1. Navigating Your Casio Calculator Dr J Frost (jfrost@tiffin.kingston.sch.uk) www.drfrostmaths.com Last modified: 26 th November 2013

2. For details on statistical calculations, press the ‘Mode’ button. Click a button.

3. You didn’t press a button for which information is provided. Click the button below to go back. < Return

4. Mode Menu < Return 1 COMP Puts the calculator in normal ‘computation’ mode. You would need to do this if you were previously using stats/table mode and want to revert back to regular calculations. 2 STATS > Go 3 TABLE > Go 4 VERIF Allows you to calculate various statistics based on a table of data, e.g. mean, variance, standard deviation, the equation of the line of best fit, strength of correlation, etc. Allows you to generate a table of values for a given function, like the table on the right. 123 014 Allows you to verify whether an equation or inequality is true.

5. Special Buttons SHIFT If you press a button after pressing SHIFT, it will use the operation indicated by the gold text above that button. < Return ALPHA If you press a button after pressing ALPHA, it will use the operation or letter indicated by the red text above that button. The letter X is particularly useful for entering a function. Click the ‘MODE’ button then ‘TABLE’ for more information.

6. Arrow Buttons You can use the up and down arrow buttons to retrieve previous calculations (a bit like your internet browser’s ‘Back’ and ‘Forward buttons!) You’ll need the left and right button for example when entering a fraction, and want to switch between numerator and denominator. The arrow buttons are also used when navigating a table (e.g. in Statistics mode) < Return

7. On Engineers are yet to discover the true nature of this button, which has eluded mankind for centuries. But some mathematicians have theorised that pressing this button turns the calculator on. < Return

8. Multi-Statements x3x3 The semi-colon allows you to write multiple different expressions, and evaluate them one at a time. [2] [+] [3] [ALPHA] [:] [4] [x] [7] [=]  5 [=]  28 < Return :

9. The Absolute Function Abs It’s particularly useful for C3/C4 at A Level, if you want to check your sketch for a function (involving the modulus function) is correct by generating a table of values. < Return

10. The Reciprocal Function x -1 < Return

11. The Factorial Function < Return x -1 x!

12. The Logarithm Function log Just as the ‘square root’ function is the opposite of ‘squaring’, log 2 for example is the opposite of finding 2 to the power of something. log 2 32 = 5, because 2 5 = 32 log 3 81 = 4, because 3 4 = 81 Use the arrow keys to move between the boxes after pressing the button. When you use the second log button with no ‘base’, it uses base 10. < Return log

13. Fractions < Return

14. Root Functions 3√3√ < Return √ √

15. Recurring Decimals < Return

16. Powers x < Return

17. Natural Logarithm ln < Return

18. Euler’s Constant e < Return e

19. Degrees, Minutes, Seconds When you have some angle or time as a decimal, press this key to convert it to degrees, minutes (a 60 th of a degree) and seconds (a 60 th of a minute). < Return Fun fact: Whereas the ‘decimal’ system is base 10 (i.e. each digit can have one of 10 values: 0 to 9), the ‘sexagesimal’ system is base 60. Subdivisions of hours and degrees are in sexagesimal.

20. Factorise FACT This finds the prime factorisation of a number. You need to enter the number first, then press =. THEN use the FACT button. < Return [120] [=] [FACT]  2 3 x 3 x 5

21. Hyperbolic Functions hyp < Return

22. Trigonometric Functions sin Trigonometry allows you to find missing sides and angles on triangle. For right-angled triangles, sin, cos and tan give the ratio of different pairs of sides. For example, to solve the following problems... < Return cos tan sin -1 x 3 x = 3sin60 60° 3 4 y = cos -1 (3/4) y

23. Brackets ( Brackets are hugely handy in ensuring operations in your expression are evaluated in a certain order. Recall that in ‘BIDMAS’, ‘Brackets’ comes first. < Return )

24. Storing values in variables STO In algebra we use variables to represent values. We can use the letters A, B, C, D, E, F, X, Y on the calculator for this purpose. < Return Store store 3 + 5 in memory as ‘A’: (Note, don’t press the ALPHA button after pressing STO) [3] [+] [5] [STO] [A] To evaluate 10A: [10] [x] [A] [=]

25. Engineering Notation ENG Engineering notation is similar to standard form, except the power of 10 can only be a multiple of 3. < Return 

26. Percentages % The % button is of fairly limited usefulness. It converts a percentage into its equivalent decimal (by dividing by 100). [90] [x] [40] [%] = 36 (this found 40% of 90) < Return

27. Comma, The comma is used for used in generating random integers, and converting between rectangular and polar coordinates. Click the RANDINT, REC or POL buttons for more information. < Return

28. Converting between decimal/surd/fraction < Return

29. Improper Fractions and Mixed Numbers < Return

30. Independent Memory M+ The independent memory is useful if you’re trying to keep a running total of calculations. Once entering an expression, press [M+] instead of [=] to add your result from the running total. To subtract the result, use [M-] To display the currently stored total, use [RCL] [M] < Return M- M (Your value will be preserved when the calculator is turned off. See the [CLR] button to see how to wipe the value.)

