Casio FX9750GII - 0CALCULATOR GRAPHIC Getting Started

Getting Started with the Casio Graphic Calculator. Chapter 1 Getting Started Chapter 2 Graph Drawing Chapter 3 Option, Variations and Catalogue Keys Chapter 4 Statistics Chapter 5 Programming Chapter 6 Other Icons Chapter 7 Miscellaneous Functions of the FX9750GII Chapter 8 Normal, Binomial and Poisson Distributions Chapter 9 Connecting the FX9750GII to other devices Chapter 10 Key Index

The 14 Main Menu Icons Select any mode from the MAIN MENU by using the arrow keys to highlight the MODE icon that you want or press any of the digits 1 ~ 9 or letters A ~ E. RUN–MAT The scientific calculator with OPTION features. To enter, and perform row/column operations on Matrices, up to dimensions of 8 x 8, basic calculations to complex number and calculus calculations, to name a few. STAT For statistical calculations and statistical graphs, with univariate or bivariate data. Statistical modelling using Binomial, Poisson and Normal distributions to name a few. To manipulate lists (this can also be done in the STAT mode) or change List Files. GRAPH To graph and analyse functions and relations, parametric graphs and polar graphs. Storage of up to 20 different functions, with the ability to solve and differentiate numerically. Equations entered can be of the form “Y=” or “X=”. DYNA To look at the effect of a changing constant or coefficient on the graph of a function. A great demonstration tool for dynamic and animating graphs. TABLE Will produce a table of values for any function and its derivatives if required. RECUR To produce tables and graphs from, and analyse, recursive relations, such as arithmetic and geometric sequences and series. Congratulations on your recent purchase of the CASIO® FX9750GII.

rectangular, parametric or polar formats. EQUA Will solve simultaneous equations (up to 6 x 6) and polynomials (degree 2 ~ 6), displaying solutions in real and complex form. Also contains an equation solver to find the value of any pronumeral (letter) in an equation entered. PRGM Program mode. Use this mode to write and store programs, you can execute (run) the programs here also. TVM Time, Value of Money and other financial and economic calculations. LINK Allows the calculator to link to a PC or another CASIO calculators to transfer programs and data, via the USB or 3-pin. Connection can also be made to a data projector and settings. E-CON Connection to data logger EA200 and Motion sensors and other data collection probes. MEM Memory. Shows memory usage and allows you to reset individual icon memory or the entire calculator. Note that resetting the calculator will delete stored data and programs. Contrast adjusts the contrast and grey scale balance. SYSTEM System setting and operating version. Language setting for calculator display.

Switching on and off In order to start your Casio FX9750GII, after you have placed the four AAA batteries into the battery compartment, do the following: Screen This is called the MAIN MENU and can be accessed by: What are the ‘Icon’ modes? There are 14 different ‘icons’ that are accessible from the MAIN MENU by using the arrows to cover the particular icon that you want to be in, or each icon has a number or letter associated with it, for quick key entry. The user can use either the number keys 1 - 9, or the letter keys A - E OR use the replay arrows to highlight the icon and then press In the RUN-MAT icon Most of the calculator performances can be executed in this mode. The calculator has T.A.L (True Algebraic Logic) embedded into its functionality. Setting up within each icon This screen display assists the user in setting up the calculator to the specifications that they require. By selecting the appropriate grey [F1], [F2], [F3], [F4], [F5] or [F6] keys you select the settings you require.

Display This mode determines the form in which answers obtained from calculations will be displayed. Mode, Fraction result, Function Type, Draw Type, Derivative, Angle, Complex mode, Co-ordinate, Grid, Axis, Label, Display and Simplify are self-explanatory settings. Example NORM 1 NORM 2 Editing entries For editing any calculations, using the replay arrows changes can be made easily to text or numerical entries. Editing can also be done by using the [DEL]ete and [INS]ert keys, move the cursor to where you want to do the editing and strike these keys to complete the editing. Toggling between the TEXT and GRAPH screen G T There are two screens that ‘sit’ on top or underneath each other, the TEXT and GRAPH window. By pressing [SHIFT] [F6] you can toggle between the two screens.

Result 8 + 1 2 ÷ 4 - 2 then EXE Example 2 Simplify (8 + 12) ÷ 4 – 2 Result ( 8 + 1 2 ) ÷ 4 - 2 then EXE Example 3 Simplify 8 + 12 ÷ (4 – 2) Result 8 + 1 2 ÷ ( 4 - 2 ) then EXE Example 4 Simplify (8 + 12) ÷ (4 – 2) Result ( 8 + 1 2 ) ÷ ( 4 - 2 ) then EXE KEY then KEY fx9750GII CHAPTER 1 | PG 9 Clear Screen Clearing the Graphical Screen so that you don’t superimpose graphs can be done either by: Basic activities in RUN-MAT icon BEDMAS to reinforce the importance of the order of mathematical operations. Enter V-Window and alter the viewing screen domain and range values as desired. OR Enter Sketch.

Result 3 a b/c then 1 a b/c then 7 + 2 a b/c then 3 a b/c then 5 then EXE Example Convert result of 3 1/7 and 2 3/5 Result SHIFT F↔D Example Convert result of 3 1/7 and 2 3/5 Result F↔D Example Enter 3/8 : Result 3 ÷ 8 then EXE then F↔D Decimal Fraction GETTING STARTED Basic activities in RUN-MAT icon cont. Fractions, decimals and percentages Fractions can be entered into calculations with the fraction key. To convert to a mixed fraction To convert to a decimal To enter a fraction without the fraction key OR

Result 3 a b/c 1 6 x 2 . 8 then EXE Decimal Fraction Example Calculate 48% of $16.40 Result 4 8 ÷ 1 0 0 x 1 6 . 4 then EXE 4 8 a b/c 1 0 0 x 1 6 . 4 then EXE Example Evaluate √25 Result SHIFT x2 2 5 then EXE Example 2 Evaluate 3√27 Result SHIFT ( 2 7 then EXE Example 3 Evaluate 2 5 Result 2 ^ 5 then EXE fx9750GII CHAPTER 1 | PG 11 Percentage key Powers and roots Fractions and decimals can be calculated together. The graphics calculator does not have a specific ‘Percentage’ key. Just remember that 48% is the same as 48/100 or 0.48.

Result ( 3 0 . 3 4 - 4 ) ( 4 7 . 5 + 4 ) then EXE Example Calculate V = (A – 4)(B + 4) where A = 30.34 and B = 47.5 Result 3 0 . 3 4 → A then EXE 4 7 . 5 → B then EXE ( A - 4 ) ( B + 4 ) then EXE GETTING STARTED Basic activities in RUN-MAT icon cont. Powers and roots cont. Algebraic Substitution Enter the calculation by replacing each letter in the formula with its corresponding number. When you have a number of algebraic substitutions to do then it would be easier to use the memory aspect of the calculator keys. There are 28 different storage places i.e. A ~ Z, θ and Γ. These are accessed via the [ALPHA] key then the associated key required. You ‘assign’ a value to the letters you want to use with the [→] button, then enter the algebraic expression into the calculator. Press [EXE] for the calculator to store the value in the memory.

Key AC/ON SHIFT F4 F5 Result Key F1 SHIFT x2 EXE Result Drawing graphs is easy using the FX9750GII! They can be drawn in the RUN-MAT or GRAPH icons. RUN-MAT icon The functions (and more) listed below (and there are many more) have been ‘installed’ into the calculator for quick graphing. Each has its own unique pre-set domain and range values. The graph as it appears on the screen gives a clear idea of the shape but no indication of the values on the horizontal or vertical axis, except for ------+------ marks on the axes. Note: There is no need to include the ‘x’. To find information on a graph’s scale View the domain and range values in V-Window. This display tells the user that on the x-axis the scale is 2, and hence the marks on the x-axis are 0, 2, 4, 6, 8, 10. The y-axis has a scale of 1 and hence the marks on the y-axis are -1, 0, 1, 2, 3, 4. KEY RESULT

Clearing the screen [Cls] Graphs that need to have the Domain and Range edited Changing the values in the V-Window is easily executed. Single editing or pre-set [F1] [F2] [F3]. Varying the Domain and Range is a necessary skill when developing the connections between the graphical, symbolic and numerical aspects of equations. Tracing functions Note: Numerous graphs can be superimposed, allowing linear programming. Separating each graph equation with a ‘ : ’ (colon) provides functions that can be traced and if necessary zoomed in on to find vertices that define the feasible region (points of intersections) etc. After each graph has been drawn then [SHIFT] [F4] [F1] key followed by [EXE] is necessary to clear the previously drawn graph, otherwise the graphs will be superimposed. Using the left and right arrows the user can trace over the graph and give accurate x and y values of many points on the curve. KEY RESULT Example For the graph y = (x - 1)/(x + 2) a suitable range could be -4 < x < 3 and -6 < y < 6 Result - 4 EXE , 3 EXE , 1 EXE , , - 6 EXE , 6 EXE , 1 EXE then EXIT Example For the graph y = x^2, (i.e. y = x2) a suitable range could be -4 < x < 3 and -6 < y < 6. Key SHIFT F1 Result KEY KEY The interpretation of the graphed functions is supplemented by the use of the Trace key. The (x, y) values of points on the curve are displayed underneath the drawn graph. fx9750GII

The ‘zooming’ is easily initiated when parts of a graph need to be seen in more detail - ‘roots’ to the equation, maximum or minimum points or other aspects under investigation. Plotting points Plotting points from tables for example is easy to do, as is drawing a line between these points. By choosing BOX [F1] you can decide what ‘new’ domain and range values will be used for the V-Window. To make the BOX use the arrows to determine where a vertex of the BOX is to be then [EXE]. Use the arrows again to complete the BOX. When you are satisfied with its position, press [EXE] and the new view window will be drawn. Note: 1. The V-window will determine how ‘close’ the point being plotted is. The dimensions of the screen are 123 pixels wide and 63 pixels deep. This is determined by the INITial settings in the V-window. More about the V-window settings later (see index at back of book). 2. In the RUN-MAT icon you do not have access to the G-Solve features. Note: The different ‘menu bars’ as listed below. FACT Scale factor for V-Window for IN ORIG The original graph drawn before zooming in or out IN The calculator will zoom in on centre of screen SQR OUT The calculator will zoom out on centre of screen RND AUTO The calculator will calculate what it thinks best for the graph to be drawn INTG Next selection window PRE Example Plot the points 2, 3 & 5, 6 Key SHIFT F4 F6 F1 F1 2 , 3 EXE EXE F6 EXE F1 5 , 6 EXE EXE SHIFT F6 EXIT F2 F1 EXE Result KEY RESULT KEY

GRAPH icon From the MAIN MENU enter into the GRAPH icon by either moving the cursor to highlight the icon or pressing the [3] key. This part of the calculator has a lot of functionality. Stores graphs, up to 20 functions that you use regularly or ‘families’ of graphs where relationships and special features can be viewed. All of the ‘Function’ key menus, such as Trace, Zoom, V-Window, Sketch, Graphical Solutions and Graph - Text are also available. It is also where you can view Graph - Graphs and Graph - Table split screens. The screen is split vertically, giving very good views of what you have chosen to see. You can draw equations and in-equations, rectangular, parametric and polar graph types. By selecting [F3] you can view the different types. How to chose the calculator settings (Set Up) G-Solve features Once you have drawn a graph then you have access to the G-Solve features. cont. on next page KEY KEY Example Collate information about the function y = (x-2)(x+1) Result (x+2) Store the expression in position Y1 ( X,θ,T - 2 ) ( X,θ,T + 1 ) a b/c ( X,θ,T + 2 ) then EXE Draw the graph F6 Open the G-Solve selections SHIFT F5 fx9750GII

