 -3 and the display should read 2. (c) 16? and the display should read 2. Note: • Root key is a function at the back of the power key, so you will need to activate it with the SHIFT key • See the key x . The x stands for the root you want to take so it is typed first. 1 -1 -3 • From the examples above you may have seen that 8 3 = index. 3 8 . 8 is called a fractional Mastering the Calculator using the Casio fx-82MS 17 5. Fractions 1 4 How do you add —– and —– ?

Normally you would have to find a common denominator of 12 63 252. So: 1 4 21 16 37 —– + —– = ——– + ——– = ——-12 63 252 252 252 Or you can use your calculator to add fractions. Find the b a — key c fraction key b On the a — key the ‘a’ represents the whole part of a mixed c b number and the ‘ — ’ represents the fraction part of a mixed number. c 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. 18 Mastering the Calculator using the Casio fx-82MS 1 4 The key storkes required for the calculation —– + —– are: 12 63

37 and the display will show 37 d 252 which is read as ——-252 Example 1 63 Find 8 — + —-9 72 Using the calculator the key strokes are: 71 and the display will show 8 d 71 d 72 which is read as 8 —-72 Note if you now press into an improper fraction. 647 the display will read ——– . So this key turns a mixed fraction 72 If you press the i. e. 8. 9861111 key a second time the decimal equivalent is displayed, Mastering the Calculator using the Casio fx-82MS 19 6. Using the x –1 key This is a very useful key in more complex calculations. Find the Example Look at this simple example 1 4 — is the same as 4 ?

-7 7 You can input this in your calculator by pressing key on your calculator. The answer should be 0. 571428571. This would be the same as if you just typed 4 ? 7 Take another example 4 ————————(8 + 3) ? 7 Type: The answer should be 0. 051948051 20 Mastering the Calculator using the Casio fx-82MS 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. Press , the display should read 7240.

If you want to multiply two numbers e. g. 8. 34 ? 10–2 ? 4. 28 ? 105. Press and the display will read 35695. 2 If you press three times then the display will read which means 3. 56952 ? 104. Pressing the mode three times gives you Mastering the Calculator using the Casio fx-82MS 21 the display The puts the calculator in scientific notation. The calculator then asks SCI 0~9? This gives you 10 digits. Notice a 04 gives the option of how many digits are displayed. The small sci appears in the screen. If you press means 3. 570 ? 104. This rounds the number to 4 digits. three times then the display will read 3. 5670?

10 which Practise using the and keys on your calculator 22 Mastering the Calculator using the Casio fx-82MS 8. Factorial x ! Look at your calculator and find the key with the symbol x! on it. You will come across this symbol when doing the Binomial Distribution. This is called the factorial key. Use the shift key to activate x! 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. ) Factorial rule 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 Mastering the Calculator using the Casio fx-82MS 23 9. Using memory To calculate the following it may be useful to use the memory key for each term: Example: ( 23 – 16 ) ( 9 – 16 ) ( 17 – 16 ) ——————— + ———————— + ———————–16 16 16 2 2 2 these keys are for memory (Use the key to activate M–) To make sure memory is clear, first press

or and make sure you are in normal calculation mode [may need to press mode 1]. An M appears in the display when you put something in memory. 24 Mastering the Calculator using the Casio fx-82MS To do the calculation 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. Example 2 calculate the following: 18 17 12 ——— + ——— + ——–17 17 17 first press the following keys:

to clear the memory then your answer should be 11. 39917438 (There are other memory keys in your calculator – the A to F keys, accessed by using SHIFT STO and RCL – try them yourselves. ) Mastering the Calculator using the Casio fx-82MS 25 10. Statistics 10. 1 Mean and standard deviation – single data ?x The formula for the mean is x = —-n The formulas for the sample standard deviation are ? ??? x1 ? x ??? n ? 1 ? ? 2 ? n? 1 or s = (sample) 2 ?n = ? ??? x1 ? x ??? ? ? (population) n Your calculator will calculate the mean and standard deviation for you (the population standard deviation ?

n or the sample standard deviation ? n-1 – in data calculations you will usually use the sample standard deviation. ) On the Casio fx-82MS, ? and s are found in s-VAR. The positions of keys needed are shown on the diagram below. input data key (Key for sum of observations, sum of observations squared, and number of observations) (key for mean, sample and population standard deviation) 26 Mastering the Calculator using the Casio fx-82MS To find the mean and standard deviation, firstly you must access the statistics mode of the calculator by using the keys followed by SD will appear in the centre of the screen.

once Note that once you are in the statistics mode, the keys shown within the blue lines are active. There are 3 such keys on the Casio fx-82MS. Make sure you can locate them. Before starting any computations always clear the statistic’s memories using Scl. Press I will use the data set A (–5, 2, 3, 4, 11) to demonstrate the use of the calculator. Note that I have shown the use of the key where necessary. Step 1: Input the observations. Use the key to input data (no need to press ). The display should read n = 5. (This means 5 observations have been input). Step 3: Display the mean and standard deviation.

