Graphics calculator instructions - … calculator instructions Contents: A B C Casio fx-9860G Texas Instruments TI-84 Plus Texas Instruments TI- spiren IB_STSL-2ed cyan magenta yellow

Graphics calculatorinstructions

Contents: A

B

C

Casio fx-9860G

Texas Instruments TI-84 Plus

Texas Instruments TI- spiren

IB_STSL-2edmagentacyan yellow black

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Y:\HAESE\IB_STSL-2ed\IB_STSL-2ed_00b\015TSL-2_00b.CDR Friday, 26 March 2010 11:59:06 AM PETER

In this course it is assumed that you have a graphics calculator. If you learn how to operate

your calculator successfully, you should experience little difficulty with future arithmetic

calculations.

There are many different brands (and types) of calculators. Different calculators do not have

exactly the same keys. It is therefore important that you have an instruction booklet for your

calculator, and use it whenever you need to.

However, to help get you started, we have included here some basic instructions for the

Casio fx-9860G, the Texas Instruments TI-84 plus and the Texas Instruments TI-nspire

calculators. Note that instructions given may need to be modified slightly for other models.

The instructions have been divided into three sections, one for each of the calculator models.

BASIC FUNCTIONS

GROUPING SYMBOLS (BRACKETS)

The Casio has bracket keys that look like ( and ) .

Brackets are regularly used in mathematics to indicate an expression which needs to be

evaluated before other operations are carried out.

For example, to evaluate 2£ (4 + 1) we type 2 £ ( 4 + 1 ) EXE .

We also use brackets to make sure the calculator understands the expression we are typing in.

For example, to evaluate 2

4+1we type 2 ¥ ( 4 + 1 ) EXE .

If we typed 2 ¥ 4 + 1 EXE the calculator would think we meant 2

4+ 1.

In general, it is a good idea to place brackets around any complicated expressions which need

to be evaluated separately.

POWER KEYS

The Casio has a power key that looks like ^ . We type the base first, press the power key,

then enter the index or exponent.

For example, to evaluate 253 we type 25 ^ 3 EXE .

Numbers can be squared on the Casio using the special key x2 .

For example, to evaluate 252 we type 25 x2 EXE .

CASIO FX-9860GA

16 GRAPHICS CALCULATOR INSTRUCTIONS


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Y:\HAESE\IB_STSL-2ed\IB_STSL-2ed_26\016TSL-2_00b.CDR Tuesday, 5 January 2010 3:27:27 PM PETER

ROOTS

To enter roots on the Casio we need to use the secondary function key SHIFT .

We enter square roots by pressing SHIFT x2 .

For example, to evaluatep36 we press SHIFT x

2 36 EXE .

If there is a more complicated expression under the square root sign you should enter it in

brackets.

For example, to evaluatep18¥ 2 we press SHIFT x

2 ( 18 ¥ 2 ) EXE .

Cube roots are entered by pressing SHIFT ( .

For example, to evaluate3p8 we press SHIFT ( 8 EXE .

Higher roots are entered by pressing SHIFT ^ .

For example, to evaluate4p81 we press 4 SHIFT ^ 81 EXE .

INVERSE TRIGONOMETRIC FUNCTIONS

The inverse trigonometric functions sin¡1, cos¡1 and tan¡1 are the secondary functions of

sin , cos and tan respectively. They are accessed by using the secondary function key

SHIFT .

For example, if cosx = 3

5, then x = cos¡1

¡3

5

¢.

To calculate this, press SHIFT cos ( 3 ¥ 5 ) EXE .

SCIENTIFIC NOTATION

If a number is too large or too small to be displayed neatly on the screen, it will be expressed

in scientific notation, which is the form a£ 10k where 1 6 a < 10 and k is an integer.

To evaluate 23003, press 2300 ^ 3 EXE . The answer

displayed is 1:2167e+10, which means 1:2167£ 1010.

To evaluate 3

20 000, press 3 ¥ 20 000 EXE . The answer

displayed is 1:5e¡04, which means 1:5£ 10¡4.

You can enter values in scientific notation using the EXP key.

For example, to evaluate 2:6£1014

13, press 2:6 EXP 14 ¥ 13

EXE . The answer is 2£ 1013.

17GRAPHICS CALCULATOR INSTRUCTIONS


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SECONDARY FUNCTION AND ALPHA KEYS

The shift function of each key is displayed in yellow above the key. It is accessed by pressing

the SHIFT key followed by the key corresponding to the desired shift function.

For example, to calculatep36, press SHIFT x

2 (p

) 36 EXE .

The alpha function of each key is displayed in red above the key. It is accessed by pressing

the ALPHA key followed by the key corresponding to the desired letter. The main purpose

of the alpha keys is to store values which can be recalled later.

MEMORY

Utilising the memory features of your calculator allows you to recall calculations you have

performed previously. This not only saves time, but also enables you to maintain accuracy

in your calculations.

SPECIFIC STORAGE TO MEMORY

Suppose we wish to store the number 15:4829 for use in a number

of calculations. To store this number in variable A, type in the

number then press I ALPHA X,µ,T (A) EXE .

We can now add 10 to this value by pressing ALPHA X,µ,T +

10 EXE , or cube this value by pressing ALPHA X,µ,T ^ 3 EXE .

ANS VARIABLE

The variable Ans holds the most recent evaluated expression,

and can be used in calculations by pressing SHIFT (¡) . For

example, suppose you evaluate 3£ 4, and then wish to subtract

this from 17. This can be done by pressing 17 ¡ SHIFT (¡)

EXE .