Other G-Solve features are shown in other chapters in this book where appropriate. This activity shows how the calculator can be used: to draw multiple lines; to see the relationship to the change in the constant ‘c’ in y = mx + c and to draw multiple parabolas; to see the relationship to the change in the coefficient ‘a’ in y = ax2 + c. A line - multiple representations for y = x + c Note: Make sure that the V-Window is appropriate to see the graphs that you will be drawing. Enter [SHIFT] [F3] then the option that you require, in this case, [F1] for INITial. Go back to the Graph Function menu with [EXIT] or [EXE]. Using, [A=-2,0,2] at the end if the equation gives the static effect of a ‘dynamic graph’. Example Draw the graphs of y = x - 2, y = x, y = x + 2 Result X,θ,T + ALPHA X,θ,T , SHIFT + ALPHA X,θ,T SHIFT . - 2 , 0 , 2 SHIFT - then EXE EXE or F6 You will see these lines drawn one at a time. SHIFT F1 then ‘Trace’ either of the three graphs. Find the... Root/s SHIFT F5 F1 Minimum SHIFT F5 F3 Maximum SHIFT F5 F2 Y-intercept SHIFT F5 F4 Y-value calculations SHIFT F5 F6 F1 X-value calculations SHIFT F5 F6 F2

A parabola - multiple representations for y = ax2 Note: Make sure that the V-Window is appropriate to see the graphs that you will be drawing. Enter [SHIFT] [F3] then change the settings to the conditions shown here. Go back to the Graph Function menu with [EXE] or [EXIT] . Using, [A=1,2,3] at the end if the equation gives the effect of a ‘dynamic graph’. Example Draw the graphs of y = 1x2, y = 2x2, y = 3x2 Result ALPHA X,θ,T X,θ,T x2 , SHIFT + ALPHA X,θ,T SHIFT . 1 , 2 , 3 SHIFT - then EXE EXE or F6 You will see parabolas being drawn one at a time. SHIFT F1 then ‘Trace’ either of the three graphs. Example 2 Draw the graphs of y = -1x2, y = -2x2, y = -3x2 Result ALPHA X,θ,T X,θ,T x2 , SHIFT + ALPHA X,θ,T SHIFT . - 3 , - 2 , - 1 SHIFT - then EXE EXE or F6 You will see parabolas being drawn one at a time. SHIFT F1 then ‘Trace’ either of the three graphs. fx9750GII

Use [ , ] to restrict the domain values. You can ‘trace’ over the graphs by pressing [SHIFT] [F3] then use the arrows to scroll each of the graphs on the screen. Graph drawing – Zooming in and out When the V-Window (Graph Viewing Window) has not been set up for the graph that you want to see, your screen will look like either of the following images. Example Draw the graphs of y = x², -2 ≤ x ≤ 1 y = -x + 4, 1 ≤ x ≤ 3 y = -2, -4 ≤ x ≤ -2 Result X,θ,T x2 , SHIFT + - 2 , 1 SHIFT - EXE - X,θ,T + 4 , SHIFT + 1 , 3 SHIFT - EXE - 2 , SHIFT + - 4 , - 1 SHIFT - Set up the V-Window and then draw the graphs. SHIFT F3 then EXE or F6 Auto Zoom Using the AUTO ZOOM the calculator will adjust the axes so that you can see ‘your graph’ better then you can adjust the V-Window to a more appropriate scale to suit what you want. KEY If you want to, change the View-Window to ‘zoom’ in on the graphs, to get a better picture (view). To get AUTO ZOOM press [SHIFT] [F2] and then [F5]. A cursor appears in the middle of the screen. You can move it to the left, right, up or down to adjust the axes the [EXE] to redraw. cont. on next page Basic activities in the GRAPH icon cont.

Auto Zoom cont. The most important viewing windows are: Trigonometric graphs have two settings that are used most often, depending what angular measure you are in. INITial Setting STanDard Setting TRIG Setting Degree OR Radian measure Note: The more graphs that you experience drawing on the FX9750GII the more familiar you will get with understanding the relationship between the graphs and their equations that are represented algebraically. Graphing and calculating unknown x values When finding the x-value(s), given a y-value, make sure that the V-Window is set up to see the graph. Example For y = (x + 1) (x + 2) (x - 1) calculate x when y = -1 Result ( X,θ,T + 1 ) ( X,θ,T + 2 ) ( X,θ,T - 1 ) then EXE or F6 SHIFT F5 then F6 for G-Solve (helps find x-values or y-values from graphs) F2 for X-CAL (x-calculation) then - 1 then EXE y=-1 cont. on next page fx9750GII

Finding the x–intercepts (roots to the equation when y = 0) and the y–intercepts (x = 0). Make sure that the V-Window is set up to see the graph efficiently. Graphing two equations and finding the intersection points. Finding the intersection points of two graphs, where f (x) = g(x).Make sure that the V-Window is set up to see the graph efficiently. Example Graph y = x+1 Result X,θ,T + 1 then EXE or F6 SHIFT F5 for G-Solve (helps find x- and y-intercepts). F1 for ROOT (x-intercept) F4 for Y-ISCT (y-intercept) Example Solve y = (x + 1) (x + 2) (x - 1) and y = x + 1 simultaneously to find the points of intersection. Result ( X,θ,T + 1 ) ( X,θ,T + 2 ) ( X,θ,T - 1 ) then EXE X,θ,T + 1 then EXE or F6 SHIFT F5 for G-Solve (helps find intersection points). or to view multiple solutions y-intercept x-intercept intersection points Basic activities in the GRAPH icon cont. Graphing and calculating unknown x-values cont. on next page

Solving trigonometric equations It is necessary to check that the domain (x-coordinates) and range (y-coordinates) are set up for graphing trigonometric graphs, through the V-Window ( [SHIFT] [F3]). By pressing the [F2] key this sets the calculator up for TRIGonometric graphs. You can alter the settings by overriding what is already there. Example Solve sin x = 0.5 between 0º ≤ x ≤ 360º Result sin X,θ,T then EXE SHIFT F3 then F2 Set up for TRIG graphs EXIT then EXE or F6 to draw the sine curve EXIT into Y2 then 0 . 5 and EXE to store EXE or F6 to draw both graphs SHIFT F5 then F5 for G-Solve (solves the two graphs simultaneously) Search for the next solution The two solutions are x = 30o and 150o KEY Solving ‘X=…’ equations. x = y entry rather than y = x in GRAPH mode. Selecting TYPE [F3] gives you access to a number of different graph types that can be drawn. For “X =” Note: That the Graph Function at the top of the screen changes to : X= To enter in ‘Y’ use the [ALPHA] key and then the [ — ] key Use this V-Window. Example cont. F5 for ISCT (intersection points) to find all others fx9750GII

Result F3 F4 2 ALPHA — + 1 then EXE then EXE or F6 to draw the graph Example 2 Draw x = y2 + 1 Result F3 F4 ALPHA — x2 + 1 then EXE then EXE or F6 to draw the graph Other settings under TYPE [F3]: Rectangular Inequalities Polar CONVert Parametric Notes: Basic activities in the GRAPH icon cont. Solving ‘X=…’ equations.

CHAPTER 3 | PG 25 OPTN, VARS and CATALOG KEY These mathematical tools can be selected in most of the MAIN MENU icons, namely, RUN-MAT, Statistics, Graph, Dynamic Graph, Tables and Program. The OPTION key will bring these tools up on the screen for use. What is in List? What is in Matrix? What is in Complex? What is in Calculus? KEY RESULT KEY RESULT KEY RESULT KEY RESULT

KEY RESULT OPTN, VARS and CATALOG cont. What is in Statistics? What is in Conversion? What is in Hyperbolic? What is in Probability? KEY RESULT KEY RESULT KEY RESULT KEY RESULT

What is in Number? What is in Angle? What is in E Symmetry? KEY RESULT KEY RESULT KEY RESULT KEY RESULT What is in Picture? KEY RESULT

OPTN, VARS and CATALOG cont. What is in Function Memory? What is in Logic? What is in Capture? What is in Time, Value and Money? KEY RESULT KEY RESULT KEY RESULT KEY RESULT KEY RESULT

The VARIATIONS key will provide commands, settings, values and solutions to equations namely: V-Window, Factor, Statistics, Graph, Dynamic graph, Table, Recursion, Equation, Financial (TVM) and String.

The CATALOGue Key provides a list of mathematical symbols, commands to enter. These can be accessed through most of the MAIN MENU icons using the OPTN or VARS keys. They can also be accessed via [SHIFT] [4] where you will need to scroll a list and select the required command required. The catalogue can be viewed through 13 different catalogues that are linked to the MAIN MENU icons for easier access to the commands required. KEY CATALOGue Key Catalogue Screen Next Screen Catalogue Screen Next Screen All Calculation Statistics Graph Program Command Change Setup Recursion Dyanmic Graph

The mathematical and statistical commands available in CATALOGue can be accessed via the OPTN or VARS keys also. Catalogue Screen Next Screen Catalogue Screen Next Screen Table Equation Financial (TVM) String Conversion Notes:

•� Univariate�(1�variable) •� Multivariate�(2�variables). There are 24 ‘list’ spaces that you can enter data into. Lists 1 to 24 can be used in any order. The lists can be used as frequency values also. Note that you can only see 4 lists at a time. The distinction between the lists and what you propose to do with them is determined by the way you set up the calculation or graph types required and the lists you are using to calculate the numerical statistics and drawing statistical graphs. Three independent graphs can be set up as univariate or multivariate data from different or from the same lists. [F1] [F6] to SET up the statistical graph types. Graphing options are: You can enter up to 999 data points in each ‘list’ space. Note: Memory space is approximately 64000 (64k) bytes and using large data sets can utilise a lot of memory space. F1 Scatter Graph F2 Line Regression F3 Time Series F4 Pie Chart F1 Histogram F2 Box and Whisker Plot (Median) F3 Bar Graph F4 Normal Distribution F5 Broken (Frequency Polygon) F1 Linear Regression F2 Median/Median Regression F3 Quadratic Regression F4 Cubic Regression F5 Quartic Regression F1 Logarithm Regression F2 Exponential Regression F3 Power Regression F4 Trigonometric Regression F5 Logistic Regression KEY RESULT Uni-variate Data Entry Example In ‘List 1’ enter the following data. Find all of the central measures values. Draw the Box and Whisker, Histogram and Normal Distribution approximation for this data. 2 3 5 6 8 7 5 3 2 9 7 4 2 1 0 9 6 8 5 3 7 6 2 5 cont. on next page

