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Casio fx-9750G Calculator Main Menu To choose a mode:

Use cursor keys to move to the icon and press EXE or press the number or letter in the bottom right-hand corner of the icon. The modes useful for Level 2 and 3 are:

• RUN usual calculations

• STAT statistical calculations and graphs

• LIST storing and editing data

• GRAPH drawing graphs

• DYNA multiple versions of a graph

• CONICS drawing conic functions

• EQUA solving equations SET UP SCREEN After choosing a mode, the set up screen can be used to select a number of options for that mode. Press SHIFT SET UP after choosing the required mode. Most modes allow the following changes

• Select type of function y = . . . etc • Select various options for a graph: axes, grid etc • Select radians or degrees • Select derivative on/off • Select type of integration Gauss/Simpson

Use cursor keys ( � � ) to highlight an option. Press the function key F1 to F6 for the required option as listed at the bottom of the screen. Press EXIT to leave the set up screen.

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Editing Press � or � to display the last calculation. Press � or � to move through previous calculations. Use cursor keys to move to the part of the calculation which is to be changed.

• Typing from this point will overwrite the previous calculation. • To insert a character, move the cursor to the right of the insertion point and press

SHIFT INS. Any number of new characters can be inserted. • Press DEL key to delete the current character.

General Functions Switching from graphics to text Press SHIFT F6 ( )G T↔ to switch between graphics and text screens. Variables The letters of the alphabet can be used to store variable values. When that letter is pressed, the value assigned to it is used in the calculation. To assign the value 2.56 to variable C, press 2.56 C→ EXE To clear this value, type AC 0 → ALPHA C EXE To input an equation Functions must be input for various options on the calculator. The variable is input using the ( ), ,X Tθ key.

This key inputs X for normal equations, θ for polar equations and T for parametric equations. To input the function 23 5 3x x− + , type ( ) ( )3 , , ^ 2 5 , , 3X T X Tθ θ− +

To input the function ( )sin 3 5x − , type ( )( )sin 3 , , 5X Tθ − Fractions Fraction calculations are carried out using the b

ca button. • Use SHIFT b

ca to convert to an improper fraction. • Use the F D↔ button to convert to and from the decimal version of the answer. • If a fraction is used as a power, it must be put in brackets.

3532 is entered as 32^(3 b

ca 5)

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Calculations requiring brackets. 5 2.87e × is entered as ( )5 2.87e ×

sin2π

is entered as ( )sin 2π ÷

23 7 3428 12 5

+ ×− ×

is entered as ( ) ( )23 7 34 28 12 5+ × ÷ − ×

456 2.4 1.8− × is entered as ( )456 2.4 1.8− × Numbers in exponential form

82.34 10× is entered as 2.34 EXP 8 It appears on the screen as 2.34E8 Calculations such as 1 400÷ giving small decimal values are displayed in exponential form unless this is switched off. To change this setting:

• Press SHIFT SET UP • Move down to highlight the display setting. • Press F3. This switches between the two options. • Press EXIT to return to the calculation screen. • For the calculation 1 400÷ ,

• Norm1 gives 2.5E-03 • Norm2 gives 0.0025

Random numbers To generate a random number between 0 and 1

• Press OPTN • Press F3 (PROB) • Press F4 (Ran#) then EXE

Factorials, permutations, combinations These functions are accessed from the OPTN menu

• Press OPTN • Press F6 to see next set of options • Press F3 (PROB) • For a factorial, press the number then F1 ( !x ) then EXE • For a permutation, type the first number then F2 ( n rP ) then the second number

and EXE eg for 9 5P press 9 F2 5 EXE giving 15120 • For a combination, type the first number then F3 ( n rC ) then the second number

and EXE eg for 12 4C press 12 F3 4 EXE giving 495

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Lists Lists are used to provide data for calculations involving, sequences, statistics and so on. There can be up to six lists in a single file. Lists may contain values to be used for statistical calculations such as mean, median and so on. Entering/Editing data in a list

• Select LIST from the main menu • Enter each number followed by EXE. The cursor automatically moves down. • To change a value, use �,�,�,� keys to move to the position, type correct

value and press EXE • To delete a number, highlight the value and press F3 (DEL). Values below move

up one position. Values in other lists are not affected. • To delete all values in a list, highlight any value in the list, press F4 (DEL-A) and

press F1 (YES) to confirm. • To insert a new cell, highlight the cell below the insertion point, press F5 (INS).

Lower cells move down and zero will be in the new cell. Change this to the required number.

Sorting values in a list

• Press F1 (SRT-A) to sort in ascending order or F2 (SRT-D) for descending order. • Input the number of lists to be sorted and EXE. (Usually one) • Respond to the “Select List (L)” prompt with the number of the list to be sorted.

If one list is to be sorted and other list(s) need to be linked to this one (eg ordered pairs)

• Press F1 (SRT-A) to sort in ascending order or F2 (SRT-D) for descending order. • For the number of lists to be sorted input 2 and EXE. • For “Select Base List (B)” prompt input the list to be sorted. (usually 1) • For “Select Second List (L)” prompt type in the list to be linked. (usually 2) • Respond to the “Select List (L)” prompt with the number of the list to be sorted. • Press EXE to perform the sort.

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Sequences Sigma Notation

The calculator can sum functions of the type ( )8

1

3 2k

k=

−�

• Press OPTN • Press F4 for CALC • Press F6 for the next list of options • Press F3 (�

• Type formula followed by start and end values separated by commas. • Press EXE

There is an optional value possible after the end value. It is used if the increment is not to be one. This can be omitted for NCEA work.

Example: To calculate the value of ( )8

1

3 2k

k=

−�

• Press OPTN • Press F4 for CALC • Press F6 for the next list of options • Press F3 (�

• Type 3ALPHA k - 2, ALPHA k,1,8 EXE The letter used (k in this case) can be any of the allowable variable names. The answer is 92 Tables/graphs of sequences The calculator can generate tables for sequences given an nth

term or recursive definition. To display a sequence:

• Select RECUR from the main menu • Press F3 (TYPE) to select the type of sequence • Press F1, F2 or F3 to choose • Type in formula, using F4 (n) to input the variable • Press F5 (RANG) to set the range of terms required then EXIT • Highlight required sequence then press F6 (TABL) to display the table of values • Press F1 (FORM) to return to the formula screen • Press F2 (DEL) and F1 (YES) to delete the data

If the sum of the values is required in the table, this must be set in the SET UP menu.

• Press SHIFT SET UP to enter the menu • The first entry is � display Press F1 or F2 to switch on/off

• Press EXIT to return to the sequence screen. • The sum will appear in the third column.

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Graphing sequences Create the table as above Press SHIFT F3 to set the view window values if necessary Press F5 (G-CON) to get a graph with pints connected OR Press F6 (G-PLT) to plot the points only Press F1 (an) to plot the sequence or F6 ( na� ) to plot the sum. Arithmetic sequence example:

• To find the first 8 terms of the sequence 3, 8, 13, 18 . . and the sum to eight terms.