31. Clear Memory CLR This allows you to delete the values you’ve stored for variables and in independent memory. < Return

32. Permutation Function nPr This function used in ‘Combinatorics’ (the study of arrangements of items and structures), allows us to find the number of ways of picking r objects from n, and putting them in a line. Example: We have 5 cards with the letters A, B, C, D, E. We want to put 3 in a line. This gives words such as ABC, AEC, DEA, etc. How many possibilities are there? [5] [nPr] [3]  60 This function tends not to be used very often – the ‘choose’ function (nCr) is much more common. < Return

33. Choose Function nCr This function used in ‘Combinatorics’ (the study of arrangements of items and structures), allows us to find the number of ways of choosing r objects from n, such that the order of the items doesn’t matter. Examples: “How many different possible lottery tickets are there?” You choose 6 numbers from 49. So: [49] [nCr] [6] [=]  13983816 < Return

34. Polar and Rectangular (Catersian) Coords Pol Cartesian coordinates are represented by x and y values (and any further dimensions). Polar coordinates however are represented by the distance of the origin, and the angle anticlockwise from the x-axis. < Return Rec (√3,1) 2 30  x y In Cartesian coordinates: (√3,1) In Polar coordinates: ( 2, 30  ) To convert Rectangular to Polar: [POL] [ √ ][3] [,] [1] [=] To convert Polar to Rectangular: [REC] [2] [,] [30] [=]

35. Statistic STAT Allows you to calculate a statistic (such as mean, variance, correlation strength) based on a data set you’ve entered. Click on the MODE button from the calculator display and then ‘Stats’ for more information. < Return

36. Rounding Rnd Rounds a number according to the current accuracy set on he calculator. < Return

37. Random Numbers RAN# < Return RanInt

38. Pi  Pi is typically used in calculations to do with circles. It is a constant with the value 3.1415... < Return 3 Circumference Area

39. Standard Form x10 x < Return

40. The Answer Button ANS < Return

41. Stats Mode < Return 1 - VAR > Click to see how to enter your data. This mode allows you to calculate various statistics based on a table of data, e.g. mean, variance, standard deviation, the equation of the line of best fit, strength of correlation, etc. You’ll be presented with various options: For your single variable, calculates things like mean, standard deviation, variance, etc. Single Variable (X) Use when you have just one variable, e.g. height, weight, shoe size. Two Variables (X, Y) Use when you have a scatter diagram, e.g. hours revised against test score. A + BX Assumes your data points roughly follow a straight line, i.e. have a linear relationship. e.g. will find a straight line of best fit for you. Use if you’re trying to find the Product Moment Correlation Coefficient (which assumes a linear relationship). _ + CX 2 Assumes y has a quadratic relationship to x, i.e. Your points roughly fit onto a parabola. ln X Assumes your data follows the model y = a ln X + b y = a + bx y = a + bx + cx 2

42. Stats Mode – Entering Data < Back A table should appear. Enter each X value in your data, pressing [=] after each one. If you have two variables, your Y value will temporarily be set to 0. If you have a second variable, use the arrow keys to move to the top of the Y column. Now enter your Y values using [=] again. Once you’ve finished entering your data, press the [AC] button to ‘commit’ your table, so that you can now calculate statistics based on it. > Click to see how you now calculate statistics based on your table. AC

43. Stats Mode – Calculating Statistics < Back Presuming you have just pressed the [AC] button while in Stats mode: < Home 1 |STAT| Use the |STAT| button (SHIFT and 1). This will present a number of options... Sum Finds the sum of the values of your variables. e.g.  x,  x 2 (useful when calculating variance),  y,  xy, etc. Var Allows you to calculate the mean of x or y, the number of items n, and the population or sample standard deviations. Reg Will find the a, b (and c) in your line or best fit, whether a + bx (if a straight line) or otherwise. Will also find your correlation coefficient r (known as the PMCC for the linear case). MinMax Unsurprisingly, will find the maximum or minimum X or Y value. Once you’ve chosen a statistic to use, it’ll appear in your calculation area. You can always combine multiple together. Once done, press [=] < Home> Practice

44. Stats Mode – Exercise < Back< Home Use your calculator to directly calculate the following statistics. Age of dwarf (x)Orcs killed in battle (y) 461423 571203 26697 1051948 A formula for estimating the number of orcs killed (y) using the age of the dwarf (x). (Use Reg  a to find the y-intercept and Reg  b to find the gradient of your line of best fit) The Product Moment Correlation Coefficient. (Use Reg  r. -1 means perfect negative correlation, 0 means no correlation, and 1 mean perfect positive correlation) Click to Reveal

45. Table Mode < Back In some exam questions you’re asked to calculate a table of values for a given function: x-0.500.5 f(x)1.50.750.50.75 f(x) = x 2 + 1/2 Your calculator can do this for you. Once in table mode, your calculator display should look like this: Now input some expression in terms of X. You can use [ALPHA]  [X] to use X in your expression. > Next

46. Table Mode < Back Now press [=]. You will be asked for the ‘Start’ number. In our table, the first value of x is -1. Type in -1 and press [=] You will now be asked for the ‘End’ number. In our table above, the last value of x is 1. Type 1 then press [=]. Finally you’re asked for the step size. This is how much x is increasing by each time. In our table, it’s 0.5. Once you press equals, you’ll be presented with a nice looking table. You can use the arrow keys to scroll through it. x-0.500.51 f(x)1.50.750.50.751.5 < Return

47. Secret Menu! 7 Hold [SHIFT] and [7] and then press [ON]. Now press [9], then [SHIFT] 5 times. After waiting for the messages to display, press [AC]. You can change the screen contrast, and pressing [AC] again activates a button test – pressing each button (in the correct order!) displays a different integer. < Return