Uni-variate cont. Example cont. Result 2 EXE 3 EXE 5 EXE 6 EXE 8 EXE 7 EXE 5 EXE 3 EXE 2 EXE 9 EXE 7 EXE 4 EXE 2 EXE 1 EXE 0 EXE 9 EXE 6 EXE 8 EXE 5 EXE 3 EXE 7 EXE 6 EXE 2 EXE 5 EXE Note: Wrongly entered scores can be edited by moving to the appropriate cell with the and typing over the score and pressing EXE Sorting data entries: F6 F1 F1 Ascending (lowest to highest) (SRT-A) F6 F1 F2 Descending (highest to lowest) (SRT-D) Enter how many list(s) to sort and then which list(s) Calculate statistics for this set of scores: F2 [CALC] F6 [SET] F1 1 Set the list to be calculated from then EXIT Make sure “1Var Freq” is set to 1 F1 [1 VAR] for the calculated statistics Scroll through the complete set of calculated statistics You can now set up the calculator to draw the statistical graphs EXIT F6 to return to the main screen F1 [GRPH] F6 [SET] F1 [GRPH1] [Graph Type] F6 then F1 [HIST] or F2 [GPH2] [Graph Type] F6 then F2 [BOX] or F3 [GPH3] [Graph Type] F6 then F4 [N-Dis] Note: You can set up any graph in any of the three [GRAPH] spaces EXIT then F1 then EXE or F2 or F3 Graph/s have been drawn Note: Lists (data) can be copied, sorted, altered and placed into other ‘list’ areas.

statistics from given data. Set up the lists so the List 1 is the x-values, List 2 is the frequency values. Score x - List 1 2 3 4 5 6 7 8 Frequency f - List 2 2 3 3 5 4 2 1 Result 2 EXE 3 EXE 4 EXE 5 EXE 6 EXE 7 EXE 8 EXE then 2 EXE 3 EXE 3 EXE 5 EXE 4 EXE 2 EXE 1 EXE F2 F6 then F1 1 EXE List 1 is now entered as the x-values then F2 2 EXE List 2 is now entered as the frequency EXIT F1 Summary statistics Scroll through the complete set of calculated statistics Bi-variate data Example Enter the following 2 variable statistics and graph a linear regression model of the data. Set up the lists so the List 1 is the Mathematics (x-values), List 2 is the English (y values). Student a b c d e f g Mathematics x - List 1 2 3 4 5 6 7 8 English y - List 2 2 3 3 5 6 7 6 Result 2 EXE 3 EXE 4 EXE 5 EXE 6 EXE 7 EXE 8 EXE then 2 EXE 3 EXE 3 EXE 5 EXE 6 EXE 7 EXE 6 EXE F2 F6 then F1 1 EXE List 1 is entered as the x-values then F1 2 EXE List 2 is entered as the y-values F1 Frequency is set at 1 Data has been set up to calculate in regression format. Note: This calculator model performs a Least Squares regression model EXIT F2 Summary statistics Scroll through the complete set of calculated statistics cont. on next page

Example 2 Enter the following two variable statistics and graph a linear regression model for the data. Set up the lists so the List 2 is the x-values, List 3 is the y-values and List 4 is the frequency. Student a b c d e f g Mathematics x - List 2 2 3 4 5 6 7 8 English y - List 3 2 3 3 5 6 7 6 Frequency f - List 4 1 2 1 1 3 2 1 Result 2 EXE 3 EXE 4 EXE 5 EXE 6 EXE 7 EXE 8 EXE then 2 EXE 3 EXE 3 EXE 5 EXE 6 EXE 7 EXE 6 EXE then 1 EXE 2 EXE 1 EXE 1 EXE 3 EXE 2 EXE 1 EXE F2 [CALC] F6 [SET] then F1 2 EXE List 2 is entered as the x-values then F1 3 EXE List 3 is entered as the y-values F2 4 EXE List 4 is entered as the frequency Data has been set up to calculate in regression format. cont. on next page Bi-variate cont. Example cont. Result You can now set up the calculator to draw the graph in regression format EXIT F6 to return to the main screen F1 [GRPH] F6 [SET] F1 [GPH1] [Graph Type] F1 [SCAT] EXIT then F1 Graph has been drawn Select the mathematical models to fit the data points F1 [CALC] F2 F1 F6 Linear model or F6 F3 F1 F6 Exponential model or F6 F2 F6 Logarithmic model

EXIT F2 Summary statistics Scroll through the complete set of calculated statistics Bi-variate cont. Editing Lists As mentioned earlier, lists can also be used for storing many types of lists. For example, recursive sequences and partial series, table values, statistical trends etc. Table values generated in the TABLE icon from the MAIN MENU can be transferred to the STAT area. Lists (data) can be copied, sorted, altered and placed into other ‘list’ areas. Place the cursor into the List column heading (destination column). Now press [OPTN], [F1] for List and [F1] again followed by the list number then [EXE]. Example Consider the following list. Enter it into List 1. Then in List 2, you require 2×List 1. List 1 1 2 3 4 5 6 7 8 9 List 2 2 4 6 8 10 12 14 16 18 Result 1 EXE 2 EXE 3 EXE 4 EXE 5 EXE 6 EXE 7 EXE 8 EXE 9 EXE then to place cursor into the List 2 column heading then 2 x OPTN F1 [List] F1 1 EXE EXE Enter the following list into List 1. Then in List 3, you require List 1×List 2 - 5. List 1 1 2 3 4 5 6 7 8 9 List 2 2 4 6 8 10 12 14 16 18 List 3 Result then to place cursor into the List 3 column heading then OPTN F1 [List] F1 1 x OPTN F1 F1 2 - 5 EXE EXE KEY

Deleting Lists Deleting list entries use either [F6] then [F3] for one entry at a time or use the [DEL] key when in the cell to be deleted. To delete the entire column use [F6] [F4] then [F1]. Note: You cannot delete rows, only columns or individual cell entries. Normal, Binomial and Poisson distributions are covered in depth in Chapter 7. Notes:

written, edited, retrieved and deleted. Access to the programming tools are through the PRGM key. The Programming Tools Menu An error in the program when it is being RUN, will be highlighted by an error message at the place the error occurs. By using the left REPLAY button, the calculator will automatically go to the error in the program, so it can be edited. Shown below are the various screens that contain the programming tools used in writing and editing programs. The manual discusses these tools in more detail, please view the appropriate pages. In preparing a programme FLOW DIAGRAMS are useful, as are DESK CHECKS. Note: In this part of the graphic calculator your imagination is the only limitation on what you can do! KEY KEY RESULT KEY RESULT KEY RESULT KEY RESULT KEY RESULT KEY RESULT KEY RESULT When you have no programmes, the first few screens will look like the images to the left. When you have programmes you will see the screens to the right. OR F1 F2 F3 F4 F5 F6 F1 F6 F2 F6 F3 F6 F4 F6 F5 F6 F6 F1 COM CTL JUMP ? CLR DISP REL I/O : STR The language is very similar to the computer language BASIC.

Example ‘Rain on the Roof’ is a simulation of raindrops that have fallen on a roof (that has been divided into 16 square) in a ‘snapshot’ in time. This is a Poisson Distribution activity that lets the ‘user’ decide how many raindrops are to fall. Bar graphs can be drawn to show the distribution to the number of raindrops that have fallen into each square. How many raindrops are to fall is given by the input value: G ‘RAIN ON THE ROOF’  “HOW MANY RAIN DROPS?” ? →G  ViewWindow 0,16.15,1,0,16,1  Graph Y=4:Graph Y=8: Graph Y=12:Graph Y=16  Graph X=4: Graph X=8: Graph X=12: Graph X=16  0→N Lbl 1 Int (Ran#x16)→A Int (Ran#x16)→B Plot A+1┘2,B+1┘2 N+1→N N>G⇒Goto 2 Goto 1 Lbl 2 0→N Example 2 ‘Number Guess Game’. The input number is entered and the reply from the program is a ‘too high’ or ‘too low’. You have 7 chances! This is a good strategy and logic game, compare the game with the notion of folding a piece of paper in half over and over again. The ‘lowest score’ is kept in memory space ‘L’. When you exit the game or turn the calculator off the memory of ‘L’ is returned to the original setting of 8. Happy guessing! Refer to the ‘Programme Mode Command List’ for entering and editing the program. (See index for page reference) ‘NUMBER GUESS’  “ GAME“ 8 → L  Lbl 1 0→C “GUESS A NUMBER” “ PLEASE” Int (Ran#x101)→N “THAT IS BETWEEN 0 X 100 YOUR GUESS IS...” Lbl 2 ?→G C+1→C G=N⇒Goto 5 C=7⇒Goto 4 G>N⇒Goto 3 “TOO LOW” “GUESS AGAIN” Goto 2 Lbl 3 “TOO HIGH” “GUESS AGAIN” Goto 2 Lbl 4  “OUT OF GUESSES TRY AGAIN” “THE NUMBER WAS” N Goto 6 Lbl 5 “YOU GOT IT IN” C “GUESSES” C

program that finds all factors of any input number, checks whether it is prime, and / or a perfect number and counts the number of factors. A program that can stimulate a project on ‘Special Numbers’, for example. The calculator executes about 550 calculations a minute. Try checking some of those 2n-1 primes! Refer to the ‘Programme Mode Command List’ for entering and editing the program. (See index for page reference) “FACTOR OF NUMBERS”  Lbl 0 ?→A 0→Z 0→K 0→N Lbl 1 0→B 0→C 0→D K+1→K Int (A÷K)→B A÷K→C B-C→D D=0⇒K D=0⇒N+1→N D=0⇒B+Z→Z A=K⇒Goto 2 Goto 1 Lbl 2 “INPUT NUMBER” A “PERFECT NUMBER CHECK” Z “” N=2⇒Goto 3 Z=2xA⇒”THE INPUT NUMBER IS A PERFECT NUMBER” “” “THERE ARE” N “FACTORS” “ALL FACTORS ARE NOW FOUND” “” “PLEASE TRY AGAIN” Goto 0 Lbl 3 “THE INPUT NUMBER IS A PRIME NUMBER” Example 4 The ‘Mendelbrot’ is a well-known use of imaginary numbers, named after its discoverer, the US mathematician Benoit Mendelbrot. The program draws part of the Mendelbrot Set. ‘Zooming In’ on a specific part of the Mendelbrot Set can be done by editing the Viewing Window in the first 4 lines of the program. The set is related to the complex function f(z)=z2 + c, with c being a constant. Many ‘spikes’ are evident around the boundaries and are very similar to each other, that is, they are smaller versions of the larger ones The program requires a lot of calculations to be made, as the screen is set to 127x63x30. That is, about ¼ million calculations in total. Try the View Window at: (a) -1.5 < x < -1.1 and -0.1 < y < 0.1 (b) -0.8 < x < -0.4 and 0.5 < y < 0.7 for example Refer to the ‘Programme Mode Command List’ for entering and editing the program. (See index for page reference) “MENDELBROT”  -2→Xmin 0.5→Xmax -1→Ymin 1→Ymax (Ymax-Ymin)÷62→V (Xmax-Xmin)÷126→H Xmin→X Ymin→Y While X29 Then Plot X, Y IfEnd Y+V→Y WhileEnd Ymin→Y X+H→X WhileEnd Stop