• Select RECUR from main menu • Press SHIFT SET UP and turn � display on (F1)

• Press EXIT • Press F3 to select type of sequence • Press F1 for general arithmetic sequence • Type in formula 5 3na n= + ( F4 for n) • Press F5 (RANG) and input start and end values: EXE after each. • Press EXIT to return to the formula screen • Press F6 (TABL) to display table of sequence values and sums • Use � and � keys to scroll down to see all values. • Use F5 or F6 to plot a continuous graph or a set of points. • F1 returns to the formula and F2 deletes the data.

To generate a geometric sequence such as 2, 6, 18, . . . .

• Press F3 (TYPE) as above • Press F1 • Type in formula 2 3 ^na n= × • Proceed as in the example above.

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Complex Numbers To set degrees or radians:

• Select RUN from menu screen. • Press SHIFT SET UP to display set up menu. • Use arrow key � to move down to angle line. • Press F1 for degrees or F2 for radians. • Press EXIT to return to usual screen.

Converting degrees to radians Angles can be converted from degrees to radians and from radians to degrees. To change degrees to radians, radians must be chosen in the SET UP menu. To change radians to degrees, degrees must be chosen in the SET UP menu.

• Press OPTN • Press F6 for next set of options • Press F5 (ANGL) • To convert degrees to radians type in value, press F1 ( � ) and EXE • To convert radians to degrees type in value, press F1 (r) and EXE

Performing complex number calculations From the RUN screen, press OPTN then F3 to display complex number options at the bottom of the screen. The letter i for complex numbers is obtained by pressing F1 from this screen. Addition, Subtraction and Multiplication To add, subtract or multiply complex numbers, enter them in the usual way using the F1 key for i. Complex numbers need to be in brackets for subtraction and multiplication. For example: ( ) ( )2 3 1 4i i+ × − will give 14 5i− as the answer. Reciprocals The reciprocal of a complex number can be found in the following way.

To calculate 1

1 i+, enter ( )1 1 i÷ + , giving 0.5 0.5i−

Modulus and Argument of a complex number (The modulus of a complex number is called absolute value in this calculator) Make sure degrees or radians are set as required. To get the modulus for the complex number 5 12i+ . Press F2 ( 5 12i+ ) and EXE This gives 13 as the answer.

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To get the argument for the complex number 5 12i+ . Press F3 ( 5 12i+ ) and EXE This gives 1.176 radians. The other options for complex numbers are to find the conjugate (F4), and to extract the real (F5) and imaginary (F6) parts of a complex number. Converting from rectangular to polar form (Make sure degrees or radians are set as required.)

• Press OPTN F6 to select options • Press F5 to select ANGL • Press F6 to see next set of options • Press F1 (Pol) • Type in the x and y values separated by a comma and close the bracket • Press EXE to obtain the answer. The first value is r and the second is θ .

Example: Type Pol(5, 6) gives 7.81, 0.876r θ= = radians Converting from polar to rectangular form (Make sure degrees or radians are set as required.)

• Press OPTN F6 to select options • Press F5 to select ANGL • Press F6 to see next set of options • Press F2 (Rec) • Type in the r and θ values separated by a comma and close the bracket • Press EXE to obtain the answer. The first value is x and the second is y.

Example: Type Rec(4, 0.74) gives 2.954, 2.697x y= = Solving equations with complex solutions The Calculator can provide solutions for quadratic and cubic equations which have complex number solutions. See the section on solving equations Page 12

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Differentiation Finding the value of a derivative at a given point. The derivative of a function can be found for any value of x by inputting the equation and the required value for x.

• Press OPTN then F4 to enter CALC screen. • Press F2 to select /d dx option • Type in the equation. • Type in the required x value • Type in the increase/decrease of x (This is optional) • Press EXE

Example: To find the derivative of sin x when 0.5x =

• Press OPTN • Press F4 • Press F2 • The screen shows / (d dx

• Type sin followed by the ( ), ,X Tθ key then a comma then 0.5 then EXE The answer is 0.8775835

The format for a calculation is ( )/ equation, -valued dx x The value of the second derivative can also be found in the same way by using the

2 2/d dx option rather than /d dx . Maximum and Minimum values The maximum or minimum value for a function over an interval can be found. This is a numerical calculation rather than an algebraic one and may not give the exact value for the derivative.

• Press OPTN • Press F4 for CALC • Press F6 for next list of options • Press F1 or F2 to select FMin or FMax • Type in function and end points for the interval • Wait for answer (the black square at top right of the screen indicates it is working) • The top number on the answer screen is the x value and the bottom number is the

y value for the Max/Min point. Only a function involving x can be used for this calculation. There is an optional variable for the precision of the calculation. This can be an integer from 1 to 9. The larger the value, the more precision but the longer it will take.

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Example: To find the minimum value for the function 23 12 4x x− + over the interval

0 to 4x x= = . • Press OPTN • Press F4 for CALC • Press F6 for next list of options • Press F1 to select FMin • Type ( ) ( )3 , , ^ 2 12 , , 4, 0, 4X T X Tθ θ− + EXE

The answer given is 2, 8x y= = − (It takes nearly a minute) The form of the input line is: FMin( function, starting value, end value) The final bracket can be omitted. The precision value if used comes after the end value. Integration The calculator can perform numerical integration using two methods. Simpson’s Rule is the one used for NCEA. For Simpson’s Rule, the equation and end points of the interval are input, together with an optional value for n, the number of divisions used. If n is not specified, the calculator will use an appropriate value. The format for entering the function is: ( )function, start point, end pointdx�

• Press OPTN then F4 to enter CALC screen. • Press F4 to select dx� option

• Type in the equation • Type in the start and end points separated by commas • Input the value of n if required • Press EXE

Example:

To find the value of the integral ( )4 2

16 2x x dx+�

• Press OPTN then F4 to enter CALC screen. • Press F4 to select dx� option

• Type ( ) ( )6 , , ^ 2 2 , , ,1, 4X T x X Tθ θ+

• Press EXE The answer given is 141. This is the exact value, but since a numerical method is being used, the answer will not always be exact.

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If the function crosses the x-axis between the start and end points being used, the total area can be found by finding separate positive and negative areas. Graph of integration Area The calculator can draw a graph for a function showing the required area on the screen and the value of the area.

• Set view window values to suit the graph. • Press SHIFT F4 (Sketch) • Press F1 to clear the screen • Press F5 ( G dx− � )

• Type in the function to be integrated with the start and end points and press EXE The form of the equation is: Function, start value, end value, tolerance The tolerance should be small (1E-5) to give an accurate answer. Example:

Find the value of the integral ( )3 2

04x x dx−�

Type: ( ) ( )4 , , , , ^ 2,0,3,1 5X T X T EXPθ θ− − EXE The graph is shown with the area shaded and the area given as 9. Integral from a drawn graph Once a graph has been drawn, the integral for any range of values can be found.