Press the display shows three alternatives x x? n x? n-1 Press gives x = 3 Press gives x? n = 5. 099019514 Press gives x? n–1 = 5. 700877126 Mastering the Calculator using the Casio fx-82MS 27 Example Use your calculator to find the mean, standard deviation and variance for data set B: –18, 1, 3, 9, 20. (the variance is the square of the standard deviation) __________________________________________________________________________ After you are in the statistics mode and cleared the statistics memories, the keystrokes required are: and the display will read 3 and the display will read 13. 87443693 and the display will read 192. 5

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. = ? x2 = ? x = n = 815 = 15 = 5 If you have made an error with inputting your data you can correct it by using the up and down key. For example, you input 4, 5, 60, 7, 9 and you meant to input 6 instead of 60. Press the reads x3 = 60, then press . You now have the correct data. key until the display In the example below, the progressive calculations are shown simply to give you some understanding of the underlying processes – you should do one or two examples in detail and then check them by calculator.

28 Mastering the Calculator using the Casio fx-82MS 10. 2 Mean and standard deviation of frequency distribution Given below is the frequency table for the weights (kg) of a random sample of 30 first year university female students. Find the standard deviation, the variance and the mean. Graduate’s weight (kg) 60 61 62 63 64 Frequency 2 14 8 1 5 Cumulative frequency 2 16 24 25 30 The calculations needed to obtain the standard deviation without statistical keys for these data are: ? x2 = 602 ? 2 + 612 ? 14 + 622 ? 8 + 632 + 642 ? 5 = 114 495 ? x = 60 ? 2 + 61 ? 14 + 62 ? 8 + 63 + 64 ? 5 = 1 853 s =

? x2 – ( ? x i ) ? n i ————————————-n–1 114 495 – ( 1 853 ) ? 30 ——————————————————- = 29 2 2 = Thus: 114 495 – 114 453. 6333 ——————————————————— = 29 1. 4264 s = 1. 2 kg and s2 = 1. 4 kg2 ?x 1853 x = —– = ———– = 61. 8 kg n 30 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. The calculator usage now has a small modification because we have been given the frequencies for the variable values. (There is no need to input each single observation. ) Mastering the Calculator using the Casio fx-82MS 29 The keystrokes required are: The display should read n = 30. and the display should read 61. 766667 and the display should read 1. 1943353 and the display should read 1. 4264369 Thus, as expected s = 1. 2 kg, s2 = 1. 4 kg2 and x = 61. 8 kg Exercise 6 Find the mean, standard deviation and variance of (a) The annual rainfall data for the years 1971 – 1990

Year Rain (mm) Year Rain (mm) 1971 1 340 1972 990 1973 1 120 1974 1 736 1975 260 1976 1 100 1977 1 379 1978 1 125 1979 1 430 1980 1 446 1981 1 459 1982 1 678 1983 1 345 1984 978 1985 1 002 1986 1 110 1987 1 546 1988 1 672 1989 1 467 1990 1 123 30 Mastering the Calculator using the Casio fx-82MS (b) The sample of snail foot lengths Snail foot length (cm) 2. 2 3. 4 2. 5 3. 3 4. 7 4. 1 1. 6 4. 3 3. 1 3. 8 3. 5 3. 1 3. 4 3. 7 3. 2 4. 5 3. 3 3. 6 4. 4 2. 6 3. 2 3. 8 2. 9 3. 2 3. 9 3. 7 3. 1 3. 3 4. 1 3. 0 3. 0 4. 7 3. 9 1. 9 4. 2 2. 6 3. 7 3. 1 3. 4 3. 5 Answers: (a) Rainfall statistics mean: µ = 1 265. 3 mm standard deviation: ?

n-1 = 336. 4 mm variance: ? 2 = 113141. 7 mm2 (b) Snail statistics mean: x = 3. 4 cm standard deviation: s = 0. 70 cm variance: s2 = 0. 49 cm2 Mastering the Calculator using the Casio fx-82MS 31 11. Linear regression To access the linear regression mode you press then a small REG appears key once followed by , accesses the keys with ? ? in blue For entering the first set of data for entering the second set of data Example Suppose we had a sample of 10 of the same type of banana. Their lengths and skin thicknesses were measured. Below is a summary of the results. Banana Length (mm) Thickness (mm) 1 16. 2 1. 1 2 15.