Example 5 ‘Fractal-Fern’ is a program that draws a fern. Editing the program can create a fern tessellation by using a series of extra loops, and dummy variables to create the fern. Refer to the ‘Programme Mode Command List’ for entering and editing the program. (See index for page reference) “FRACTAL-FERN”  ViewWindow 1,14,0,1,11,0 0→C 0→H 4.3→E Lbl 0 H+1→H H>1000⇒Goto 6 C→A Plot A+E,B+1 Ran#→r r<.01⇒Goto 1 r<.07⇒Goto 4 r<.85⇒Goto 2 Goto 3 Lbl 1 0→C .16B→B Goto 0 Lbl 2 .85A+.04B→C -.04A+.85B+1.6→B Goto 0 Lbl 3 .2A-.26B→C .23A+.22B→B Goto 0 Lbl 4 -.15A+.2B→C .26A+.24B→B Go to 0 Lbl 6 Graph Y=-1 Example 6 ‘Dice Simulation’ is a program that utilises the ‘List’ space to draw various statistical graphs and displays the 99% confidence level. Additional statistical information can be obtained by editing the program. You must place values into List 1 for the number of throws of the dice that you want. The program will replace these with the randomly generated numbers between 1 and 6. The maximum list length is 999 or determined by the memory space available. Refer to the ‘Programme Mode Command List’ for entering and editing the program. (See index for page reference) “DICE SIMULATION”  ?→W 1→P Lbl 1 Int (Ran#x6)+1→List 1[P] P+1→P P W⇒Goto 1 Lbl 2 ClrGraph S-WindAuto S-Gph1 DrawOn, Hist, List1,1 S-Gph2 DrawOff S-Gph3 DrawOff DrawStat S-Gph1 DrawOff S-Gph2 DrawOn,MedBox,List1,1 S-Gph3 DrawOff DrawStat S-Gph1 DrawOff S-Gph2 DrawOff S-Gph3 DrawOn,N-Dist,List1,1 DrawStat 1-Variable List1 “ χ +2.58x�n÷√n”: χ +2.58x�n÷√n “ χ -2.58 x�n÷√n” : χ +2.58x�n÷√n

graphs where relationships and special features can be viewed. All of the Function key menus, such as Trace, Zoom, V-Window, Sketch, Graphical Solutions and Graph - Text are available. It is also where you can view Graph - Graphs and Graph - Table split screens. The screen is split vertically, giving very good views of what you have chosen to see. Set Up KEY Example Collate information about the function y = (x-2)(x+1) Result (x+2) Store the expression in position Y1 ( X,θ,T - 2 ) ( X,θ,T + 1 ) a b/c ( X,θ,T + 2 ) then EXE Draw the graph F6 or EXE For selection SHIFT F5 From the above find the... Root/s SHIFT F5 F1 Minimum SHIFT F5 F3 Maximum SHIFT F5 F2 Y-intercept SHIFT F5 F4 Y-value calculations SHIFT F5 F6 F1 X-value calculations SHIFT F5 F6 F2

Dyna Dyna [4] ‘Dynamic Graphs’ can be used to illustrate the changing shapes of selected functions and varying one of the coefficients in the equation and view the changing nature of the ‘family of graphs’. Graph [3] re-visited The ‘Graph’ mode can also have Graph - Graph or Graph - Table. You can ‘toggle’ between the table and the graph. Graph - Graph The Left split screen is the Main screen and the Right split screen is where the ‘zooming’ in/out will be drawn. Hence, the original graph can be seen as you manipulate the Right screen, for the desired view. Graph - Table The Left split screen is the Main screen and the Right split screen is where the x-, y-, and derivative values are displayed as you ‘Trace’ the graph. When [EXE] is pressed the table values will be generated. These Table values can be stored as a List ifdesired for further investigation. KEY Change dual screen to ‘G to T’ Change dual screen to ‘G & G’ Example Graph y=x3 - x2 and view the x-intercepts closely. Example Graph y=x2 ÷ 4 and compare table values to graph values. Press [EXE] to get the table entry. cont. on next page Example Investigate the differing shape of Y = Asin (1x + 0) Result Make sure the V-Window [SHIFT] [F3] is appropriate to view the graph(s). Select the graph type required F5 (B-In) EXE

The Graph and Text Screens given Equations Equations [8] The use of this mode can have you solving simultaneous equations [F1], up to 6 unknowns or solving quadratic and cubic equations and other polynomials (up to degree 6) [F2] and the Equation Solver [F3]. This mode of operation is self explanatory and can be used to investigate Linear Programming, or the relationship between ‘roots’ of polynomial equations. Table Table [7] The use of the ‘Table’ mode can create lists such as a sequence or table of values generated by a given relationship, a graph of the table or a table and a dual graph of the table values and table. You can ‘toggle’ between the table and the graph. Setting the calculator up for the different screen displays is through SETUP. Choose your settings by scrolling with the up and down REPLAY keys. KEY Prior to you seeing the dynamic graph a message will come on the screen (left). This is where the calculator generates the differing views in relation to the coefficient starting, finishing and pitch values that has been chosen for the displaying of the ‘family of graphs’. Store the expression to override “B” 1 to override “C” 0 then EXE Change the variable F4 [VAR] 3 EXE Set the dynamic range F2 [SET] - 5 EXE , 5 EXE then EXIT F6 to draw graph

Simultaneous Equations 2 Equations–2 Unknowns TO 6 Equations–6 Unknowns The calculator can solve simultaneous linear equations up to 6 unknowns, any other linear equation systems > 6 unknowns should be solved in the RUN-MAT icon from the MAIN MENU using matrices. The calculator can solve systems of equations in the form: ax + by = c dx + ey = f Solving Polynomial Equations The calculator can solve quadratic and cubic equations and other polynomials up to degree 6, any other polynomials of degree > 6 should be solved in the GRAPH icon from the MAIN MENU. A quadratic equation: ax2 + bx + c = 0. For solving 2 simultaneous equations - 6 simultaneous equations enter the appropriate number of unknowns via the Function key and then enter the coefficients of each equation and solve. KEY then KEY then Equations cont. Example Solve 2x + 3y = 7 3x – 4y = 2 Result Enter the coefficients of the equation 2 EXE 3 EXE 7 EXE 3 EXE - 4 EXE 2 EXE then F1 or EXE to solve the equation Example Solve x2 − 3x + 2 = 0 Result Enter the coefficients of the equation 1 EXE - 3 EXE 2 EXE then F1 or EXE to solve the equations cont. on next page

Solving Other Types of Equations Example 2 Solve 2x2 + 4x − 5 = 0 Result Enter the coefficients of the equation 2 EXE 4 EXE - 5 EXE then F1 or EXE to solve the equations Example 3 Solve x2 + 2x + 4 = 0 Result Change the format of complex mode SHIFT MENU F2 EXIT Enter the coefficients of the equation 2 EXE 4 EXE - 5 EXE then F1 or EXE to solve the equations A cubic equation: ax 3 + bx 2 + cx + d = 0. A quartic equation format: ax 4 + bx 3 + cx 2 + dx + e = 0. A quintic equation format: ax 5 + bx 4 + cx 3 + dx 2 + ex + f = 0, etc. For solving the appropriate degree polynomial, enter the appropriate degree via the Function key and then enter the coefficients of each equation and solve. Note: In solving the polynomial equations the solutions can be displayed in polar and rectangular format if the solutions are complex. Note: The following error message is due to incorrect mode settings. Use SETUP and then scroll down to change the settings, as required by pressing the appropriate Function key(s). KEY KEY SOLVer Using the Solver tool type in the equation without rearranging and solve using [F6] or [EXE]. Using the Solver in EQUAtion mode: Enter in the equation. You are ‘greeted’ with the screen shown above. This is where you enter in the equation and solve the equation with the information about the ‘known’ variable values and solve for the ‘unknown’ variable. cont. on next page

Example Solve 2x + 1 = 5 Result Enter the equation 2 X,θ,T + 1 SHIFT . 5 then EXE to store F6 to solve Note: You are able to use any letter of the alphabet as the ‘dummy’ variable in the equation, using the ALPHA and SHIFT keys and corresponding key. Example 2 Force = Mass × Acceleration i.e. F = MA, find the value of the mass of the object, if the Force = 1000 Newtons and the acceleration = 10 ms-2. Given that F = MA and F=1000, A=10 find M. Result Enter the equation and set all the variables to 0 ALPHA tan SHIFT . ALPHA 7 ALPHA X,θ,T then EXE to store 0 EXE 0 EXE 0 EXE Variables are all set to 0 Other Examples Solve 5x + 4 = 2x - 7 Result 5 X,θ,T + 4 SHIFT . 2 X,θ,T - 7 then EXE to store then F6 to solve Solve x2 = 4x - 3 Result X,θ,T x2 SHIFT . 4 X,θ,T - 3 then EXE to store then F6 to solve Solve sin x = 1/√2 Result sin X,θ,T SHIFT . 1 ÷ SHIFT x2 2 then EXE to store then F6 to solve Note: there are TWO solutions to a quadratic equation and using Solver will only find one solution. The calculator will display only one solution (the PRINCIPAL) in the radian or degree setting. Solving Other Types of Equations cont. cont. on next page

Change the known variables to those defined in the problem 1 0 0 0 EXE 0 EXE 1 0 EXE Move the ‘cursor’ so that it is ‘sitting’ over the top of the variable that you want to calculate the answer to, in this case ‘M’. then F6 [SOLV] Solving Other Types of Equations cont. Example 3 Given that V=U+AT and U=20 ms-1, V=70 ms-1 and A=10 ms-2, find T. Result Enter the equation ALPHA 2 SHIFT . ALPHA 1 + ALPHA X,θ,T ALPHA ÷ then EXE to store Set all the variables as per the equation 7 0 EXE 2 0 EXE 1 0 EXE 0 EXE Move the ‘cursor’ so that it is ‘sitting’ over the top of the variable that you want to calculate the answer to, in this case ‘T’. then F6 [SOLV] Note: Any algebraic or trigonometric equation can be solved in this area of the calculator BUT only one solution is found at any one time (based on the Newton-Raphson Method), hence multiple solutions to equations should be solved in the GRAPH icon from the MAIN MENU. Conics Conics [7] The use of this mode can see the user investigate the properties of the conics sections. Varying the expressions for standard conic equations the student can investigate the conics and their associated equations and properties. Use the arrow keys to select the conic type required. Note also that the different selections are for various ways of drawing and finding focal points, directrix, asymptotes and centres of the parabola, ellipse, circle and hyperbola. You are also able to select rectangular, polar or parametric formats for each of the conic sections. cont. on next page

Conics cont. Note: The other conic equation types behave in a similar fashion to the example worked above. Note: The SB-62 cabling (3-pin) or the USB (5 pin) cabling are required for the data transfer. Example Find the directrix, symmetry line, length, vertex and the focal points for the parabola x = 2(y – 3)² + 1 Result Enter in the appropriate coefficients 2 EXE 3 EXE 1 EXE Make sure that the domain and range are set up adequately, via the V-Window. SHIFT F3 As a ‘rule of thumb’ start with the V-Window set at the STD view by pressing the F3 key, view the graph and then change the x- and y- settings to suitable values. In this case - 1 EXE 1 0 EXE 1 EXE - 1 EXE 6 EXE 1 EXE then EXIT and F6 [DRAW] The G-Solve tools can be employed SHIFT F5 for each aspect of the conic section you require Focus Symmetry Directrix Vertex Length Link Link [C] The ‘Link’ mode is where communication with a personal computer can be made, a printer for printing screen images or transmitting and receiving data or pictures from one calculator to another. Items can be selected one at a time or in groups or the entire calculator memory can be ‘relocated’.