• Draw the required graph of ( )y f x= • Press SHIFT F5 (G-Solv) • Press F6 for the next set of options • Press F3 for dx�

• Select graph with � or � keys if necessary • Move the pointer using � and EXE to set lower limit • Move the pointer using � and EXE to set upper limit • The value of the integral will appear at the bottom of the screen and the graph will

be shaded to show the area involved. This method only works for a graph in the form y = . . .

y

x1 2 3 4 5 – 1

2

4

6

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Solving Equations The calculator can solve sets of linear simultaneous equations with up to 6 variables, as well as quadratic and cubic equations. Simultaneous Equations

• Choose EQUA from the main menu • Press F1 to select simultaneous equations • Press F1 to F5 to select the number of variables • Enter the coefficients. (the form of the equation is at the top of the screen). Press

EXE after each entry – the cursor will move to the next position. • Press F1 to solve the equations.

If there is data already stored in the machine, a warning will be given before new data is entered. To clear the old data:

• Select the number of variables • Press F2 to select Delete • Press F1 to confirm • Select numbers of unknowns again and continue as above.

Example: Solve:

2 3 143 6

4 2 8

x y z

y zx y z

− + =− = −

+ − = −

• Choose EQUA from the main menu • Press F1 to select simultaneous equations • Press F2 to select 3 variables • Type in each number followed by EXE (2 EXE -1 EXE 3 EXE etc) • Press F1 (SOLV) to obtain the answers

The answers are 2, 1, 3x y z= = − = If there are no solutions to the set of equations, the calculator will give a Mathematical Error message - (Ma Error). Quadratic and Cubic Equations The calculator can solve quadratic or cubic equations in the form

2

3 2

0

0

ax bx c

ax bx cx d

+ + =+ + + =

• Choose EQUA from the main menu • Press F2 to select Polynomial • Press F1 or F2 to select the degree of the equation

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• Enter the coefficients. (the form of the equation is at the top of the screen). Press EXE after each entry – the cursor will move to the next position.

• Press F1 to solve the equations. If the equation has imaginary roots (complex numbers) these will be displayed in the form a bi+ . These are required for Level 3 Calculus. Example: Solve 25 11 12 0x x+ − =

• Choose EQUA from the main menu • Press F2 to select Polynomial • Press F1 to select degree 2 • Enter the coefficients. 5 EXE 11 EXE -12 EXE • Press F1 to solve the equations.

The answers are 0.8 and -3 Example: Solve 3 22 3 20 0x x x− − − =

• Choose EQUA from the main menu • Press F2 to select Polynomial • Press F2 to select degree • Enter the coefficients. 1 EXE -2 EXE -3 EXE -20 EXE • Press F1 to solve the equations.

The answers are 4, 1 2 , 1 2i i− + − − . The last two answers are complex numbers. Newton Raphson Method When an equation is entered, the calculator will solve it using the Newton Raphson method. There is no control over the number of iterations. The calculator gives the most accurate answer possible. The method may fail depending on the equation which is input.

• Choose EQUA from the main menu • Press F3 to select Solver • Use DEL to delete any equation present (Yes to confirm) • Type in the equation. (It does not have to equal zero) and press EXE (The equals

sign is SHIFT decimal point) Use ( ), ,X Tθ for x.

• Press F6 to solve the equation The Lft and Rgt are values on either side of the solution. The closer together these numbers are, the better the solution.

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Example: Solve 5 3 1 0x x+ + =

• Choose EQUA from the main menu • Press F3 to select Solver • Use DEL to delete any equation present (Yes to confirm) • Type ( ), ,X Tθ ^5+3 ( ), ,X Tθ +1 = 0 and press EXE.

• Type in an approximate value for x if known. • Press F6 to solve. • The answer is - 0.331989

Both Lft and Rgt are the same, indicating a very accurate answer. The method does not work with functions such as , ln , sinxe x x etc.

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Graphs Graphs will remain in the memory even after the calculator is switched off. Press F2 (DEL) to delete a highlighted graph. Press F1 (Yes) to confirm. Most scientific function graphs can be drawn with view window settings set automatically. Setting the axes Press SHIFT F3 at any time to see the view window and alter values Press EXIT to leave this screen. This screen allows changes to be made for the following: Xmin – minimum value on x-axis

Xmax – maximum value on x-axis Xscale – spacing of increments on x-axis Ymin – minimum value on y-axis

Ymax – maximum value on y-axis Yscale – spacing of increments on y-axis

Choosing F1 (INIT) sets an initial range of values Choosing F2 (TRIG) sets an initial range for trig graphs. The values depend on the choice of degrees or radians. Values such as 2π can be used. Choosing F3 (STD) sets a standard range of values. (-10 to +10) Initial values for polar graphs are found by scrolling down past the bottom of the first screen. F4 (STO) and F5 (RCL) allow six different view windows to be stored and recalled for later use. Types of Graph The following types of graph can be drawn:

• Standard .....y = used for most graphs in NCEA • Vertical line x c= where c is a constant • Polar graphs ...r = not needed for NCEA • Parametric graphs (Parm) used for Level 3 Calculus • Inequalities ....y > for showing an area which obeys the condition.

Choosing graph type

• From main menu select GRAPH (press 5) (Individual graphs can also be drawn directly from RUN by pressing SHIFT F4 and then F5 (GRPH). The equation is entered in the usual way.

• Press F3 (TYPE) • Use F1 to F4 to select type of graph required.

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Graphing y = . . . . or x = . . . • Press SHIFT F3 to see the view window and change values if necessary. • Choose GRAPH from the main menu • Press F1 for y = . . . or F4 for x = . . .

• Type graph equation in an empty line. Use ( ), ,X Tθ for the variable

• Press EXE to store graph. • Enter other graphs if needed. • Press F6 to draw all selected graphs. • Press EXIT to return to the list of graphs. • Press F1 ( SEL) to choose which graphs on the list are to be drawn. (Graphs will

be drawn if the = sign is highlighted in the list ) • The set up screen (SHIFT SET UP) can be used to turn axes, grid and labels

on/off. • Press F5 (GMEN) to store graphs in the memory (RCL to recall later)

Graphing in parametric form

• Press SHIFT F3 to see the view window and change values if necessary. • Choose GRAPH from the main menu • Press F3 (PARM) • Type graph equation in two empty lines, one for x and one for y. Use ( ), ,X Tθ

for the variable – it will appear as T on the screen. • Press EXE to store graph. • Enter other graphs if needed. • Press F6 to draw all selected graphs. • Press EXIT to return to the list of graphs. • Press F1 ( SEL) to choose which graphs on the list are to be drawn. (Graphs will

be drawn if the = sign is highlighted in the list ) • The set up screen (SHIFT SET UP) can be used to turn axes, grid and labels

on/off. • Press F5 (GMEN) to store graphs in the memory (RCL to recall later)

Graphing an inequality

• Press SHIFT F3 to see the view window and change values if necessary. • Choose GRAPH from the main menu • Press F6 to see next list of options. • Press F1 to F4 to select type of inequality ( , , ,y Y y y> < ≥ ≤ ) • Type graph equation. Use ( ), ,X Tθ for the variable.