If you start an expression with an operator such as + , ¡ ,

etc, the previous answer Ans is automatically inserted ahead of

the operator. For example, the previous answer can be halved

simply by pressing ¥ 2 EXE .

If you wish to view the answer in fractional form, press FJID .

Values can be stored into the variable letters A, B, ...., Z. Storing a value in memory is useful

if you need that value multiple times.



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RECALLING PREVIOUS EXPRESSIONS

Pressing the left cursor key allows you to edit the most recently evaluated expression, and is

useful if you wish to repeat a calculation with a minor change, or if you have made an error

in typing.

Suppose you have evaluated 100 +p132. If you now want to evaluate 100 +

p142, instead

of retyping the command, it can be recalled by pressing the left cursor key. Move the cursor

between the 3 and the 2, then press DEL 4 to remove the 3 and change it to a 4. Press EXE

to re-evaluate the expression.

LISTS

Lists enable us to store sets of data, which we can then analyse and compare.

CREATING A LIST

Selecting STAT from the Main Menu takes you to the list editor

screen.

DELETING LIST DATA

To delete a list of data from the list editor screen, move the cursor to anywhere on the list

you wish to delete, then press F6 (B) F4 (DEL-A) F1 (Yes).

REFERENCING LISTS

Lists can be referenced using the List function, which is accessed by pressing SHIFT 1.

For example, if you want to add 2 to each element of List 1 and display the results in List 2,

move the cursor to the heading of List 2 and press SHIFT 1 (List) 1 + 2 EXE .

Casio models without the List function can do this by pressing OPTN F1 (LIST) F1

(List) 1 + 2 EXE .

STATISTICS

Enter the data into List 1. To obtain

the descriptive statistics, press F6 (B)

until the GRPH icon is in the bottom

left corner of the screen, then press

F2 (CALC) F1 (1 VAR).

To enter the data f2, 5, 1, 6, 0, 8g into List 1, start by moving

the cursor to the first entry of List 1. Press 2 EXE 5 EXE ....

and so on until all the data is entered.

Your graphics calculator is a useful tool for analysing data and creating statistical graphs.

We will first produce descriptive statistics and graphs for the data set:

5 2 3 3 6 4 5 3 7 5 7 1 8 9 5.



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To obtain a boxplot of the data,

press EXIT EXIT F1 (GRPH)

F6 (SET), and set up StatGraph 1

as shown. Press EXIT F1

(GPH1) to draw the boxplot.

To obtain a vertical bar chart of the

data, press EXIT F6 (SET) F2

(GPH 2), and set up StatGraph 2

as shown. Press EXIT F2

(GPH 2) to draw the bar chart (set Start

to 0, and Width to 1).

We will now enter a second set of data,

and compare it to the first.

Enter the data set 9 6 2 3 5 5 7 5 6 76 3 4 4 5 8 4 into List 2, then press

F6 (SET) F2 (GPH2) and set up

StatGraph 2 to draw a boxplot of this

data set as shown. Press EXIT F4

(SEL), and turn on both StatGraph 1

and StatGraph 2. Press F6 (DRAW)

to draw the side-by-side boxplots.

STATISTICS FROM GROUPED DATA

To obtain descriptive statistics for the

data in the table alongside, enter the data

values into List 1, and the frequency

values into List 2.

Data Frequency

2 3

3 4

4 8

5 5

Press F2 (CALC) F6 (SET), and change the 1 Var Freq

variable to List 2. Press EXIT F1 (1Var) to view the statistics.

TWO VARIABLE STATISTICS

Consider the data x 1 2 3 4 5 6 7

y 5 8 10 13 16 18 20

To find sx and sy, the standard deviations of x and y, enter

the x values into List 1 and the y values into List 2 using the

instructions on page 19.



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GRAPHICS CALCULATOR INSTRUCTIONS 21

Press F2 (CALC) F2 (2VAR) to obtain the two variable

statistics. sx is given by x¾n= 2. Use the H key to scroll

down to find sy, which is given by y¾n¼ 5:08 .

FINDING ¾ AND THE LINE OF BEST FIT

We can use our graphics calculator to find the line of best fit connecting two variables. We can

also find the values of Pearson’s correlation coefficient r and the coefficient of determination

r2, which measure the strength of the linear correlation between the two variables.

We will examine the relationship between the variables x and y

for the previous data.

Enter the x values into List 1 and the y values into List 2.

To produce a scatter diagram, press F1 (GRPH) F6 (SET),

and set up StatGraph 1 as shown. Press EXIT F1 (GPH 1)

to draw the scatter diagram.

To find the line of best fit, press F1 (CALC) F2 (X).

We can see that the line of best fit is y ¼ 2:54x+ 2:71, and

that r ¼ 0:998, indicating a very strong positive correlation

between x and y.

Press F6 (DRAW) to view the line of best fit.

CALCULATING Â2

To calculate Â2 for the data alongside,

select STAT from the Main Menu, then

press F3 (TEST) F3 (CHI).

A1 A2

B1 21 28

B2 13 24

Press F2 ( I MAT), then enter the values of the table into

matrix A, using the instructions given on page 24.

Press EXIT twice to return to the Â2 Test screen, highlight

Execute, then press EXE .

So, Â2 ¼ 0:526 . The p-value and the degrees of freedom are also given. The expected

values are stored in matrix B.