the user. Each section of the calculators ‘storage’ memories can be deleted or copied singularly or ‘totally’ RESET or backed up. You can search for particular files using the search function [F3]. System System [E] The calculator operation and use can be checked and modified. Each section of the calculator’s memory ‘storage’ can be deleted either singularly or ‘totally’ RESET. Contrast The light that ‘hits’ the screen can be reduced or the intensity of the colour on the screen can be made lighter or darker to suit the user. Version Operating system version number – linked to version releases from CASIO®. Reset Resetting the graphic calculator to the predetermined manufacturers specifications (as set when you initially placed in the batteries). Resetting the calculator serves three main purposes: 1. It clears any previous operations that the current user may not be familiar with or want to use. 2. It returns the calculator to its initial default settings. 3. Viewing and deleting specific areas of the calculator memory, usually in this case to ‘free up’ memory. Power Properties Power properties setting to 10 or 60 minutes to power off. Language Select the language to be used on the calculator. To select view the MEMORY USAGE, press [F1] for the Main Memory. Then use the down arrow followed by [F1] to reset the storage space memory to zero. You will see a message screen giving you a choice. Press either [F1] for ‘Yes’ or [F6] for ‘No’. To select view the MEMORY USAGE, press [F1] for the Main Memory. Then use the down arrow followed by [F1] to reset the storage space memory to zero. You will see a message screen giving you a choice. Press either [F1] for ‘Yes’ or [F6] for ‘No’. KEY

TVM TVM [A] In this icon economic and accounting formulae can be selected and used to calculate various time, value or money problems. Notes:

Result 2 F1 + 3 then EXE to store Set the values for ‘n’ F5 [SET] 1 EXE 1 0 EXE then EXIT Select TABLe and scroll to see the remaining values of the sequence F6 [TABL] Giving the answer = <5, 7, 9, 11, 13, 15, 17, 19, 21, 23, . . . . . .> Note: the third column on the worksheet has a ∑an this is accessed through the SET UP via [SHIFT] [MENU] and adjusting the appropriate settings for Sigma ∑ display to be on [F1]. CLIP and PASTE Cutting and pasting from a document (via emulator) or from a particular icon on the hand-held FX9750GII and pasting it into another working area. KEY 1. Copy and paste from a document 2. Working to be transferred to another area of the calculator using COPY/CUT and PASTE. After the expression or equation is entered access CLIP [SHIFT] [8] and use the right (or left) replay arrow to highlight the required text to be copied or cut, press [EXE] then move to the area for pasting the copied text to be pasted by accessing PASTE [SHIFT] [9]. KEY RESULT Sequence and Series [in RECUR] MISCELLANEOUS FUNCTIONS

You may have noticed the calculator can provide complex number answers, for example when finding the roots to equations where the graph does not ‘cut’ the x-axis. Here the calculator that performs complex number calculations in either a + ib form or polar form (lzl and arg z). Differentiation [in RUN-MAT] The calculator can perform differentiation at any point and draw any derived function required. Answer: -4 - 7i and 8.06 cis (-2.09) (2 d.p.) The real part and imaginary parts of the complex number can be separated, conjugates can be found and of course the complex number can be treated as a coordinate point for graphical representations. Example Simplify (1 - 2i)(2 - 3i) and change the answer to polar form Result Key in the expression OPTN F3 ( 1 - 2 F1 ) ( 2 - 3 F1 ) EXE Change to polar form to insert F2 [Abs] ( ) EXE to insert DEL F3 [Arg] EXE Example Evaluate the slope of the curve f(x) = (x - 2)eX at x = 3 Result Key in the expression Note: A comma is required then the x-value OPTN F4 F2 ( X,θ,T - 2 ) SHIFT In X,θ,T , 3 ) EXE KEY KEY cont. on next page fx9750GII CHAPTER 7 | PG 55

namely f(x), f´(x) and f´´(x) in the Y1, Y2 and Y3 ‘spaces’ respectively. [Remember to place the ,X) after the first and second derivative.] Example Find the integral of y = x2 - 1 between x = 2 and x = 4. Result Integral value only OPTN F4 F4 X,θ,T x2 - 1 , 2 , 4 ) then EXE Example cont. Drawing the function f(x) = (x-2)eX and its first and second derivatives. Comment on the relationships between the graphs drawn. Result Enter the function SHIFT F4 [SKTCH] F5 [GRPH] F1 [Y=] ( X,θ,T - 2 ) SHIFT In X,θ,T SHIFT VARS F6 F5 Enter the first derivative SHIFT F4 [SKTCH] F5 [GRPH] F1 [Y=] OPTN F4 F2 ( X,θ,T - 2 ) SHIFT In X,θ,T , X,θ,T ) SHIFT VARS F6 F5 Enter the second derivative SHIFT F4 [SKTCH] F5 [GRPH] F1 [Y=] OPTN F4 F3 ( X,θ,T - 2 ) SHIFT In X,θ,T , X,θ,T ) SHIFT VARS F6 F5 then EXE cont. on next page Differentation [in RUN-MAT] cont. Integration [in RUN-MAT] Integration can be displayed as the definite integral value only or the graph of the required integral and the definite integral value. The calculator uses Simpsons Rule to evaluate definite integrals. If you do not specify the number of steps used by Simpsons Rule, then the calculator will use 512 steps in the calculation of the request. MISCELLANEOUS FUNCTIONS

Piecewise Functions [in RUN-MAT] Piecewise functions can be entered in the usual way and then the domain values for each can be defined and finally drawn. Example cont. Do not forget to set up the Domain and Range values through the View Window. SHIFT F3 , - 5 . 1 EXE 7 . 5 EXE 1 EXE - 5 EXE 1 5 EXE EXIT Graph and integral value SHIFT F4 , F5 F5 X,θ,T x2 - 1 , 2 , 4 then EXE Example Draw f(x) ={ x , x < -1 Result x2 , -1 < x < 1 lx-2l , 1 < x < 3 √x , x > 3 Key in the desired functions, separating each with a colon ‘ : ’ and defining the interval using ‘ [ ’ and ‘ ] ’. SHIFT F4 F5 F1 X,θ,T , SHIFT + - 1 0 , - 1 SHIFT - SHIFT VARS F6 F5 , SHIFT F4 F5 F1 X,θ,T x2 , SHIFT + - 1 , 1 SHIFT - SHIFT VARS F6 F5 , SHIFT F4 F5 F1 OPTN F3 F2 ( X,θ,T - 2 ) , SHIFT + 1 , 3 SHIFT - SHIFT VARS F6 F5 , SHIFT F4 F5 F1 SHIFT x2 X,θ,T , SHIFT + 3 , 1 0 SHIFT - cont. on next page fx9750GII CHAPTER 7 | PG 57

Finding regions that satisfy constraints as used in linear programming. Algebraic substitution – numeric [in RUN-MAT] This activity shows how the calculator can be used to substitute numerical values into algebraic expressions. Algebraic substitution is where an independent numerical variable, usually x, is substituted into an equation for a dependent variable, usually y. To have ‘?’ and ‘:’ statements: You are able to trace the ‘different parts’ of a Piecewise Function using [SHIFT] [F1], then the replay arrows. Make sure that you have an appropriate View-Window to see the graphs drawn. By separating each graph by a colon ‘:’ the calculator generates them as a ‘collective’. Tracing each to find vertices etc is activated in the usual way, i.e. [SHIFT] [F1] and then arrows to trace the graph and the to move from one graph to another. Piecewise Functions [in RUN-MAT] cont. Example cont. Set the V-Window to [INIT] SHIFT F3 F1 EXIT then EXE Example Function Graph cont. on next page KEY RESULT “?” KEY RESULT “:” MISCELLANEOUS FUNCTIONS

Example Calculate the value of the following when x = -2, 0, 2 and 4, in the expression 2x2 + 4x – 1. Result Enter the expression SHIFT VARS F4  X,θ,T SHIFT VARS F6 F5 2 X,θ,T x2 + 4 X,θ,T - 1 then EXE A ‘?’ will display, this is the calculators way of saying, “Enter in a number.” Enter in the number - 2 then EXE the answer -1 is displayed, the calculator has done the calculation: 2×(-2)2 + 4×(-2) – 1 = -1 EXE this brings up the ‘?’ again 0 then EXE Repeat the above sequence, calculating the expression of 2x2 + 4x – 1 for each of the x-values required. Note: Differentiation d/dx and d2/dx2 is via [SHIFT] [OPTN] [F4] for CALCulus. Factorisation checking [in RUN-MAT] Checking that you have factorised (put into brackets) or expanded (removed the brackets) correctly: The ‘calculator’s logic’ will return a ‘0’ if incorrectly done or a ‘1’ if correctly done. As this calculator is a ‘numerical manipulator’ and NOT a ‘symbolic manipulator’ the student MUST learn how to factorise (put into brackets) or expand (remove from brackets). cont. on next page Example Expand (x + 5)(x + 2) Result Enter in the equation in bracketed and the expanded form ( X,θ,T + 5 ) ( X,θ,T + 2 ) SHIFT . X,θ,T x2 + 7 X,θ,T + 1 0 then EXE The result 1 indicates that it is correctly expanded. The result 0 indicates that it is incorrectly expanded. fx9750GII CHAPTER 7 | PG 59

Result Enter in the equation in bracketed and the expanded form X,θ,T x2 + 3 X,θ,T - 4 0 SHIFT . ( X,θ,T + 8 ) ( X,θ,T - 5 ) then EXE Matrix/Matrices [in RUN-MAT] This area of the calculator utilises all of Matrix addition, subtraction and multiplication properties. Transformation Geometry can be investigated or linear programming, up to 8 variables i.e. A matrix size of order 8 x 8. You can edit up to 26 different matrices of differing order and there is an automatic space for the answer matrix. Define the matrices in the usual way, firstly its order rows x columns. Then enter the matrix values. You ‘do’ the operations in RUN-MAT mode. Via [F1] define the matrix dimensions, enter in the values of each matrix then to +, - or × open OPTN then [F2] for the Matrix operations. Factorisation checking [in RUN-MAT] cont. The result 1 indicates correct factorisation. The result 0 indicates incorrect factorisation. Example Calculate [2 - 8] x [ 1 -3 4 ] Result 0 -1 3 Enter the dimensions into Mat A and then the first values F1 EXE 2 EXE 3 EXE Dimensions entered 1 EXE - 3 EXE 4 EXE 0 EXE - 1 EXE 3 EXE then EXIT Example cont. Enter the second dimensions into Mat C and then the second values EXE 1 EXE 2 EXE Dimensions entered 2 EXE - 8 EXE Complete the calculation EXIT EXIT OPTN F2 F1 ALPHA In x F1 ALPHA X,θ,T then EXE MISCELLANEOUS FUNCTIONS