• Press EXE to store graph. • Enter other graphs if needed. • Press F6 to draw all selected graphs. • Press EXIT to return to the list of graphs.

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• Press F1 ( SEL) to choose which graphs on the list are to be drawn. (Graphs will be drawn if the = sign is highlighted in the list )

• The set up screen (SHIFT SET UP) can be used to turn axes, grid and labels on/off.

• Press F5 (GMEN) to store graphs in the memory (RCL to recall later) When an inequality is graphed, the region obeying the inequality is shaded. For the inequality 1y x> − , the region above the line will be shaded. Other Graphing functions Trace The trace function moves a pointer around the graph, giving coordinates and the derivative at each point if turned on. Trace can also find the point of intersection of graphs.

• After drawing the graph(s) press F1 to show the pointer in the centre of the graph.

• Use arrow keys � and � to move the pointer between the graphs. • Use arrow keys � and � to move the pointer along the graph. • The coordinates of the point are shown at the bottom of the screen. • If the derivative is On in the set up screen, the value of the derivative is also

shown. • Press F1 again to stop the trace function.

Graphing a specific range A graph can be drawn within a specific set of x values using the following format. Function, [ ]start point, end point, EXE The square brackets are on the keys SHIFT + and SHIFT – Example: Sketch the graph of 2 4, for 0 4y x x= − ≤ ≤

Enter ( ), , ^ 2 4,0,4X Tθ − EXE Zoom Once a graph is drawn, there are various ways of zooming in on part of the graph. The most useful are explained below. Others are described in the annual. Box Zoom This method draws a box around the section of the graph which is to be enlarged. The part inside the box then fills the screen.

• Draw the required graphs • Press F2 (Zoom) • Press F1 (Box)

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• Use cursor keys (�, �, �, �) to move to one corner of the required box then EXE

• Use the keys to move to a diagonally opposite corner and press EXE • The part of the graph inside the box now fills the screen. • To return to the original screen, press F2 then F6 then F1 (ORIG)

Factor Zoom This zooms in/out by a given factor, using the position of the pointer as the centre of the new screen.

• Draw the required graphs • Press F2 (Zoom) • Move the pointer to the required position(it starts at the origin) • Press F2 (FACT) • Type in the required factors for x and y • Press EXIT to return to the graph screen • Press F3 (IN) to enlarge (press F4 (OUT)m to reduce) • Press F6 then F5 (PRE) to return to original.

In Zoom, pressing F5 (AUTO) will adjust the graph so that it fills the screen along the y axis. In Zoom, pressing F6 then F2 (SQR) will make circle graphs circular if they appear elliptical originally. Solving equations from a graph Once a graph is drawn, it can be used to find solutions to ( ) 0f x = , y-intercepts, maximum and minimum values, integral values and points of intersection of graphs. Finding roots of the equation ( ) 0f x =

• Draw the graph of ( )y f x= • Press SHIFT F5 (G-Solv) • Press F1 (ROOT) • Use � or � keys to choose the required graph if there is more than one drawn. • Find the first root from the left by pressing EXE • The value of the root is displayed at the bottom of the screen • Press � to find the next root to the right (or � to move to the left)

This method only works for a graph in the form y = . . . or an inequality.

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Maximum and minimum values The local maximum and minimum values for a graph can be found.

• Draw the graph(s) of ( )y f x= • Press SHIFT F5 (G-Solv) • Press F2 (MAX) or F3 (MIN) • Select the required graph using � or � keys if necessary • Press EXE to get the maximum value

If there is more than one maximum or minimum value, use the � key to move between them. This method only works for a graph in the form y = . . . or an inequality. Finding y–intercepts The y-intercepts for a graph are found as follows.

• Draw the graph(s) of ( )y f x= • Press SHIFT F5 (G-Solv) • Press F4 (Y-ICPT) • Select the required graph using � or � keys if necessary • Press EXE

This method only works for a graph in the form y = . . . or an inequality. Finding points of intersection for two graphs The following method is used to find the points of intersection for any two graphs drawn on the screen.

• Draw the required graphs of ( )y f x= • Press SHIFT F5 (G-Solv) • Press F5 (ISCT) • If only two graphs are drawn, the intersection will be found immediately. If not,

choose the required two graphs by pressing � to show the equation of each graph and EXE as their equations are displayed at top left.

• When the second graph is chosen, wait for the point of intersection to appear. • Press � to get the next point of intersection if it exists.

This method only works for a graph in the form y = . . . or an inequality. Finding one coordinate given the other Once a graph is drawn, the value of y can be found given a value of , or the value of x given y can be found.

• Draw the required graph of ( )y f x= • Press SHIFT F5 (G-Solv) • Press F6 to move to the next set of options

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• Press F1 (Y-CAL) or F2 (X-CAL) • Input the x or y value at the cursor • Press EXE • If there is more than one answer use � and � arrows to move between them.

Drawing a Tangent to a curve A tangent can be drawn at any point on an existing graph.

• Draw the graph as usual • Press SHIFT F4 (SKTCH) • Press F2 (Tang) • Use arrow keys to move the cursor to the required point and press EXE

A normal can be drawn in the same way, by choosing F3 (Norm) from the sketch menu. Graphing an Inverse Function Once a graph is drawn, its inverse can be drawn on the same axes.

• Draw the graph as usual • Press SHIFT F4 (SKTCH) • Press F4 (Inv)

The inverse will be drawn. Dynamic Graphs In a dynamic graph, a basic graph is drawn and the coefficients can then be changed to show the effect of the changes on the original graph. All the graphs are drawn on the same set of axes for the comparison. The following basic graphs are built-in:

( )

( )( )( )

2

2

3 2

sin

cos

tan

y ax b

y a x b c

y ax bx c

y ax bx cx d

y a bx c

y a bx c

y a bx c

= +

= + +

= + += + + += +

= +

= +

Others can be entered as necessary. Dynamic graphs can be rectangular, polar or parametric.

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The steps are as follows: • Select or input a function • Choose which coefficient is to be varied (The dynamic coefficient) • Assign values to each coefficient • Specify the range for the dynamic coefficient • Specify the speed of drawing • Draw the graph.