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SOLVING EQUATIONS

SOLVING LINEAR EQUATIONS

To solve the linear equation 3:2x ¡ 4:2 = 7:4, select EQUA from the Main Menu, then

press F3 (SOLV).

Enter the equation by pressing 3:2 X,µ,T ¡ 4:2 SHIFT .(=) 7:4 EXE .

Highlight X= with the cursor and press F6 (SOLV) to solve the equation.

So, the solution is x = 3:625 .

SOLVING QUADRATIC EQUATIONS

To solve the quadratic equation 3x2 + 2x ¡ 11 = 0, select

EQUA from the Main Menu. Press F2 (POLY) then F1 (2).

Enter the coefficients 3, 2 and ¡11 and then press F1 (SOLV)

to solve the equation.

So, the solutions are x ¼ ¡2:28 or 1:61 .


WORKING WITH FUNCTIONS

GRAPHING FUNCTIONS

Selecting GRAPH from the Main Menu takes you to the Graph

Function screen, where you can store functions to graph. Delete

any unwanted functions by scrolling down to the function and

pressing F2 (DEL) F1 (Yes).

To graph the function y = x2¡3x¡5, move the cursor to Y1

and press X,µ,T x2 ¡ 3 X,µ,T ¡ 5 EXE . This stores

the function into Y1. Press F6 (DRAW) to draw a graph of

the function.


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Y:\HAESE\IB_STSL-2ed\IB_STSL-2ed_00b\022TSL-2_00b.CDR Wednesday, 27 January 2010 9:18:21 AM PETER

To view a table of values for the function, press MENU and

select TABLE. The function is stored in Y1, but not selected.

Press F1 (SEL) to select the function, and F6 (TABL) to view

the table. You can adjust the table settings by pressing EXIT

and then F5 (SET) from the Table Function screen.

ADJUSTING THE VIEWING WINDOW

When graphing functions it is important that you are able to view all the important features

of the graph. As a general rule it is best to start with a large viewing window to make sure

all the features of the graph are visible. You can then make the window smaller if necessary.

The viewing window can be adjusted by pressing SHIFT F3

(V-Window). You can manually set the minimum and maximum

values of the x and y axes, or press F3 (STD) to obtain the

standard viewing window ¡10 6 x 6 10, ¡10 6 y 6 10:

FINDING POINTS OF INTERSECTION

It is often useful to find the points of intersection of two graphs, for instance, when you are

trying to solve simultaneous equations.

We can solve y = 11¡ 3x and y =12¡ x

2simultaneously

by finding the point of intersection of these two lines. Select

GRAPH from the Main Menu, then store 11 ¡ 3x into Y1

and12¡ x

2into Y2. Press F6 (DRAW) to draw a graph of

the functions.

To find their point of intersection, press F5 (G-Solv) F5

(ISCT). The solution x = 2, y = 5 is given.

If there is more than one point of intersection, the remaining

points of intersection can be found by pressing I .

FINDING x-INTERCEPTS

In the special case when you wish to solve an equation of the form f(x) = 0, this can be

done by graphing y = f(x) and then finding when this graph cuts the x-axis.

To solve x3 ¡ 3x2 + x + 1 = 0, select GRAPH from the

Main Menu and store x3 ¡ 3x2 +x+1 into Y1. Press F6

(DRAW) to draw the graph.

To find where this function cuts the x-axis, press F5 (G-Solv)

F1 (ROOT). The first solution x ¼ ¡0:414 is given.

Press I to find the remaining solutions x = 1 and x ¼ 2:41 .



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TURNING POINTS

To find the turning point or vertex of y = ¡x2 + 2x+ 3, select GRAPH from the Main

Menu and store ¡x2 + 2x+ 3 into Y1. Press F6 (DRAW) to draw the graph.

From the graph, it is clear that the vertex is a maximum, so to

find the vertex press F5 (G-Solv) F2 (MAX). The vertex is

(1, 4).

FINDING THE TANGENT TO A FUNCTION

To find the equation of the tangent to y = x2 when x = 2,

we first press SHIFT MENU (SET UP), and change the

Derivative setting to On. Draw the graph of y = x2, then

press SHIFT F4 (Sketch) F2 (Tang).

Press 2 EXE EXE to draw the tangent at x = 2.

The tangent has gradient 4, and equation y = 4x¡ 4.

FINANCIAL MATHEMATICS

Suppose we invest $5000 at 7:2% p.a. compounded annually. To

find the value of the investment after 10 years, select TVM from

the Main Menu and press F2 (CMPD) to display the compound

interest screen.

Set up the screen as shown:

Note: All money being invested is considered as outgoings

and is entered as a negative value.

There are no payments into the account during the term

of the investment, so PMT is set to 0.

Press F5 (FV) to find the future value.

So, the investment amounts to $10 021:16.

MATRICES

STORING MATRICES

To store the matrix

0@

2 31 45 0

1A, select RUN¢MAT from the

Main Menu, and press F1 (IMAT). This is where you define

matrices and enter their elements.

To define the matrix as matrix A, make sure Mat A is

highlighted, and press F3 (DIM) 3 EXE 2 EXE EXE .

This indicates that the matrix has 3 rows and 2 columns.



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Enter the elements of the matrix, pressing EXE after each entry.

Press EXIT twice to return to the home screen when you are

done.

BASIC FUNCTIONS


The TI-84 Plus has bracket keys that look like ( and ) .