Result Change Y= to X= and the store the equation F3 F4 EXIT F1 then 2 EXE F6 or EXE to draw the graph Linear programming with vertical lines: converting x = c to y = mx + c [in GRAPH] Note: When solving linear programming problems coordinates involved with vertical lines cannot be solved using G-Solve. Converting them to y = mx+c form can assist and give you access to G-Solve. When drawing any graphs make sure that the V-Window is appropriate to see the graphs that you will be drawing. [SHIFT] [F3]. Select [F1], in this case for INITial conditions, as a starting point or use the domain and range values on the grid system that is given in the question to define the View-Window settings. Now use the [EXIT] or [EXE] key to go back to the Graph Func: window. Vertical lines x = c, found by menu trail: [F3] for TYPE then [F4] for x = c format. In linear programming inequalities are required to find the ‘feasible region’ that satisfies the given constraints. You are able to draw inequalities with x ≥ or < or > or ≤ on the FX9750GII but finding intersection points involving vertical lines cannot be performed. You need to ‘trick’ the calculator into thinking that it is drawing a vertical line in the y = mx + c format. KEY RESULT Example 2 Type into the ‘Y2’ space ‘1x – 2’, then try y = 1000x – 2000. Result Y2=1x-2 1 X,θ,T - 2 EXE then F6 Y2=1000x-2000x 1 0 0 0 X,θ,T - 2 0 0 0 EXE then F6 The latter produces a ‘vertical line’ very similar to x = 2 over this Viewing window. But, you have essentially tricked the calculator into drawing a ‘vertical line’. You can check that they are NOT the same by doing a Trace – [SHIFT] [F1] and using the up / down arrows to trace either x = 2 and y = 1000x – 2000 (or similar). cont. on next page fx9750GII CHAPTER 7 | PG 61

constraints over the domain 0 x 25 and range 0 y 25: x + y 15 y 6 4x + y 24 x 2 y 2x Answer: Rearranging to make y the ‘subject’ gives: y 15 – x y 6 y 24 - 4x x 2 y 2x Result Then enter in the constraints and then draw them F3 F6 F4 Change Y= to Y 1 5 - X,θ,T EXE 6 EXE 2 4 - 4 X,θ,T EXE 1 0 0 0 X,θ,T - 2 0 0 0 EXE 2 X,θ,T EXE then F6 to draw Note: You cannot see the line y = 1000x – 2000. Find the intersection points (vertices) of the lines that intersect SHIFT F5 for G-Solve then F5 for [ISCT] (intersection) then select two lines at a time and generate the 5 intersection points. Y1 & Y4 gives (2 , 13) Y1 and Y3 gives (3 , 12) Y2 and Y4 gives (2 , 6) Y2 and Y5 gives (3 , 6) Y3 and Y5 gives (4 , 8) The V-Window [SHIFT] [F3] becomes: Becomes y 1000x - 2000 cont. on next page Linear programming with vertical lines: converting x = c to y = mx + c [in GRAPH] cont. Using the original equations: y 15 – x y 6 y 24 - 4x x 2 y 2x gives: Note: You can see the line x = 2 but G-Solve is not available for the vertical line x = 2. Some interpretation is required if the substitution line for x = c is not ‘extremely’ vertical on the region the constraints are drawn. Factorials, Combinations and Permutations – Calculations [in RUN-MAT] Combinations and Permutations – x!, nCr and nPr respectively KEY RESULT MISCELLANEOUS FUNCTIONS

A table of values, finding the numerical values from a given formula or function. i.e. y = 3x + 1 can generate this table: x 1 2 3 y = 3x+1 4 7 10 Or a sequence = 5n2 - 4 n 1 2 3 y=5n2-4 1 16 41 Example How many arrangements are there of 8 people standing in a line? Result Enter either 8 F1 or 8 F2 8 Example 2 How many ways can we choose a committee of 7 people from a group of 11 women and 8 men if there have to be 3 men and 4 women on the committee? Result Enter 1 1 F3 4 number of combinations of women Enter 8 F3 3 number of combinations of men Enter 1 1 F3 4 x 8 F3 3 total number of ways of getting this committee Example Generate a table of values for the relationship y = 2x +7 for -3 ≤ x ≤ 4 Result Enter the relationship into the Y1 space 2 X,θ,T + 7 EXE Enter the setting for the variable ‘x’ F5 - 3 EXE 4 EXE 1 EXE Note: The pitch is, how large are your steps in moving from one x-value to the next. EXIT then F6 for the table of values x -3 -2 -1 0 1 2 3 4 y = 2x+7 1 3 5 7 9 11 13 15 Factorials, Combinations and Permutations – Calculations [in RUN-MAT] cont. fx9750GII CHAPTER 7 | PG 63

Converting between units of measure can be performed on the FX9750GII using the CONVersion which is accessed via the OPTN key. The [F1] key is the conversion tool, note that it is on each conversion page. Example Convert 20 m/s into km/h (kilometres per hour). Result Enter 2 0 F6 F3 [VELO] 1 or EXE m/s selected F1 [ ] F3 [VELO] 2 or EXE km/h selected then EXE cont. on next page KEY RESULT Example 2 Convert the area of 2000 m2 into km2 . Result Enter 2 0 0 0 F3 [AREA] 2 or EXE m2 selected F1 [ ] F3 [AREA] 4 or EXE km2 selected then EXE Commonly used keys Some of the functions available as keys on a scientific calculator are not immediately obvious on a graphics calculator. Some searching is required in the OPTN menu. Below is a table of some commonly used functions and where they are found on the graphics calculator. An example is shown for each. Length Area Volume Time Temperature Velocity Mass Force Pressure Energy Power MISCELLANEOUS FUNCTIONS

Permutations nPr OPTN, F6, F3 (PROB), F2 Combinations nCr OPTN, F6, F3 (PROB), F3 Random Numbers Ran# OPTN, F6, F3 (PROB), F4 then the desired random number generator. Absolute Value Abs OPTN, F6, F4 (NUMB), F1 Integer Part of Answer Int OPTN, F6, F4 (NUMB), F2 Fractional Part of Answer Frac OPTN, F6, F4 (NUMB), F3 Degrees to Radians º OPTN, F6, F5 (ANGL), F1 (Ensure angle set to radians) Radians to Degrees r OPTN, F6, F5 (ANGL), F2 (Ensure angle set to degrees) Rectangular Coordinates to Polar Coordinates Pol( OPTN, F6, F5 (ANGL), F6, F1 cont. on next page Commonly used keys cont. fx9750GII CHAPTER 7 | PG 65

Polar Coordinates to Rectangular Rec( OPTN, F6, F5 (ANGL), F6, F2 Differentiation for first or second derivatives d/dx or d2/dx2 OPTN, F4, F2 (CALC), F6, F2 or F3 Integration for area under curves ∫dx OPTN, F6, F5 (ANGL), F6, F4 Notes: MISCELLANEOUS FUNCTIONS

Although this could have been covered in the Statistics Chapter this topic needs to be treated separately. This is the Normal Distribution (N.D.) ‘menu’. P( calculates the N.D. shading from the left, Q( calculates the N.D. shading from the centre and R( calculates the N.D. shading from the right. Graph Y = has the sequence: [SHIFT] [F4] [F5] [F1] Excluding the ‘Graph’ will give the Normal Distribution probability value being displayed only. Using the z-score transformation within the calculation on the calculator is also a good technique for the student to use. KEY RESULT Example Find the probabilities related to a z-score of -1. Result Graph Y=P(-1) SHIFT F4 F5 F1 OPTN F6 F3 F6 F1 - 1 ) EXE Graph Y=Q(1) SHIFT F4 F5 F1 OPTN F6 F3 F6 F2 1 ) EXE Graph Y=R(-1) SHIFT F4 F5 F1 OPTN F6 F3 F6 F3 - 1 ) EXE Example 2 Scientists studying a species of fish find that adults have a mean weight of 2.4 kg and a standard deviation of 0.3 kg. Find the probability a randomly selected fish weighs between 2.2 kg and 2.9 kg. Result OPTN F6 F3 F6 F2 ( 2 . 9 - 2 . 4 ) ÷ 0 . 3 ) + F2 ( 2 . 6 - 2 . 4 ) ÷ 0 . 3 ) then EXE Note: 2.2 is on the left of the mean and has an equivalent probability value for 2.6, that is, Prob(2.2 < µ < 2.4) = prob(2.4 < µ < 2.6) giving Prob(2.2 < x < 2.9) = 0.6999 (4dp) As Graphs fx9750GII CHAPTER 8 | PG 67

Data that you have entered in the ‘List’ can also be used to model the data to be normally distributed, that is, assuming the data is normally distributed. By using the z-score transform and using ‘µ’ and ‘�’ generated from the data in the list will be used to do the appropriate normal distribution calculations. Enter the data into a list space and then generate the summary statistics associated with the data. Make a note of the required information and in RUN-MAT mode generate the desired calculations based on the Normal Distribution. Normal Distribution Analysis [in STAT] Left, Central and Right selections for Inverse Normal calculations in STAT mode. Example Find the values of k such that Prob(Z < k) = 0.45 Result F5 F1 F3 F1 0 . 4 5 EXE then EXE Example 2 Find the values of k such that Prob(-k < Z < k) = 0.45 Result F5 F1 F3 F3 0 . 4 5 EXE then EXE Example 3 Enter the following data and assuming N.D. find the probability that a score of 5 or more is achieved. 1 1 4 5 7 8 4 1 2 4 7 8 5 4 7 Result Enter the data into list 1 1 EXE 1 EXE 4 EXE 5 EXE 7 EXE 8 EXE 4 EXE 1 EXE 2 EXE 4 EXE 7 EXE 8 EXE 5 EXE 4 EXE 7 EXE then F2 [CALC] F1 [1VAR] In RUN-MAT mode, complete the desired (1 variation) statistical calculations. Required Prob(x > 3) = Prob((3 - 4.533)/2.418) using the z-score transformation. SHIFT F4 F5 F1 , OPTN F6 F3 F6 F3 ( 3 - 4 . 5 3 3 3 ) ÷ 2 . 4 1 8 ) then EXE Prob(x > 3) = 0.7370 (4 d.p.) NORMAL, BINOMIAL AND POISSON DISTRIBUTIONS

Example 3 Find the values of k such that Prob(k < Z ) = 0.45 Result F5 F1 F3 F2 0 . 4 5 EXE then EXE Example 4 A machine produces ball bearings with the weights of each normally distributed with a mean of 2700 mg and a standard deviation of 12 mg. If 10% of the ball bearings are rejected as being overweight for the mechanism they are to fit into, find the maximum acceptable weight to the nearest mg. Require the Prob(X > k) = 10% = 0.1, Area = 0.1, � = 12 and μ = 2700. Result F5 F1 F3 F2 0 . 1 EXE 1 2 EXE 2 7 0 0 EXE then EXE The maximum acceptable weight is 2715 mg (4 sig. fig.). Example Calculate the probability that from 10 trials there are two successful outcomes and the probability of a success is 0.5. Result F5 F5 F1 F1 2 EXE 1 0 EXE 0 . 5 EXE then EXE Probability = 0.0439 (4 d.p.) Binomial Distribution calculations [in STAT] The Binomial Distribution(B.D.) has 2 parameters, the number of trials (n) and the probability of success (p). Change the data as being VARiable (you enter in the data) from LIST - press [F2]. KEY RESULT Individual B.D. Cumulative B.D. Inverse B.D. fx9750GII CHAPTER 8 | PG 69

Example 2 Calculate the probability that from 10 trials there are at most two successful outcomes and the probability of a success is 0.5. Here x < 4 or x ≤ 3, i.e. x = 0, 1, 2 or 3. Result F5 F5 F2 F2 3 EXE 1 0 EXE 0 . 5 EXE then EXE Prob(x ≤ 3) = 0.0547 (4 d.p.). Example Calculate the probability that a carpet of size 1 square metre will have 2 flaws when the carpet generally has on average 1.8 flaws in it per square metre? Result F5 F6 F1 F1 F2 2 EXE 1 . 8 EXE then EXE Probability = 0.2678 (4dp) Example 2 Calculate the probability that from a carpet of size 1 square metre will have at most three flaws and the carpet generally has on average 1.8 flaws per square metre? Here x < 4 or x ≤ 3, i.e. x = 0, 1, 2 or 3. Result F5 F6 F1 F2 F2 3 EXE 1 . 8 EXE then EXE Probability = 0.8913 (4 d.p.) Poisson Distribution calculations [in STAT] The Poisson Distribution (P.D.) has only one parameter, λ, the mean. Change the data as being VARiable (you enter in the data) from LIST - press [F2] as illustrated with Normal and Binomial Distributions. KEY RESULT KEY RESULT NORMAL, BINOMIAL AND POISSON DISTRIBUTIONS