To draw a dynamic graph:

• Select DYNA from the main menu • Set view window values if necessary • Press F5 (B-IN) • Choose function from the list and press F1 (Sel) to select • Press F4 (VAR) to get the coefficient menu • Use F1 (Sel) to select dynamic coefficient (First variable automatically chosen) • Type in required values for any other variables • Press F2 (RANG) to select the range of values for the dynamic coefficient • Press F3 (SPEED) to change to drawing speed if needed • Press F6 (DYNA) to draw the graphs.

There are several other options available for drawing these graphs. Refer to the calculator manual for these. Other Options As well as the above, it is possible to do the following:

• Plot individual points on a graph • Draw any line on the graph • Draw horizontal and vertical lines • Draw freehand • Write text on the graph • Draw two graphs on a split screen • Create a table of coordinates from a drawn graph

These functions are described in the calculator manual.

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Conic Sections The calculator can graph circles, parabolas, ellipses and hyperbolas. The basic general equations for these graphs are built in. As well, various features of each type can be drawn or calculated. Conic sections are accessed by pressing CONICS from the main menu. Circle The following forms of the circle equation are built in: ( ) ( )2 2 2x h y k r− + − = (h, k) is the centre, r is the radius

2 2 0ax ay bx cy d+ + + + = To draw a circle:

• Select CONICS from the main menu • Set view window values if necessary (SHIFT F3) • Use � key to move down to the required equation • Press EXE • Enter the values listed on the screen pressing EXE after each • Press F6 to draw the circle.

If the circle is drawn elliptical rather than circular, this can be corrected in the following way:

• Draw the graph • Press F2 • Press F6 to see the next list of options • Press F2 (SQR) • Press SHIFT F3 to see the view window settings.

Circle analysis Once a circle is graphed, the coordinates and the centre can be found as follows:

• Draw the circle as above • Press F5 (G-Solv) • Press F1 (CNTR) for the centre or F2 (RADS) for the radius

Ellipse The built in form of the ellipse is:

( ) ( )2 2

2 2 1x h y k

a b

− −+ =

To draw an ellipse:

• Select CONICS from the main menu • Set view window values if necessary (SHIFT F3) • Use � key to move down to the required equation

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• Press EXE • Enter the values listed on the screen pressing EXE after each • Press F6 to draw the ellipse.

Ellipse analysis Once an ellipse has been drawn, the focuses and x/y intercepts can be found.

• Draw the ellipse as above • Press F5 (G-Solv) • Press F1 (FOCS) for one focus. (Press � or � keys to swap between foci) • Press F2 (X-IN) or F3 (Y-IN) for the x or y intercepts • Press � or � keys to swap between intercepts on any axis.

If there are no intercepts, a “NOT FOUND” message will appear. Hyperbola The built in forms of the hyperbola are:

( ) ( )

( ) ( )

2 2

2 2

2 2

2 2

1

1

x h y ka b

y k x h

a b

− −− =

− −− =

To draw a hyperbola.

• Select CONICS from the main menu • Set view window values if necessary (SHIFT F3) • Use � key to move down to the required equation • Press EXE • Enter the values listed on the screen pressing EXE after each • Press F6 to draw the hyperbola.

Hyperbola analysis Once the graph has been drawn, the following features can be determined. Focus, x/y intercepts, vertex. The asymptotes can also be drawn on the graph.

• Draw the hyperbola as above • Press F5 (G-Solv) • Press F1 (FOCS) for one focus. (Press � or � keys to swap between foci) • Press F2 (X-IN) or F3 (Y-IN) for the x or y intercepts • Press � or � keys to swap between intercepts on any axis. • Press F4 (VTX) to find the vertices (Press � or � keys to swap between

vertices) • Press F5 to draw the asymptotes.

If there are no intercepts, a “NOT FOUND” message will appear.

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Parabola The built in forms of the parabola are:

( )

( )

2

2

2

2

x a y k h

x ay by c

y a x h k

y ax bx c

= − +

= + +

= − +

= + +

To draw a parabola.

• Select CONICS from the main menu • Set view window values if necessary (SHIFT F3) • Use � key to move down to the required equation • Press EXE • Enter the values listed on the screen pressing EXE after each • Press F6 to draw the parabola.

Parabola analysis Once a parabolic graph is drawn, it can be used to find the following features. Focus, axis of symmetry, directrix, vertex and latus rectum

• Draw the hyperbola as above • Press F5 (G-Solv) • Press F1 (FOCS) for the focus • Press F2 (SYM) to draw in the line of symmetry • Press F3 (DIR) to draw the directrix • Press F4 (VTX) to find the vertex • Press F5 (LEN) to find the latus rectum.

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Statistics Basic Statistical calculations Calculations such as mean, median etc are done from a list of data. (See Lists Page 4) Data can be sorted in order using the LIST menu. Data can also be entered directly into the STAT screen The calculations provided for one-variable data (in order on the screen) are: x Mean

x� Sum of values 2x� Sum of squares

x nσ Population standard deviation

1x nσ − Sample standard deviation n Number of values minx Minimum value in list Q1 Lower quartile Med Median Q3 Upper quartile

x nx σ− Data mean – standard deviation

x nx σ+ Data mean + standard deviation maxX Maximum value in list Mod Mode Two variable data provides some of the same calculations as above for each of x and y. The omissions are maximum and minimum values, median and quartiles. The extra calculation provided is:

xy� Sum of xy

• Select STAT from the main menu • Type data into a list with EXE after each value. (See Lists Page 4) • Press F2 (CALC) to see calculation options • Press F1 (1VAR) or F2 (2VAR) for one or two variable calculations • Scroll down using arrow keys to see all the values. • Press EXIT to return to the list of data

Mean or median from a frequency table It is possible to calculate mean or median from a frequency table using the LIST menu, rather than the STAT menu.

• Select LIST from the main menu, or type data directly into STAT screen • Type data values into List1 • Type frequency values into List2 • Move the cursor to an empty cell. (The answer goes into the cell which is

highlighted. – Make sure it is empty) • Press OPTN F1 • Press F6 for the next set of choices

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• Press F3 for mean or F4 for median • Press F6 twice • Press F1 (List) then 1 then a comma then F1 then 2 and close bracket. • Press EXE

The mean/median will appear in the highlighted cell. Basic Statistical graphs View window values are set automatically for statistical graphs. Box and whisker plot First enter the data into a list. (Use LIST or STAT for this)

• Select STAT from the main menu • Press F1 (GRPH) to see graph menu • Press F6 (SET) to set graph type • Use � key to move to Graph Type • Press F6 to see second set of options • Press F2 (Box) for box and whisker plot ( not F3) • Adjust Xlist entry if the list of data is not in List1 • Use � key to scroll down and press EXE to end • Press F1 (GPH1) to see the plot • Press F1 at this stage to see basic statistics for the data (F6 to see the graph again)

Histogram First enter the data into a list. (Use LIST or STAT for this)

• Select STAT from the main menu • Press F1 (GRPH) to see graph menu • Press F6 (SET) to set graph type • Use � key to move to Graph Type • Press F6 to see second set of options • Press F1 (Hist) • Adjust Xlist entry if the list of data is not in List1 • Use � key to scroll down and press EXE to end • Press F1 (GPH1) to see the plot • Press F1 at this stage to see basic statistics for the data (F6 to see the graph again)

Changing the pitch will change the number of bars drawn in the histogram. Scatter Diagram First enter the data into a list. (Use LIST or STAT for this) The x values go in List1 and the y values in List2

• Select STAT from the main menu • Press F1 (GRPH) to see graph menu • Press F6 (SET) to set graph type • Use � key to move to Graph Type

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• Press F1 (Scat) for scatter diagram • Use � key to scroll down and press EXE to end • Press F1 (GPH1) to see the plot • Press F1 at this stage to see basic statistics for the data including regression

values. (F6 to see the graph again) • Press F1 again to see the line of best fit.