For example, to evaluate 2£ (4 + 1) we type 2 £ ( 4 + 1 ) ENTER .



4+1we type 2 ¥ ( 4 + 1 ) ENTER .

If we typed 2 ¥ 4 + 1 ENTER the calculator would think we meant 2

4+ 1.



POWER KEYS

The TI-84 Plus has a power key that looks like ^ . We type the base first, press the power

key, then enter the index or exponent.

For example, to evaluate 253 we type 25 ^ 3 ENTER .

Numbers can be squared on the TI-84 Plus using the special key x2 .

For example, to evaluate 252 we type 25 x2 ENTER .

ROOTS

To enter roots on the TI-84 Plus we need to use the secondary function key 2nd .

We enter square roots by pressing 2nd x2 .

For example, to evaluatep36 we press 2nd x

2 36 ) ENTER .

The end bracket is used to tell the calculator we have finished entering terms under the square

root sign.

TEXAS INSTRUMENTS TI-84 PLUSB



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Cube roots are entered by pressing MATH 4: 3p

( .

To evaluate3p8 we press MATH 4 : 8 ) ENTER .

Higher roots are entered by pressing MATH 5: x

p.

To evaluate4p81 we press 4 MATH 5 : 81 ENTER .



SIN , COS and TAN respectively. They are accessed by using the secondary function key

2nd .


5, then x = cos¡1

¡3

5

¢.

To calculate this, press 2nd COS 3 ¥ 5 ) ENTER .

SCIENTIFIC NOTATION

If a number is too large or too small to be displayed neatly on the screen, it will be expressed

in scientific notation, which is the form a£10k where 1 6 a < 10 and k is an integer.

To evaluate 23003, press 2300 ^ 3 ENTER . The answer

displayed is 1:2167e10, which means 1:2167£ 1010.

To evaluate 3

20 000, press 3 ¥ 20 000 ENTER . The answer

displayed is 1:5e¡4, which means 1:5£ 10¡4.

You can enter values in scientific notation using the EE function,

which is accessed by pressing 2nd , .

For example, to evaluate 2:6£1014

13, press 2:6 2nd , 14 ¥

13 ENTER . The answer is 2£ 1013.

SECONDARY FUNCTION AND ALPHA KEYS

The secondary function of each key is displayed in blue above the key. It is accessed by

pressing the 2nd key, followed by the key corresponding to the desired secondary function.

For example, to calculatep36, press 2nd x

2 (p

) 36 ) ENTER .

The alpha function of each key is displayed in green above the key. It is accessed by pressing

the ALPHA key followed by the key corresponding to the desired letter. The main purpose

of the alpha keys is to store values into memory which can be recalled later.

MEMORY






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Suppose we wish to store the number 15:4829 for use in a number

of calculations. To store this number in variable A, type in the

number, then press STOI ALPHA MATH (A) ENTER .

We can now add 10 to this value by pressing ALPHA MATH

+ 10 ENTER , or cube this value by pressing ALPHA MATH

^ 3 ENTER .

ANS VARIABLE

The variable Ans holds the most recent evaluated expression,

and can be used in calculations by pressing 2nd (¡) .

For example, suppose you evaluate 3 £ 4, and then wish to

subtract this from 17. This can be done by pressing 17 ¡

2nd (¡) ENTER .

If you start an expression with an operator such as + , ¡ ,

etc, the previous answer Ans is automatically inserted ahead of

the operator. For example, the previous answer can be halved

simply by pressing ¥ 2 ENTER .

If you wish to view the answer in fractional form, press

MATH 1 ENTER .


The ENTRY function recalls previously evaluated expressions, and is used by pressing 2nd

ENTER .

This function is useful if you wish to repeat a calculation with a minor change, or if you have

made an error in typing.

Suppose you have evaluated 100 +p132. If you now want to evaluate 100 +

p142, instead

of retyping the command, it can be recalled by pressing 2nd ENTER .

The change can then be made by moving the cursor over the 3 and changing it to a 4, then

pressing ENTER .

If you have made an error in your original calculation, and intended to calculate 1500+p132,

again you can recall the previous command by pressing 2nd ENTER .

Move the cursor to the first 0.

You can insert the 5, rather than overwriting the 0, by pressing 2nd DEL (INS) 5 ENTER .





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LISTS

Lists are used for a number of purposes on the calculator. They enable us to store sets of

data, which we can then analyse and compare.

CREATING A LIST

DELETING LIST DATA

To delete a list of data from the list editor screen, move the cursor to the heading of the list

you want to delete then press CLEAR ENTER .

REFERENCING LISTS

Lists can be referenced by using the secondary functions of the keypad numbers 1-6.

For example, suppose you want to add 2 to each element of List1 and display the results in

List2. To do this, move the cursor to the heading of L2 and press 2nd 1 + 2 ENTER .

STATISTICS

Enter the data set into List 1. To obtain

descriptive statistics of the data set, press

STAT I 1:1-Var Stats 2nd 1 (L1) ENTER .

To obtain a boxplot of the data, press 2nd

Y= (STAT PLOT) 1 and set up Statplot1 as

shown. Press ZOOM 9:ZoomStat to graph the

boxplot with an appropriate window.

To obtain a vertical bar chart of the data, press

2nd Y= 1, and change the type of graph to

a vertical bar chart as shown. Press ZOOM

9:ZoomStat to draw the bar chart. Press

WINDOW and set the Xscl to 1, then GRAPH

to redraw the bar chart.