8 1. 2 3 16. 5 1. 1 4 14. 9 1. 0 5 16. 9 0. 9 6 16. 8 1. 2 7 15. 6 1. 1 8 15. 6 1. 2 9 15. 7 0. 9 10 15. 4 0. 8 STEPS 1. To put the calculator into regression mode press (1 = Linear Regression; there are 5 other types) 2. Think of the sample of bananas as having two variables: – let x be the variable length of banana – let y be the variable thickness of banana once then 32 Mastering the Calculator using the Casio fx-82MS For each banana you have to put in both numbers. To put in the first set of numbers, press the following keys: is used for the 1st variable is used for the 2nd variable Continue in this manner

After you have input all the numbers. The display should read n = 10 To find the linear regression equation in the form y = a + bx you need to find the value of a and b. These keys are found under Press a is 0. 3651 Press b is 0. 0430 ?the equation is y = 0. 3651 + 0. 0430x To find the correlation coefficient press r = 0. 1928 There is not a high correlation between the thickness of bananas and the length of bananas tested. The calculator will also give you other statistics about this sample. Use mean thickness (1. 055mm) or the standard deviation (0. 64mm). x: to get the 15. 94

Mastering the Calculator using the Casio fx-82MS 33 x ? n–1 : 0. 6432 Press to get y: 1. 05 0. 1433 y ? n–1 : You can also use the thickness then press to predict the length, given the thickness. If 0. 6 is the = 5. 47mm. Similarly, if the length is 12mm then press to get 0. 88 mm as the predicted thickness. 34 Mastering the Calculator using the Casio fx-82MS 12. Trigonometric functions The keys involved are: Important: Make sure that your calculator is in the correct mode. For example, if your calculator has R or G on the display and you wish to work in degrees, press mode twice and then select 1 for degrees.

Your screen should now display D. Example 1 In the right-angled triangle below, the length of the side opposite the 20° angle needs to be calculated. x cm 20? 5 cm To find the length of the side labelled x cm, use x 5 ? x = 5 tan 20° tan 20° = Mastering the Calculator using the Casio fx-82MS 35 The keystrokes on the calculator are: or The display should read 1. 819851171, so the length of x is about 1. 8 cm. Example 2 In the right-angled triangle below, the length of the hypotenuse needs to be calculated. 7 cm x cm 20? To find the length of the side labelled x cm, use: sin 20° = 7 x 7 ? x= sin 20°

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 ? in degrees: 2 cm ? 1 cm 36 Mastering the Calculator using the Casio fx-82MS In the diagram, cos ? = 1 2 To find the value of ? , you need to use the cos–1 key. The calculator keystrokes are: Note: You must first get the value of the division by using the brackets. Your display should read 60°. If it does not, check that you are in degree mode. 13. 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 shift key: The ‘log’ key uses base 10 and the ‘ln’ key uses base e (natural logarithm). Mastering the Calculator using the Casio fx-82MS 37 Example 1 Solve equation 2 a = 20 Taking logs of both sides; log 2a = log 20 ? a log 2 = log 20 ? a= log 20 log 2 To find the value of a, the keystrokes are: The display should read 4. 3219281. So, 24. 32 ? 20 . Confirm this by using the Example 2 Given log y = 1. 584 , find the value of y log y = 1. 584 ? y = 10 1. 584 key. The 10 x key is above the log key.

Hence the keystrokes are: The display should read 38. 370725 Example 3 (harder) Given logx 6 = 1. 5 , find the value of x log x 6 = 1. 5 log 6 = 1. 5 log x log 6 ? = log x 1. 5 ? To find log x, the calculator keystrokes are: 38 Mastering the Calculator using the Casio fx-82MS The display should read 0. 5187675. Since this is the value of log x, you still need to find x where x = 100. 5187675 Without removing the answer of 0. 5187675 on your display, press: Your display should now read 3. 3019272 Note: You could use the ‘ln’ key instead of the ‘log’ key – the answer would still be the same. Try it! 14.