Curve Fitting The statistical regression functions of the calculator can be used to find the equation which fits a given set of data. The functions supported are:

• Straight line (linear) • Quadratic • Cubic • Quartic • Logarithmic • Exponential • Power law • Sine

Polynomials (quadratic, cubic, quartic) The number of points required to determine a polynomial is one more than the degree of the polynomial. The form for each of these polynomials is: Quadratic 2ax bx c+ + three points required Cubic 3 2ax bx cx d+ + + four points required Quartic 4 3 2ax bx cx dx e+ + + + five points required To determine the equation of a polynomial:

• Select LIST from the main menu or enter directly into the STAT screen • Enter the x values into List1 and the y values into List2 (EXE after each value) • Press MENU for the main menu • Select STAT • Press F2 (CALC) • Press F3 (REG) • Choose F1, F3, F4, F5 for linear, quadratic, cubic or quartic • The values of the coefficients a, b, c, . . . will be given on the screen • Press F1 or F2 to see the basic statistics for the data.

If the data fits one of the polynomials exactly, the coefficients given will also be exact. Example: Find the cubic equation which fits the data (1, 11), (3, 40), (5, 170), (6, 283) Four points are needed to determine a unique cubic equation.

• Select LIST from the main menu or enter directly into the STAT screen • Enter the x values into List1 and the y values into List2 (EXE after each value)

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• Press MENU for the main menu • Select STAT • Press F2 (CALC) • Press F3 (REG) • Choose F3 for a cubic equation • The values of the coefficients a, b, c, d will be given on the screen

The value for c is given as -1.6E-10. This has to be interpreted as zero. The equation is 2 22 5y x x= + − Exponential model If a set of data is approximately exponential, the equation in the form bxy ae= can be found.

• Select LIST from the main menu or enter directly into the STAT screen • Enter the x values into List1 and the y values into List2 (EXE after each value) • Press MENU for the main menu • Select STAT • Press F2 (CALC) • Press F3 (REG) • Press F6 to set next set of options • Press F2 (Exp) • The values of the coefficients a, b will be given on the screen

The closer the points fit an exponential model, the closer the value of r will be to one. Power law model If a set of data is approximately exponential, the equation in the form by ax= can be found.

• Select LIST from the main menu or enter directly into the STAT screen • Enter the x values into List1 and the y values into List2 (EXE after each value) • Press MENU for the main menu • Select STAT • Press F2 (CALC) • Press F3 (REG) • Press F6 to set next set of options • Press F3 (Pwr) • The values of the coefficients a, b will be given on the screen

The closer the points fit an exponential model, the closer the value of r will be to one. Example: Find the power law function which best fits the data (1, 5), (3, 19), (5, 35), (8, 60)

• Select LIST from the main menu or enter directly into the STAT screen • Enter 1, 3, 5, 8 into List1 EXE after each • Enter 5, 19, 35, 60 into List2 EXE after each • Press MENU • Select STAT

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• Press F2 then F3 then F6 • Press F3 (Pwr) • The results appear on the screen.

The power law model is 1.1985.038y x= Fitting a Sine Model to data A model of the form sin( )y a bx c d= + + can be fitted to appropriate data values.

• Select LIST from the main menu or enter directly into the STAT screen • Enter the x values into List1 and the y values into List2 (EXE after each value) • Press MENU for the main menu • Select STAT • Press F2 (CALC) • Press F3 (REG) • Press F6 to set next set of options • Press F4 (Sin) • The values of the coefficients a, b will be given on the screen

The angle must be set to radians for this option. (Use SHIFT SET UP for this.) Example:

Find the sine function which fits the data ( ) 30,7 , , 4 , ,1 , ,7 , ,1

8 4 2 4π π π π� � � � � � � �� � � � � � � �� � � � � � � �

(8π

can be entered as 8π ÷ )

• Enter the x values into List1 and the y values into List2 (EXE after each value) • Press MENU • Select STAT • Press F2 then F3 then F6 • Press F4 (Sin) and wait. It will take nearly a minute

The coefficients appear on the screen

3, 4, 1.57079, 4a b c d= = = = The sine function is:

( )

( )3sin 4 1.57079 4

3sin 2 2 0.785395 4

y x

x

= + +

= + +

The value 0.785395 is approximately 4π

which was used to generate the data.

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Distributions The calculator can determine probabilities for the Normal, Binomial and Poisson distributions. Normal distribution The area under the normal curve can be found by specifying the mean ( )µ and standard

deviation ( )σ for the distribution. The upper and lower boundaries for the required probability are also entered. If the upper limit is ∞ , enter a large number for the limit. (eg 1EXP6) If the lower limit is −∞ , enter a large negative number for the limit. (eg -1EXP6)

• Select STAT from the main menu • Press F5 (DIST) • Press F1 (NORM) • Press F2 (Ncd) Do not use F1 here • Enter each value and press EXE after each one • Press F1 to calculate the probability • Press EXIT to return to previous screen

Example: For the normal distribution with mean 50 and standard deviation 10, find the probability that a value is greater than 70.

• Select STAT from the main menu • Press F5 (DIST) • Press F1 (NORM) • Press F2 (Ncd) Do not use F1 here • Enter 70 EXE 1EXP6 EXE 10 EXE 50 EXE • Press F1 to calculate the probability • The answer is 0.02275

Graphing the normal distribution It is possible to graph the normal curve showing the areas associated with three common probabilities. The value of the probability is also given. The following graphs can be drawn. P(t) Q(t) R(t) The procedure for drawing each graph is the same except for the choice of function as shown above (P, Q, R).

• Select RUN from main menu • Press SHIFT F4 (Sketch)

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• Press F1 (CLS) and EXE • Press F5 (GRPH) • Press F1 ( Y = ) • Press OPTN F6 then F3 (PROB) • Press F6 for next set of options • Press P( or Q( or R( to get required graph above. • Type in value for Standard Normal variate, close bracket and EXE • The graph will be drawn and the associated probability is shown on the screen.