Press STAT 1 to access the list editor screen.

To enter the data f2, 5, 1, 6, 0, 8g into List 1, start by moving

the cursor to the first entry of L1. Press 2 ENTER 5 ENTER

.... and so on until all the data is entered.

Your graphics calculator is a useful tool for analysing data and creating statistical graphs.

We will first produce descriptive statistics and graphs for the data set:

5 2 3 3 6 4 5 3 7 5 7 1 8 9 5.



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We will now enter a second set of data, and

compare it to the first.

Enter the data set 9 6 2 3 5 5 7 5 6 7 6

3 4 4 5 8 4 into List 2, press 2nd Y= 1,

and change the type of graph back to a boxplot

as shown. Move the cursor to the top of the

screen and select Plot2. Set up Statplot2 in the

same manner, except set the XList to L2. Press

ZOOM 9:ZoomStat to draw the side-by-side

boxplots.


To obtain descriptive statistics for the

data in the table alongside, enter the data

values into List 1, and the frequency

values into List 2.

Press STAT I 1 : 1-Var Stats 2nd

1 (L1) , 2nd 2 (L2) ENTER .

Data Frequency

2 3

3 4

4 8

5 5


Consider the data

To find sx and sy, the standard deviations of x and y, enter

the x values into List 1 and the y values into List 2 using the

instructions on page 30.

Press STAT I 2:2-Var Stats, then 2nd 1 (L1) , 2nd 2

(L2) ENTER to obtain the two variable statistics.

sx is given by ¾X = 2. Use the H key to scroll down to find

sy, which is given by ¾y ¼ 5:08.

FINDING r AND THE LINE OF BEST FIT

We can use our graphics calculator to find the line of best fit connecting two variables. We can

also find the values of Pearson’s correlation coefficient r and the coefficient of determination

r2, which measure the strength of the linear correlation between the two variables.

We will examine the relationship between the variables x and y for the data above.

Enter the x values into List 1 and the

y values into List 2.

To produce a scatter diagram, press

2nd Y= (STAT PLOT) 1, and set up

Statplot 1 as shown. Press ZOOM 9 :

ZoomStat to draw the scatter diagram.

x 1 2 3 4 5 6 7

y 5 8 10 13 16 18 20



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We will now find r and the line of best fit. Press STAT I

4:LinReg(ax+b) to select the linear regression option from the

CALC menu.

Press 2nd 1 (L1) , 2nd 2 (L2) , VARS I 1 1 (Y1).

This specifies the lists L1 and L2 as the lists which hold the

data, and the line of best fit will be pasted into the function Y1.

Press ENTER to view the results.

The line of best fit is given as y ¼ 2:54x+2:71. If the r and

r2 values are not shown, you need to turn on the Diagnostic by

pressing 2nd 0 (CATALOG) and selecting DiagnosticOn.

You can view the line of best fit by pressing GRAPH .

CALCULATING Â2

To calculate Â2 for the data alongside,

enter the values of the table into matrix

A, using the instructions given on page

36.

A1 A2

B1 21 28

B2 13 24

Press STAT J , then select C:Â2-Test... from the TESTS

menu. Highlight Calculate, then press ENTER .

So, Â2 ¼ 0:526. The p-value and the degrees of freedom are

also given. The expected values are stored in matrix B.

SOLVING EQUATIONS


To solve the linear equation 3:2x ¡ 4:2 = 7:4, we rearrange

the equation to 3:2x¡ 11:6 = 0, so that one side is equal to

zero.

Press MATH then 0 to select 0:Solver...

Press N , then enter the equation into eqn:0= by pressing 3:2

X,T,µ,n ¡ 11:6 ENTER .

Highlight X= with the cursor and press ALPHA ENTER (SOLVE)

to solve for x.

So, the solution is x = 3:625.

The r value of ¼ 0:998 indicates a very strong positive

correlation between x and y.



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GRAPHING FUNCTIONS

Pressing Y= selects the Y= editor, where you can store functions

to graph. Delete any unwanted functions by scrolling down to

the function and pressing CLEAR .

To graph the function y = x2 ¡ 3x ¡ 5, move the cursor to

Y1, and press X,T,µ,n x2 ¡ 3 X,T,µ,n ¡ 5 ENTER . This

stores the function into Y1. Press GRAPH to draw a graph of

the function.

To view a table of values for the function, press 2nd GRAPH

(TABLE). The starting point and interval of the table values can

be adjusted by pressing 2nd WINDOW (TBLSET).



The TI-84 Plus does not have a built-in method to solve quadratic

equations. We must write our own program.

To solve the quadratic equation 3x2 + 2x¡ 11 = 0,

press PRGM J 1 to create a new program, label the program

QUADRAT, then press ENTER .

Enter the code for the program as shown alongside.

The Disp and Prompt commands are accessed from the I/O menu

of the PRGM screen. You can enter = by pressing

2nd MATH 1.

Press 2nd MODE (QUIT) when you are done.

To use the program, press PRGM , then 1:QUADRAT. Press

ENTER to start the program.

As prompted, enter the coefficients A, B and C, pressing ENTER

after each one.

So the solutions are x ¼ ¡2:28 and 1:61.


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Some useful commands for adjusting the viewing window

include:

ZOOM 0:ZoomFit : This command scales the y-axis to fit

the minimum and maximum values of

the displayed graph within the current

x-axis range.

ZOOM 6:ZStandard : This command returns the viewing

window to the default setting of

¡10 6 x 6 10, ¡10 6 y 6 10.