Degrees, minutes, seconds The key involved is This key can be used for problems involving degrees, minutes and seconds or hours, minutes and seconds. Mastering the Calculator using the Casio fx-82MS 39 Example 1 Suppose that you have a trigonometric problem where the angle involved is given in degrees and minutes. e. g. Find x where x = 4 ? sin 25° 36 ’ The keystrokes involved are: The display should show 1. 728343, so x is approximately 1. 73 Example 2 If you wish to convert an angle in degrees to its equivalent in degrees, minutes and seconds: e. g. 34. 88°, the keystrokes are: The display should read 34°52°48.

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 read 13. 638611 (hours). 40 Mastering the Calculator using the Casio fx-82MS Mastering the Calculator using the Casio fx-82MS 41 Review calculator exercises 1. Perform the following calculations (i) (5 + 4) ? 3 (ii) 12. 5 – 8 ? 0. 5 3? 6–8 (iii) ——————-4 12. 8 (iv) ———————-16. 5 – 3. 8 7 ? 0. 41 + 17 (v) ——————————(4 + 7) ? 2 2. 4 (vi) —–3 -4 (vii) 145. 6 – 17. 2 ? 5 2 2 (viii) 345. 6 – 17. 2 ? 5 3 ? 27 (ix) 25 + ——————-1.

02 30 0. 2000 0. 1366 (x) ( 4. 1333 – 3. 000 ) ± 2. 015 —————— + —————–6 6 ( 20 – 30 ) ( 50 – 60 ) ( 100 – 90 ) (xi) ————————— + ———————— + ———————–90 60 30 2 2 2 2 2 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) ? x (ii) ? x2 (iii) (? x)2 Explain in words what each of these mean. 42 Mastering the Calculator using the Casio fx-82MS Calculator solutions 1. (i) (5 + 4) ? 3 Make sure your calculation is in comp mode. = 27 (ii) 12. 5 – 8 ? 0. 5 3?

6–8 (iii) ——————-4 Either (3 ? 6 – 8) ? 4 = or 3 ? 6 – 8 = ? 4 = = -3. 5 = 2. 5 12. 8 (iv) ———————-16. 5 – 3. 8 Either 12. 8 ? (16. 5 – 3. 8) = or 16. 5 – 3. 8 = x–1? 12. 8 = 7 ? 0. 4 + 17 (v) —————————(4 + 7) ? 2 Either … ? ((4 + 7) ? 2) = or … ? (4 + 7) ? 2 = 2. 4 (vi) —–3 -4 Either 2. 4 ? (3 ? 4) =, or 2. 4 ? 3 ab/c 4 = (vii) 145. 6 – 17. 2 ? 5 2 = 1. 007874 = 0. 9 = 3. 2 = 9. 296.. Either 145. 6 – 17. 2×2 ? 5 = v =, or v (145. 6 – 17. 2×2 ? 5) = (viii) 345. 6 – 17. 2 ? 5 Either 345. 6 – 17. 2×2 = v ? 5 = or (345. 6 – 17. 2×2) 2 = 1. 41.. v? 5= = 39. 4985 3 ?

27 (ix) 25 + ——————-1. 02 30 25 + 3 ? 27 ? 1. 02 ? v 30 = 0. 2000 0. 1366 (x) ( 4. 1333 – 3. 000 ) ± 2. 015 —————— + —————–6 6 2 2 = 1. 3325 or 0. 9341 Mastering the Calculator using the Casio fx-82MS 43 Calculator keys: 0. 1366 x2 ? 6 + . 2 x2 ? 6 = v = x 2. 015 = + 4. 1333 – 3 = 4. 1333 – 3 – = ( 20 – 30 ) ( 50 – 60 ) ( 100 – 90 ) (xi) ————————— + ———————— + ———————–90 60 30 Calculator keys: 2 2 2 = 6. 1111 (100 – 90) x2 ? 90 + (50 – 60) x2 ? 60 + (20 – 30) x2 ? 30 = 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) ? x (ii) ? x2 (iii) (? x)2 Explain in words what each of these mean. To do this on the calculator, you must be in SD mode. Enter the data: mode 1 2. 5 M+ 6. 2 M+ (–) 2. 1 M+ . 04 M+ 8. 2 M+ 7. 4 M+ 2. 1 M+ (–) 1. 7 M+ Press the key that says ? x ( (i) 22. 64 ) This gives the total growth over the last 8 years Press the key that says ? x2 ( of the squares of the growth in each year Press ? x and x2. This gives the square of the sum of the growth. (ii) 178. 4016 ) This gives the sum (iii) 512. 5696 44 Mastering the Calculator using the Casio fx-82MS Your notes