Example: Show the Normal graph for the probability ( )1.5P Z >

• Select RUN from main menu • Press SHIFT F4 (Sketch) • Press F1 (CLS) and EXE • Press F5 (GRPH) • Press F1 ( Y = ) • Press OPTN F6 then F3 (PROB) • Press F6 for next set of options • Press R( • Type in 1.5 close the bracket and EXE

Inverse Normal The inverse Normal requires the mean and standard deviation and a value for “Area” This value is the required percentile written as a decimal. i.e. the 95th percentile is entered as 0.95

• Select STAT from the main menu • Press F5 (DIST) • Press F1 (NORM) • Press F3 (InvN) • Enter each value and press EXE after each one • Press F1 to calculate the probability • Press EXIT to return to previous screen

Example: Find the 95th percentile for the normal distribution with mean 50 and standard deviation of 10.

• Select STAT from the main menu • Press F5 (DIST) • Press F1 (NORM) • Press F3 (InvN) • Enter 0.95 EXE 10 EXE 50 EXE • Press F1 to calculate the probability • The answer is given as 66.448

This means that 95% of the values for this distribution are below 66.448

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Binomial distribution The calculator can determine individual and cumulative probabilities for the binomial distribution. The number of trials (Numtrial) and probability of success (p) must be entered. Individual and cumulative probabilities are handled differently. Individual binomial probability

• Select STAT from the main menu • Press F5 (DIST) • Press F5 (BINM) for the binomial distribution • Press F1 (Bpd) • Press F2 (var) to enter a single variable • Enter required x value EXE • Enter the number of trials EXE • Enter the probability p EXE • Press F1 to calculate the answer • Press EXIT to return to previous screens

Example: Find the probability of 6 success from a binomial distribution with 10 trials and probability of success 0.35

• Select STAT from the main menu • Press F5 (DIST) • Press F5 (BINM) for the binomial distribution • Press F1 (Bpd) • Press F2 (var) to enter a single variable • Enter 6 EXE 10 EXE 0.35 EXE • Press F1 to calculate the answer • The answer is 0.068909

Cumulative binomial probability If the binomial probability is required for a range of values, these values must be entered into a list first. This list is then specified when calculating the probabilities.

• Select STAT from the main menu • Enter the required x values into List1 • Press F5 (DIST) • Press F5 (BINM) for the binomial distribution • Press F2 (Bcd) (Cumulative) • Press F1 if necessary to accept List • Set List to List1 if necessary • Enter the number of trials EXE • Enter the probability p EXE • Press F1 to calculate the answer • Press EXIT to return to previous screens

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The results on the screen are interpreted in the following way. The first line is the probability for the first value of x in the list The second line is the sum of the probabilities for the first two values on the list. The third number is the sum of the first three probabilities and so on. The numbers 1, 2, 3, 4, . . down the left are not the x values from the list. The cumulative value is always given starting from x = 0. Example: For the binomial distribution with 10 trials and probability of success 0.35, find the probability of 0, 1, 2 ,3 or 4 successes. i.e ( )4P X ≤

• Select STAT from the main menu • Enter into List1 0 EXE 1 EXE 2 EXE 3 EXE 4 EXE • Press F5 (DIST) • Press F5 (BINM) for the binomial distribution • Press F2 (Bcd) (Cumulative) • Press F1 if necessary to accept List • Set List to List1 if necessary • Enter the number of trials 10 EXE • Enter the probability p 0.35 EXE • Press F1 to calculate the answer

The answers appear as follows: 1 0.0134 meaning ( )0P X =

2 0.0859 meaning ( )0,1P X ≤

3 0.2616 meaning ( )0,1,2P X ≤

4 0.5138 meaning ( )0,1,2,3P X ≤

5 0.7514 meaning ( )0,1,2,3, 4P X ≤ The answer to the question is ( )4P X ≤ = 0.7514 To see the full value of any decimal answer, highlight it – the full value appears at the bottom of the screen. Poisson Distribution The calculator can determine individual and cumulative probabilities for the Poisson distribution. The mean ( )µ for the distribution must be entered. Individual and cumulative probabilities are handled differently. Individual Poisson probability

• Select STAT from the main menu • Press F5 (DIST) • Press F6 to see next set of options • Press F1 (POISN) for the Poisson distribution • Press F1 (Ppd)

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• Press F2 (var) to enter a single variable • Enter required x value EXE • Enter the mean EXE • Press F1 to calculate the answer • Press EXIT to return to previous screens

Example: Find the probability of 8 successes for a Poisson distribution with mean 5.4

• Select STAT from the main menu • Press F5 (DIST) • Press F6 to see next set of options • Press F1 (POISN) for the Poisson distribution • Press F1 (Ppd) • Press F2 (var) to enter a single variable • Enter required x value EXE • Enter the mean EXE • Press F1 to calculate the answer • The answer is 0.080991

Cumulative Poisson probability If the Poisson probability is required for a range of values, these values must be entered into a list first. This list is then specified when calculating the probabilities.

• Select STAT from the main menu • Enter the required x values into List1 • Press F5 (DIST) • Press F6 to see next set of options • Press F1 (POISN) for the Poisson distribution • Press F2 (Pcd) (Cumulative) • Press F1 if necessary to accept List • Set List to List1 if necessary • Enter the mean EXE • Press F1 to calculate the answer • Press EXIT to return to previous screens

The results on the screen are interpreted in the following way. The first line is the probability for the first value of x in the list The second line is the sum of the probabilities for the first two values on the list. The third number is the sum of the first three probabilities and so on. The numbers 1, 2, 3, 4, . . down the left are not the x values from the list. The cumulative value is always given starting from x = 0. Example: Find the probability of 2, 3, or 4 successes for a Poisson distribution with mean 4.2

• Select STAT from the main menu • Enter the required x values into List1 1 EXE 2 EXE 3 EXE 4 EXE

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• Press F5 (DIST) • Press F6 to see next set of options • Press F5 (POISN) for the Poisson distribution • Press F2 (Pcd) (Cumulative) • Press F1 if necessary to accept List • Set List to List1 if necessary • Enter the mean 4.2 EXE • Press F1 to calculate the answer • The answer appears as follows

1 0.0779 meaning ( )0,1P X =

2 0.2102 meaning ( )0,1, 2P X =

3 0.3954 meaning ( )0,1,2,3P X =

4 0.5898 meaning ( )0,1, 2,3,4P X = The answer to the question is ( )2,3, 4P X = = 0.5898 – 0.0779 = 0.5119

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Confidence Intervals Confidence intervals can be calculated for population mean, population proportion and for difference of two means. The confidence level for these intervals is entered as a decimal. So for 95% confidence, 0.95 must be entered. The calculation of confidence intervals for NCEA will involve the entry of variables rather than doing a calculation for a list of data. Confidence interval for a Population mean (single sample)

• Choose STAT from the main menu • Press F4 (INTR) • Press F1 (Z) • Press F1 (1- S) - one sample • Press F2 (var) to enter variables rather than use a list • Type in confidence level (C-Level) as a decimal and EXE • Type in standard deviation (σ ) and EXE • Type in sample mean ( x ) and EXE • Type in number in sample (n) and EXE • Press F1 to calculate the interval • The left and right limits of the interval are given • Press EXIT to return to the previous screen

Example: Calculate a 95% confidence interval for a sample of size 60 having a sample mean of 50. The standard deviation is 10.