If neither of these commands are helpful, the viewing window

can be adjusted manually by pressing WINDOW and setting the

minimum and maximum values for the x and y axes.




We can solve y = 11 ¡ 3x and y =12¡ x

2simultaneously

by finding the point of intersection of these two lines.

Press Y= , then store 11¡ 3x into Y1 and12¡ x

2into

Y2. Press GRAPH to draw a graph of the functions.

To find their point of intersection, press 2nd TRACE (CALC)

5:intersect. Press ENTER twice to specify the functions Y1

and Y2 as the functions you want to find the intersection of,

then use the arrow keys to move the cursor close to the point of

intersection and press ENTER once more.

The solution x = 2, y = 5 is given.



done by graphing y = f(x) and then finding when this graph cuts the x-axis.

For example, to solve x3 ¡ 3x2 + x + 1 = 0, press Y= and

store x3 ¡ 3x2 + x+ 1 into Y1. Then press GRAPH .

To find where this function first cuts the x-axis, press 2nd

TRACE (CALC) 2:zero.



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Move the cursor to the left of the first zero and press ENTER ,

then move the cursor to the right of the first zero and press

ENTER . Finally, move the cursor close to the first zero and

press ENTER once more. The solution x ¼ ¡0:414 is given.

Repeat this process to find the remaining solutions x = 1 and

x ¼ 2:414 .

TURNING POINTS

To find the turning point or vertex of y = ¡x2+2x+3, press

Y= and store ¡x2+2x+3 into Y1. Press GRAPH to draw

the graph.

From the graph, it is clear that the vertex is a maximum, so press

2nd TRACE (CALC) 4:maximum.

Move the cursor to the left of the vertex and press ENTER , then

move the cursor to the right of the vertex and press ENTER .

Finally, move the cursor close to the vertex and press ENTER

once more. The vertex is (1, 4).


To find the equation of the tangent to y = x2 when x = 2, we

first draw the graph of y = x2. Press 2nd PRGM (DRAW)

5:Tangent, then press 2 ENTER to draw the tangent at

x = 2.

The tangent has gradient 4, and equation y = 4x¡ 4.


Suppose we invest $5000 at 7:2% p.a. compounded annually. To

find the value of the investment after 10 years, press (APPS)

1:Finance... to display the finance menu, then 1 to select

1:TVM Solver...

Set up the TVM screen as shown:

Note: All money being invested is considered as outgoings

and is entered as a negative value.

There are no payments into the account during the term

of the investment, so PMT is set to 0.

Highlight FV and press ALPHA ENTER (SOLVE) to find the

future value. The investment amounts to $10 021:16.



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MATRICES

STORING MATRICES

To store the matrix

0@

2 31 45 0

1A, press 2nd x

-1 (MATRIX) to

display the matrices screen, and use I to select the EDIT

menu. This is where you define matrices and enter the elements.

Press 1 to select 1:[A]. Press 3 ENTER 2 ENTER to define

matrix A as a 3£ 2 matrix.

Enter the elements of the matrix, pressing ENTER after each

entry.

Press 2nd MODE (QUIT) when you are done.

GETTING STARTED

Pressing takes you to the home screen, where you can choose which application you

wish to use.

The TI-nspire organises any work done into pages. Every time you start a new application,

a new page is created. You can navigate back and forth between the pages you have worked

on by pressing ctrl J or ctrl I

From the home screen, press 1 to open the Calculator application. This is where most of the

basic calculations are performed.

SECONDARY FUNCTION KEY

The secondary function of each key is displayed in grey above the primary function. It is

accessed by pressing the ctrl key followed by the key corresponding to the desired secondary

function.

BASIC FUNCTIONS


The TI-nspire has bracket keys that look like ( and ) .



For example, to evaluate 2£ (4 + 1) we type 2 £ ( 4 + 1 ) enter .

TEXAS INSTRUMENTS TI-nSPIREC



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4+1we type 2 ¥ ( 4 + 1 ) enter .

If we typed 2 ¥ 4 + 1 enter the calculator would think we meant 2

4+ 1.



POWER KEYS

The TI-nspire has a power key that looks like ^ . We type the base first, press the power

key, then enter the index or exponent.

For example, to evaluate 253 we type 25 ^ 3 enter .

Numbers can be squared on the TI-nspire using the special key x2 .

For example, to evaluate 252 we type 25 x2 enter .

ROOTS

To enter roots on the TI-nspire we need to use the secondary function ctrl .

We enter square roots by pressing ctrl x2 .

For example, to evaluatep36 we press ctrl x

2 36 enter .

Higher roots are entered by pressing ctrl ^ , which creates the ¤p¤ template.

Enter the root number in the first entry, and the number you wish to find the root of in the

second entry. Use the arrow keys to navigate around the template.

ROUNDING OFF

You can instruct the TI-nspire to round off values to a

fixed number of decimal places.

Press the tab button until the Display Digits drop-box

is highlighted. Use the H key to select Fix 3, then press

enter three times to return to the page you were working

on.

To unfix the number of decimal places, select Float from the Display Digits drop-box.

DECIMAL EXPANSION OF FRACTIONS

If you press 5 ¥ 8 enter , the calculator will simply return the fraction 5

8. To find the

decimal expansion of 5

8, press 5 ¥ 8 ctrl enter .

For example, to round to 3 decimal places, from the home

screen select 8 : System Info > 2 : System Settings...