There are four types of confidence interval calculations, one statistic (1-S), two statistic (2-S), one proportion (1-P), and 2 proportions (2-P). Note: You will have a choice of 4 different options of confidence intervals. 1-S, 2-S, 1-P, and 2-P. Use the function to select the one that fits with the statistics. Confidence Intervals 1-S type Confidence Intervals 2-S type Example Consider the following collected statistics. A sample was taken of worm lengths at different areas of a market garden. Test at the 95% confidence level, to see if there is a statistical difference between the worm lengths of this sample and the ‘true’ population mean. Sample n = 56 Mean = 10.4 Standard deviation = 2.3 Result Set the calculator up so that inputted statistics is being used, not ‘raw data’. As you can see raw data can be using in the LIST columns. F4 F1 Z-score F1 [1-S] F2 [VAR] 0 . 9 5 EXE 2 . 3 EXE 1 0 . 4 EXE 5 6 EXE then EXE This gives the interval [9.7976, 11.002], hence the ‘true’ population mean for the worm lengths is in this interval, at the 95% confidence level. [9.7976, 11.002] Example Consider the following collected statistics. Two samples were taken of worm lengths at different areas of a market garden. Test at the 90% confidence level, to see if there is a statistical difference between the worm lengths of two samples. Sample 1 Sample 2 n = 45 n = 80 Mean = 5.4 Mean = 5.3 Standard deviation = 1.2 Standard deviation = 1.15 Result KEY RESULT KEY RESULT C-Level is at the 95% level cont. on next page fx9750GII CHAPTER 8 | PG 71

Confidence Intervals 2-P type Is used in a similar way to the three types illustrated above when comparing two population proportions. Enter into the statistics icon. Choose [INTR] [F4] then [F1] for Z-score. You now have a choice of 4 different options of confidence intervals. 1-S, 2-S, 1-P, and 2-P. This problem is a 2-P. So, press [F4]. Confidence Intervals 2-S type cont. Example Consider the following collected statistics. A sample was taken of worm lengths at different areas of a market garden. Test at the 99% confidence level, to see what the ‘true’ population proportion is, if 55 out of 100 worms found were greater than 9.3cm in length. Result F4 F1 Z-score F3 [1-P] 0 . 9 9 EXE 5 5 EXE 1 0 0 EXE then EXE This gives the interval [0.42185, 0.67814], hence the true population proportion lies between 42% and 68% (2 sig.fig.) of worms with a length greater than 9.3 cm. [0.42185, 0.67814] Remember: The larger the sample size the more accurate the sampling results. i.e as n gets larger then the population statistic interval gets smaller.] If n = 1000, then these results would be calculated - a much smaller interval Example cont. F4 F1 Z-score F2 [2-S] F2 [VAR] 0 . 9 EXE 1 . 2 EXE 1 . 1 5 EXE 5 . 4 EXE 4 5 EXE 5 . 3 EXE 8 0 EXE then EXE This gives the interval [-0.26235, 0.46235], hence there is NO statistical difference between the two samples as 0 is contained within the interval. [-0.26235, 0.46235] C-Level is at the 90% level C-Level is at the 99% level Notes: NORMAL, BINOMIAL AND POISSON DISTRIBUTIONS

CHAPTER 9 | PG 73 A number of devices can be connected to the FX9750GII and other CASIO graphic calculators via the EA-200 data logger. [Previous data logger model EA-100 is also described as this data logger needs to have the data transferred to the calculator using small programs to send the information to the data logger and to receive the data collected back to the calculator for analysis. There are devices that can be used in supporting the use of the calculator in the classroom, bringing real life data into the classroom for analysis, as with the EA-2 motion detector. These two extensions can be easily attached to the G.C. and the information transferred to the STAT icon. Then use the statistical functions to model the data. Connect various sensors to the EA-100 and EA-200 Data Analyser to collect various data relating to physics, chemistry, biology, and mathematics and analyse it with the graphic calculator. 1. Temperature Probe The temperature probe that comes with the data analyser uses a thermistor to measure the temperature of liquids. Changes in the temperature of the thermistor causes a corresponding change in its resistance, which is then converted to a temperature value. 2. Voltage Probe The voltage probe that comes with the data analyser can be used to read a voltage in the range of ±10 Volts. This probe is designed with Auto-ID resistance, so connecting it to the data analyser automatically switches to voltage sampling. The black probe should be connected to ground, while the red probe should be connected to signal voltage. 3. Light Probe The light probe that comes with the data analyser uses a photosensitive element called a Cds to measure brightness, which is then converted to a numeric value. The value produced does not correspond to any standard unit of measurement, but simply indicates a relative measure of brightness in the range of 100 to 999. 4. Motion Detector EA-2 is a sonar ranging device with a sensing range of 0.6 to about 8 meters. The EA-2 emits ultrasonic pulses and detects pulses returned as echoes from the target. It can be connected to the CASIO EA-100 data analyser to accumulate and analyse data. 5. Other devices [Venier probes] These can be purchased separately such as: Dissolved Oxygen Probe, Drop Counter; EKG Sensor, Electrode Amplifier, Flow Rate Sensor, Force Sensors, Gas Pressure Sensor, GPS Sensors, Gas Chromatograph, Hand Dynamometer to name a few. Please consult the User manual for aligning other probes to ‘hank shake’ An overview of the Data Logger. The EA-100 Data Logger features: 6 Channels: 3 analog inputs, 1 ultra-sonic motion detector input, 1 digital input, 1 digital output. The unit automatically recognises the type of probe being connected to each channel. One temperature probe, one light probe and one voltage probe are included in the pack. Other types of probes are available. You can measure motion, temperature, light, force, sound, pH and more with the use of appropriate probes. The Data Logger allows for the display of data from the specified channel during the sampling to confirm when sampling is taking place and when the sampling has finished. You can collect data from up to five channels simultaneously (The 6th is reserved for time). The unit can collect data at rates of up to 10,000 data points per second for up to 250 data points (maximum entry for each column in STAT or LIST icon is 250 data values) per channel. cont. on next page

A Quick Guide to Using the EA-100 Data logger - Manual Set Up Step 1: Be sure to connect an Auto-ID probe to CH1, CH2, CH3 or SONIC channel. Step 2: Switch the Data Analyser to Communications mode by pressing the [MODE] key (“Done” appears on the screen). Setting Time Interval, Number of Samples and Time Type Time Interval Setting Step 1: To access, press [SHIFT] [MODE]. Step 2: Press [Data Log] to scroll through available settings. Settings are: Milliseconds: 10, 20, 50, 100, 200, 500 Seconds: 1, 2, 5, 10, 20, 30, 60 Press [Trigger] to set the Time Interval and to advance to the next setting Time Interval Setting Step 1: Press [Data Log] to scroll through available settings: 0, time recording off; 1, absolute time recording; 2, relative time recording Step 2: Press [Trigger] to set the Time Setting. Data Collection & Transfer Data Collection “Ready” appears on the display. Step 1: Press [Trigger] for the Data Analyser to begin collecting data. Step 2: “Done” appears when data collection is complete. Data Transfer to a Graphics Calculator Connect the calculator to the Data Analyser (Press plugs in firmly). Step 1: Run the program “MANUAL” in the Program Mode of the calculator. Data will automatically be transferred to the calculator and a graph of this data displayed. Data Analyser - Multimeter Mode In this mode, the Data Analyser can perform a variety of different sampling operations using a selection of units. This mode can be used to sample voltage, resistance, current, period, frequency and distance. Sampling can be performed using CH1, CH2, CH3, SONIC or DIG IN. To enter Multimeter Mode Press [MODE] key. MULTIMETER indicator is displayed. To select channel Press [CH-View] key continuously until desired channel is displayed.

To change sampling unit Press [Data Log] key continuously until desired unit is displayed. Note: The Data Analyser’s Auto Power Off feature is not active in this mode. Data Analyser - Program Mode Equipment Set Up Step 1: Connect the calculator to the Data Analyser using the cable. Press ends in firmly. A definite “Click” sound is heard. Be sure to connect an Auto-ID probe to CH1, CH2, CH3 or SONIC channel Step 2: Switch the Data Analyser to Communications mode by pressing the [MODE] key (“Done” appears on the screen) Step 3: Turn the calculator on. Access the Program Mode of the calculator. Select and execute the program you have written to be used with an activity. Step 4: Follow the prompts on the calculator display whilst also taking note of the procedure for the activity. Data Collection, Transfer and Analysis “Ready” appears on the display. Step 1: Press [Trigger] for the Data Analyser to begin collecting data. Step 2: Depending on the activity, data can be collected “Real Time” or data can be collected then displayed on the calculator graphically on completion of the data collection. Step 3: “Done” appears on the Data Analyser display when data collection is complete. Step 4: The program will normally contain instructions which automatically transfers the data to the calculator. Step 5: A graph of the data will also be displayed and further mathematical analysis can be performed. Using the EA-100 Data Logger with a probe This activity looks at: •� use�the�data�analyser�to�collect�data�on�time�and�temperature. •� transfers�data�from�the�data�analyser�to�the�calculator. •� use�the�calculator�to�graph�the�relationship�between�time�and�temperature. •� use�a�mathematical�model�to�model�the�collected�data. •� Application�of�Newton’s�Law�of�Cooling. Data Transfer to a Graphics Calculator. Step 1: Connect the calculator to the Data Analyser (Make sure that the plugs are in firmly. Step 2: In RUN mode and using PRGM [SHIFT] [VARS] . Alternatively a ‘short’ program in the PRGM icon from the MAIN MENU will do this data transfer from the Data Logger to the calculator very quickly. The example shown in this worksheet is to show how heat is lost from a hot cup of water when it is placed in a room, free standing, to cool. Two experiments are conducted, one with a simple cup of water and the second with a cup of water with a metal spoon placed in the water to act as a “radiator” to compare and to see if there is any difference in the cooling rates. then [F6] and [F4] [F4] for Receive. For List 1 etc [OPTN] [F1] & [F1] again. List 1 is TIME and List 2 is the TEMPERATURE reading.