• Choose STAT from the main menu • Press F4 (INTR) • Press F1 (Z) • Press F1 (1- S) - one sample • Press F2 (var) to enter variables rather than use a list • Type in confidence level 0.95 EXE • Type in standard deviation (σ ) 10 EXE • Type in sample mean ( x ) 50 EXE • Type in number in sample (n) 60 EXE • Press F1 to calculate the interval • The left and right limits of the interval are given as 47.469 and 52.53

The 95% confidence interval for the population mean µ is: 47.469 52.53µ< < Confidence interval for the difference between two population means

• Choose STAT from the main menu • Press F4 (INTR) • Press F1 (Z) • Press F2 (2- S) - two samples • Press F2 (var) to enter variables rather than use a list

Casio fx-9750G 37

• Type in confidence level (C-Level) as a decimal and EXE • Type in both standard deviations ( 1, 2σ σ ) and EXE after each • Type in first sample mean ( 1x ) and EXE • Type in number in first sample (n1) and EXE • Type in second sample mean ( 2x ) and EXE • Type in number in second sample (n2) and EXE • Press F1 to calculate the interval • The left and right limits of the interval are given • Press EXIT to return to the previous screen

Example: A sample of 50 from population1 gives 1x = 60 and 1σ = 12 A sample of 70 from population2 gives 2x = 40 and 2σ = 10 Find a 99% confidence interval for the difference between the population means.

• Choose STAT from the main menu • Press F4 (INTR) • Press F1 (Z) • Press F2 (2- S) - two samples • Press F2 (var) to enter variables rather than use a list • Type in confidence level (C-Level) 0.99 EXE • Type in both standard deviations 12, 10 and EXE after each • Type in first sample mean 60 and EXE • Type in number in first sample 50 and EXE • Type in second sample mean 40 and EXE • Type in number in second sample 70 and EXE • Press F1 to calculate the interval • The left and right limits of the interval are given as 14.653 and 25.346

The confidence interval for the difference between the population means is: ( )1 214.653 25.346µ µ< − < Confidence interval for a population proportion For this confidence interval, the number in the sample and the number of “successes” (x) must be given. If a proportion is given in the question (fraction, decimal or percentage), this must converted to an x value. For example if a sample of 400 drivers is taken and 56% have no one else in the car, the value of x is 56% of 400 = 224.

• Choose STAT from the main menu • Press F4 (INTR) • Press F1 (Z) • Press F3 (1- P) - one sample • Press F2 (var) to enter variables rather than use a list • Type in confidence level (C-Level) as a decimal and EXE

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• Type in the number of “Successes” (x) and EXE • Type in number in sample (n) and EXE • Press F1 to calculate the interval • The left and right limits of the interval are given as well as the sample proportion

( p̂ ) • Press EXIT to return to the previous screen

Example: A sample of 400 drivers shows that 56% (224 drivers) travel alone. Find a 95% confidence interval for the proportion of all drivers who travel alone.

• Choose STAT from the main menu • Press F4 (INTR) • Press F1 (Z) • Press F3 (1- P) - one sample • Press F2 (var) to enter variables rather than use a list • Type in confidence level (C-Level) 0.95 EXE • Type in the number of “Successes” 224 EXE • Type in number in sample 400 EXE • Press F1 to calculate the interval • The left and right limits of the interval are given as well as the sample proportion

( p̂ ) The confidence interval is: 0.51135 0.60864π< <

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Index page Arithmetic sequence 6 Binomial distribution 32 Box and whisker graph 26 Circle 22 Combinations 3 Complex numbers 7 Confidence intervals 36 Conic sections 22 Cubic equations 12 Curve fitting 27 Degrees to radians 7 Differentiation 9 Distributions 30 Editing 2 Ellipse 22 Equation input 2 Equations 12 Exponential curve fitting 28 Exponential form 3 Factorials 3 Fractions 2 Geometric sequence 6 Graphing functions 17 Graphs 15 Histogram 26 Hyperbola 23 Inequality graphs 16 Integration 10 Lists 4 Main Menu 1 Maximum/minimum values 9 Mean/median 25 Newton-Raphson method 13 Normal distribution 30 Parabola 24 Parametric graphs 16 Permutations 3 Poisson distribution 33 Polar/rectangular form 8 Polynomial curve fitting 27 Power law curve fitting 28 Quadratic equations 12 Random numbers 3 Scatter diagram 26 Sequence graphing 5 Sequences 5 Set up screen 1 Sigma notation 5 Simultaneous equations 12 Sine model curve fitting 29 Sorting data lists 4 Statistical graphs 26 Statistics 25 Variables 2

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NCEA Level 2 page Algebra/Equations 90284 Solving equations from graphs 18 Quadratic equations 12 Simultaneous equations 12 Graphs 90285 Standard y = graphs 16 Circle graph 22 Calculus 90286 Derivative value 9 Maximum/minimum 9 Area from integration 10 Tangents 20 Coordinate geometry 90287 y-intercept 19 Point of intersection of lines 19 Sampling 90288 Random numbers 3 Mean, median, mode 25 Standard deviation 25 Quartiles 25 Graphs 26 Probability and normal distribution 90289 Random numbers 3 Normal distribution 30 Sequences 90290 Generating sequences 5 Tables/graphs 5 Arithmetic sequence 6 Geometric sequence 6 Sigma notation 5 Trigonometry 90291 Radians/degrees 7 Trigonometric equations 90291 Trig graphs 16 Model sine graph 29

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NCEA Level 3 Statistics

Page Confidence Intervals 90642 Population mean 36 Difference between means 36 Population proportion 37 Probability 90643 Permutations/combinations 3 Solve Equations 90644 Simultaneous equations 12 Newton-Raphson method 13 Inequalities 16 Solving equations 12 Distributions 90646 Normal distribution 30 Inverse normal 31 Binomial 32 Poisson 33

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NCEA Level 3 Calculus

Page Differentiation 90635 Maximum/minimum values 9 Tangents/normals 20 Sketch graphs 15 Integration 90636 Areas under graphs 10 Equations, complex numbers 90638 Complex numbers 7 Polar/rectangular form 8 Solve equations 12 Conic sections 90639 Conic sections 22 Circles 22 Ellipse 22 Hyperbola 23 Parabola 24 Parametric form 16 Intersection of graphs 19