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sin , cos and tan respectively. They are accessed by using the secondary function key

ctrl .


5, then x = cos¡1

¡3

5

¢.

To calculate this, press ctrl cos 3 ¥ 5 ) enter .

SCIENTIFIC NOTATION

You can enter very large or very small values by

expressing them in scientific notation, which is in the

form a£ 10k where 1 6 a < 10 and k is an integer.

You can do this using the EE button.

For example, to evaluate2:6£ 1014

13, press 2:6 EE 14

¥ 13 enter . The answer is 2£ 1013.

MEMORY





Suppose we wish to store the number 15:4829 for use in a

number of calculations. To store this number in variable

A, type in the number then press ctrl var (stoI) A

enter .

We can now add 10 to this value by pressing + 10

enter or cube this value by pressing ^ 3 enter .

ANS VARIABLE

The variable Ans holds the most recent evaluated expression, and can be used in calculations

by pressing ctrl (¡) .

For example, suppose you evaluate 3 £ 4, and then wish to subtract this from 17. This can

be done by pressing 17 ¡ ctrl (¡) enter .

A

A





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If you start an expression with an operator such as + , ¡ , etc, the previous answer Ans

is automatically inserted ahead of the operator. For example, the previous answer can be

doubled simply by pressing £ 2 enter .


Pressing the N key allows you to recall and edit previously evaluated expressions.

To recall a previous expression, press the N key until the desired expression is highlighted,

and press enter . The expression then appears in the current entry line, where it can be

edited.

LISTS

Lists are used for a number of purposes on the calculator. They enable us to store sets of

data, which we can then analyse and compare.

In order to perform many of the operations involving data lists on the TI-nspire, you need to

name your lists as you define them.

CREATING A LIST

Selecting 3 : Lists & Spreadsheet from the home screen

takes you to the list editor screen.

Move the cursor to the heading of List A and use the

green alphabet keys to enter a name for the list, for

example data.

DELETING LIST DATA

To delete a list of data from the list editor screen, move the cursor to the heading of that list,

and press N to highlight the whole column. Press J to delete the list.

REFERENCING LISTS

Once you have named a list, you can use that name to

reference the list in other operations.

Suppose you want to add 2 to each element of the data list

we created in the above example, and display the results

in List B. Move the cursor to the shaded row of List B,

and press = data + 2 enter .

To enter the data f2, 5, 1, 6, 0, 8g into List A, start

by moving the cursor to the first entry of List A. Press 2

enter 5 enter .... and so on until all the data is entered.



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STATISTICS

Your graphics calculator is a useful tool for analysing data

and creating statistical graphs.

We will first produce descriptive statistics and graphs for

the data set:

Enter the data into List A and name this list one.

To obtain the descriptive statistics, press 1 : Calculator to open the Calculator application,

press menu , then select 5 : Statistics > 1 : Statistical Calculations > 1 : One-Variable

Statistics.

Press enter to choose

1 list. Select one from

the X1 List drop-box,

and press enter .

We will now draw some statistical graphs for the data.

Press 5 : Data & Statistics to open the Data

and Statistics application. You will see the data points

randomly scattered on the screen. Move the cursor to the

bottom of the screen until the “Click to add variable” box

appears. Press enter , then select one. The points will

order themselves into a dotplot along the horizontal axis.

To obtain a vertical bar

chart of the data, press

menu , then select

1 : Plot Type > ...

3 : Histogram.

To obtain a boxplot of

the data, press menu ,

then select 1 : Plot Type > 2 : Box Plot.

We will now add a second set of data, and compare it to

the first.

Use the ctrl J command to return to the page

containing the list of data.

Enter the set 9 6 2 3 5 5 7 5 6 7 6 3 4 4 5 8 4 into

List B, and name the list two.

Use the ctrl I command to navigate back to the page

containing the boxplot of one.


5 2 3 3 6 4 5 3 7 5 7 1 8 9 5.


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To view boxplots of both data sets, we need to split the

page into two sections. Press ctrl , then select

5 : Page Layout > 2 : Select Layout > 3 : Layout 3.

Press ctrl tab to navigate between the sections, then

press menu 5 to open a new Data and Statistics

application. Draw another boxplot in this section, this

time using the data in two.

In order to compare the boxplots, the horizontal scales

should be the same. Press menu , then select

5 : Window/Zoom > 1 : Window Settings.

Set the X range from 0 to 10. Press ctrl tab , and do

the same with the other boxplot.


To obtain descriptive statistics

for the data in the table

alongside, enter the data values

into List A, and label the list

data. Enter the frequency

values into List B, and label the

list freq.

Data Frequency

2 3

3 4

4 8

5 5


Consider the data x 1 2 3 4 5 6 7

y 5 8 10 13 16 18 20

To find sx and sy, the standard deviations of x and y,

enter the x values into List A and label the list one, then

enter the y values into List B and label the list two.

Press 1 : Calculator to open the Calculator

application. Press menu , then select 5 : Statistics

> 1 : Stat Calculations ... > 1 : One-Variable

Statistics. Press enter to choose 1 list. Select data from

the X1 List drop-box and freq from the Frequency List

drop-box, then press enter .



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Press 1:Calculator to open the Calculator application,

press menu , select 5:Statistics > 1:Stat Calculations...

> 2:Two-Variable Statistics. Select one from the X List

drop-box, two from the Y List drop-box, then press enter

to display the two variable statistics.