Procedure Step 1: Heat approximately 250 ml of water. Bring it to the boil (approx 100° C). Step 2: Place the thermometer probe into the cup of water after it has been heated. Step 3: Set the rate of sampling of the EA-100 at 10 seconds and the number of samples to be taken at 200. Start the data gathering with the EA-100 and relax for the next 33 minutes and 10 seconds. Step 4: Transfer the data from the EA-100 to the calculator. Step 5: Analyse the data collected as a time series. Fit an appropriate mathematical model to the data collected. Step 6: Repeat the experiment with the spoon in the cup of water. Analysis of the Results The trend of the two curves displays the rate of cooling for the water. You may expect some results to differ as this is dependent on different surface areas, different composition containers, addition of insulating materials, etc. The analysis is done in the STAT icon, setting the statistical graph to be either a time series or scattergraph. From the value of r2 and comparing the two mathematical models, the exponential model is the ‘best fitting’. Result #2: With the spoon: Transfer the data from the Data Logger into List 3 and List 4 of the calculator. Making comparisons between the cooling (i) without and (ii) with the spoon (radiator). The spoon ‘absorbs’ the heat – heats up – (logarithmically). So the initial temperature is lower, but the cup of water cools at similar rates. Without spoon: y = 81.985-0.000355 With spoon: y = 77.958e-0.000325 Result #1: Without the spoon: An exponential model: An exponential model: The theoretical model displayed. y = 77.958e-0.000325 A power model: Graphically, viewing both time series or scattergraphs simultaneously: Note: Newton’s Law of Cooling states: That the time a substance takes to cool off depends on the temperature difference between the substance and the surroundings. Time (sec) Temp (oC) select [F1] [F6] will draw the two graphs. then [F4] Then turn StatGraph1 and StatGraph2 on by pressing [F1].

Analysis of the Results Calculator to calculator connection is via the SB-62 cabling. Data transfer of files, screen captures, lists and other items can be transferred. Note that the calculators can be of different models as shown in the pictures below. The receiving calculator needs to be set up first and the transfer calculator. Make sure that the cabling is securely placed in to the docking port. Follow the prompts that appear on the screen with the Function keys. The EA-200 Data Logger features: Using the E-CON2 icon from the MAIN MENU. The introduction of this new icon to the MAIN MENU on the FX9750GII has enabled the setting up of the devices that can be attached to the calculator easy by following the prompts on the screen using the WIZard via SET [F1]. SET [F1] Wizard setup – follow the prompts. SET [F1] [F2] Advanced wizard setup – follow the prompts. MEM [F2] To save and recall data collected. [F3] for manual operation, via written programs (consult the EA-200 User manual), calculator model type, data logger model type. [F4] Activate the data collecting from the data logger and probe in use. [F5] Graphing of data results setup – follow the prompts. [F6] Need some help – follow the prompts. Using the HELP Function key – use the down arrow to view more information to assist you in using the E-CON2 icon. The EA-200 has a master connection for the graphic calculator ‘instructing the analyser’ and can be connected to a maximum of 6 graphic calculators to also receive the data (see picture to right).

Calculator to computer data transfer Calculator to calculator connection is via the 5-pin/USB cabling. Follow the Function keys for setting up this feature via LINK from the MAIN MENU. Calculator to data projector data transfer Calculator to calculator connection is via the 5-pin/USB cabling. Follow the Function keys for setting up this feature via LINK from the MAIN MENU. Notes:

Key Primary Function Combined with SHIFT Combined with ALPHA Trace F1 Turns trace function on/off. Selects first function menu item Zoom F2 Turns zoom function on. Selects second function menu item V-Window F3 Displays View Window parameter input screen. Selects third function menu item Sketch F4 Displays sketch menu. Selects fourth function menu item G-Solv F5 Displays graph solve menu. Selects fifth function menu item G  T F6 Switches display between graph and text screens. Selects sixth function menu item SHIFT Activates shift functions of other keys and function menus OPTN Displays option menu PRGM VARS Displays the variable data menu. Displays program command menu SET UP MENU Returns to the Main Menu. Shows the set up display A -LOCK ALPHA Allows entry of alphanumeric characters shown in red Locks/Unlocks entry of alphanumeric characters √ R x2 Press after entering value to calculate square Press before entering value to calculate square root Enters character r x√ θ ^ Press between two values to make second value exponent of first Press between entering values for X and Y to show xth root of y Enters character θ QUIT EXIT Back steps to the previous menu Returns directly to initial screen of the mode Moves cursor upward. Scrolls through the screen items Switches to previous function in trace mode Moves cursor downward. Scrolls screen. Switches to next function in trace mode Moves cursor to left. Scrolls screen. Press after EXE to display calculation from end Picture /screen capture Moves cursor to right. Scrolls screen. Press after EXE to display calculation from beginning ‘cut’ and 'paste' A X,θ, T Allows input of variable X, θ and T Enters letter A

Combined with ALPHA 10x B log Press before entering value to calculate common logarithm Press before entering exponent value of 10 Enters letter B ex C In Press before entering value to calculate natural logarithm Press before entering exponent value of e Enters letter C sin-1 D sin Press before entering value to calculate sine Press before entering value to calculate inverse sine Enters letter D cos-1 E cos Press before entering value to calculate cosine Press before entering value to calculate inverse cosine Enters letter E tan-1 F tan Press before entering value to calculate tangent Press before entering value to calculate inverse tangent Enters letter F d/c G a b/c Press between entering fraction values. Converts fraction to decimal Displays improper fractions Enters letter G H F D Converts a fraction to a decimal value or a decimal value to a fraction. Sends a shot of the current screen to a connected device Enters letter H 3√ I ( Enters open parenthesis in formula Press before entering value to calculate cube root Enters letter I x-1 J ) Enters close parenthesis in formula Press after entering value to calculate reciprocal Enters letter J K , Enters a comma Enters letter K L  Assigns value to a value memory name Enters letter L CAPTURE M 7 Enters number seven ... ‘paste’ Enters letter M CLIP N 8 Enters number eight Allows insertion of characters at cursor location Enters letter N PASTE O 9 Enters number nine Turns power off Enters letter O INS DEL Deletes character at current cursor location View a lists of commands which can be copied to the screen OFF AC/ON Turns power on. Clears the display CATALOG P 4 Enters number four Enters letter P Q 5 Enters number five Enters letter Q R 6 Enters number six Enters letter R { S x Multiplication function Enters open curly set bracket Enters letter S

Key Primary Function Combined with SHIFT Combined with ALPHA } T ÷ Division function Enters close curly set bracket Enters letter T List U 1 Enters number one ‘Hot key’ for list Enters letter U Mat V 2 Enters number two ‘Hot key’ for Matrix Enters letter V W 3 Enters number three Enters letter W [ X + Addition function. Specifies positive value Enters open bracket Enters letter X ] Y - Subtraction function. Specifies negative value Enters close bracket Enters letter Y i Z 0 Enters number zero Enters the imaginary number i Enters letter Z = SPACE . Enters decimal point Enters character equals Enters a blank space π " EXP Allows entry of exponent Inputs the value of pi. Enters the pi symbol Enters speech marks for displaying statements Ans (-) Enter before value to specify as negative number Recalls the most recent calculation result displayed  EXE Displays result of calculation Inputs a new working line on the screen

A PAGE Algebra Algebraic substitution 12, 57 Analysis of the Results 76 Angle 27 Auto zoom 20 B Binomial distribution calculations in STAT 68 Bi-variate 34 C Calculator settings 17 Calculus 25 Capture 28 Catalogue Key 25, 31 Change sampling unit 75 Channel 74 Clear Screen 9 , 15 Clip and Paste 72 Combinations 62 Commonly used keys 64 Complex Numbers 54 Complex 25 Computer data transfer 78 Confidence Intervals 1-P type 71 1-S type 70 2-P Type 71 2-S type 70 Confidence Intervals in STAT 70 Conics 5, 50 Connection to other devices 73 Contrast 52 Conversions 26, 63 Convert Decimal 10 Mixed fraction 10 D DATA Data Analyser Data Analysis 75 Multimeter Mode 74 Program Mode Equipment Set Up 75 Data collection, Transfer and Analysis 74, 75 Data Entry 32 Data Logger 73 Data projector data transfer 78 Data transfer to a graphics calculator 75 Data Transfer 75

D - G D cont. PAGE Decimal 10 Deleting Lists 37 Differentiation 54 Display 8 Distribution Binomial distribution calculations in STAT 68 Normal Distribution Analysis RUNMAT 66 Normal Distribution Analysis STAT 67 Poisson Calculation in STAT 69 Domain edited 15 Dyna 5, 45 E E Symmetry 27 EA100 Manual Set Up 74 With a probe 75 E-Con 5 Editing Entries 8 Lists 36 Equa 5 Equations 23, 46 Equipment Set up – Program Mode 75 F Factorials, Combinations and Permutations 62 Factorisation checking 58 Fractions Fraction without Fraction key 10 Fractions 10 Function Memory 28 G Getting started 7 Graph Basic activities 18 Calculating unknown x values 21 Domain 15 Graph 5 Graph and Text 8 Graph Drawing 14 Graph – Graph 46 Graph icon 17 Graph revisited 46 Graph’s scale 14 Graph – Table 46 Intercepts 22 Intersection points 22 Range 15

20 G-Solve features 17 H Hyperbolic 26 I Icon modes 7 Inequalities 57 Integration 55 Intercepts 22 Intersection points 22 K Key Index 79 L Language 52 Light Probe 73 Line 18 Linear programming with vertical lines 60 Link 5, 51 List Deleting 37 Editing 36 List 35 M Main Menu Icons 5 Manual Set Up – EA100 Data Logger 74 Matrix/Matrices 25, 59 Memory Function 28 Manager 52 MEM 5 Mixed Fraction 10 Money 28 Motion Detector 73 Multimeter Mode 74 N Normal Distribution Analysis in RUN-MAT 66 Analysis in STAT 67 Number of Samples 74 Number 27 O Option, Variations and catalogue keys 25 Other Icons 44 G - O

O cont. PAGE Other cont. Types of Equations 48 Other Devices Connection to 73 Venier Probes 73 P Parabola 19 Paste 72 Percentage Percentage key 11 Percentages 10 Permutations 62 Picture 28 Piecewise functions 20, 56 Plotting points 16 Poisson Distribution Calculations in STAT 69 Polynomial Equations 47 Power Properties 52 Powers and Roots 11 PRGM 5 Probability 26 Probe – EA100 Data logger 75 Procedure 76 Programme Programming Icon 38 Programme Mode Command List 42 Programme Mode Equipment Set up 75 Programming tools menu 38 R Racing functions 15 Range edited 15 RECUR Recur 5 Sequence and Series 71 Reset 52 Results Analysis 76 Returning to previous ‘Menus’ 8 Roots and Powers 11 RUN MAT Basic Activities 9 Icon 14 Normal Distribution Analysis 66 RUN-MAT 5, 7 S Samples 74 Sampling unit 75 Screen 7 O - S

71 Series 71 Setting Time Interval, Number of Samples and Time Type 74 Setting up within each icon 7 Simultaneous Equations 47 Solving Other Types of Equations 48 Polynomial Equations 47 Trigonometric equations 23 ‘X=...’ equations 23 STAT Binomial distribution calculations 68 Confidence Intervals 70 Distribution Poisson Calculations 69 Normal Distribution Analysis 67 Stat 5 Statistics 26, 32 Substitution – Algebraic 12, 57 Switching on and off 7 System Contrast 52 Language 52 Power properties 52 Reset 52 System 5, 52 Version 52 T Table Table of Values 62 Table 5, 45 Temperature Probe 73 Text and graph 8 Time Interval 74 Type 74 Time, Value and Money 28 TVM 5, 53 Transfer – Data Collection 74 Trigonometric equations 23 U Uni-variate 32 Unknown x-values 21 V Value 28 Values – Table 62 Variation 25 Version 52 S - T

V cont. Vertical Lines – Linear Programming 60 Voltage Probe 73 X ‘X=...’ equations 23 X-values 21 Z Zoom Auto 20 In and out 16 V - Z