Scroll up through the results to find sx, which is given

by ¾x = 2, and sy, which is given by ¾y ¼ 5:08.

FINDING r AND THE LINE OF BEST FIT

We can use our calculator to find the line of best fit connecting two variables. We can also

find the values of Pearson’s correlation coefficient r and the coefficient of determination r2,

which measure the strength of the linear correlation between the two variables.

We will examine the relationship between the variables x and y for the data above.

Enter the x values into List A and label the list one, then

enter the y values into List B and label the list two.

To draw a scatter diagram of the data, press 5:Data

& Statistics. Select one for the variable on the horizontal

axis and two for the variable on the vertical axis. We will

now find r and the line of best fit.

Press 1:Calculator menu , then select 5:Statistics>

1:Stat Calculations... > 3:Linear Regression (mx+b).

Select one from the X List drop-box, two from the Y List

drop-box, then press enter .

We can see that the line of best fit is

y ¼ 2:54x+ 2:71, and that r ¼ 0:998.

CALCULATING Â2

To calculate Â2 for the data

alongside, enter the values of the

table into matrix A, using the

instructions given on page 44.

A1 A2

B1 21 28

B2 13 24

Press menu , then select 5:Statistics > 7:Stat Tests...

> 8:Â22-way Test . Select a from the drop-box, then

select OK.

So, Â2 ¼ 0:526 . The p-value and the degrees of freedom

are also given.


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SOLVING EQUATIONS


To solve the linear equation 3:2x¡ 4:2 = 7:4,

press menu from the Calculator application and select

3:Calculations > 1:Numerical Solve.

Enter the equation by pressing 3:2 X ¡ 4:2 = 7:4,

then press , X enter .

The solution is x = 3:625.


The TI-nspire does not have a built-in method to solve

quadratic equations. We must write our own program.

To solve the quadratic equation 3x2 + 2x ¡ 11 = 0,

press menu from the Calculator application, then select

8:Functions and Programs > 1:Program Editor >

1:New... . Label the program quadrat, and select OK.

Enter the code for quadrat (a, b, c) as shown alongside.

You can enter Disp by pressing menu 6:I/O > 1:Disp.

When you are done, press menu , then select 2:Check

Syntax & Store > 1:Check Syntax & Store to store the

program.

Press ctrl tab to move the cursor to the other side of

the screen, and enter quadrat (3, 2, ¡11) enter .

So, the solutions are x ¼ ¡2:28 or 1:61.


GRAPHING FUNCTIONS

Selecting 2 : Graphs & Geometry from the home screen

opens the graphing application, where you can graph

functions.

To graph the function y = x2 ¡ 3x¡ 2, press X x2

¡ 3 X ¡ 2 enter .



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To view a table of values for the function, press menu ,

then select 2 : View > 9 : Add Function Table.

The page splits into 2, with the graph on one side and the

table of values on the other side.





To adjust the viewing window, press menu then select 4 : Window . The most useful

options are:

1 : Window Settings : With this option you can set

the minimum and maximum values for the x and y axes

manually.

5 : Zoom-Standard : This option returns the viewing

window to the default setting of ¡10 6 x 6 10,

¡20

36 y 6 20

3.

A : Zoom-Fit : This option scales the y-axis to fit the

minimum and maximum values of the displayed graph

within the current x-axis range.

Pressing ctrl G removes the function entry line, allowing you to use the full screen to view

the graph. Press ctrl G again to bring the function entry line back.


When locating points on a graph, it is advised that you set the accuracy level to Float 4 for

ease of reading.



For example, we can solve y = 11¡3x and y =12¡ x

2simultaneously by finding the point of intersection of

these two lines.

Store y = 11¡ 3x into f1(x) and y =12¡ x

2into

f2(x). Press menu , then select

6 : Points & Lines > 3 : Intersection Point(s).

Move the cursor over one of the lines and press enter , then move the cursor over the other

line and press enter . The intersection point (2, 5) is displayed. So, the solution to the

equations is x = 2, y = 5.



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done by graphing y = f(x) and then finding when the graph cuts the x-axis.

For example, to solve x3 ¡ 3x2 + x + 1 = 0, store

x3 ¡ 3x2 + x+ 1 into f1(x).

To find where this graph cuts the x-axis, press menu ,

then select 5 : Trace > 1 : Graph Trace. Use the J

key to move the cursor along the curve until you reach

the zero. A z will appear on the screen.

If you need to move the coordinates to make them easier

to read, press enter to paste the coordinates to the screen,

then esc to exit the trace command. Move the cursor

over the coordinates, and hold the key until the hand

closes. Use the cursor keys to drag the coordinates, then

press esc .

The solution x ¼ ¡0:414 is given. Repeat this process

to find the remaining solutions x = 1 and x ¼ 2:414 .

TURNING POINTS

To find the turning point or vertex of y = ¡x2+2x+3,

store ¡x2 + 2x+ 3 into f1(x).

Press menu , then select 5 : Trace > 1 : Graph Trace.

Use the I key to move the cursor along the curve until

the vertex is reached. An M will appear on the screen

to indicate a local maximum. The vertex is at (1, 4).


To find the equation of the tangent to y = x2 when

x = 1, we first draw the graph of y = x2. Press menu

then select 5 : Trace > 1 : Graph Trace. Press 1

enter , and the point (1, 1) is located. Press enter esc

to store the point.

Press menu , then select

6 : Points & Lines > 7 : Tangent.

Move the cursor towards the point (1, 1) until the word point appears, then press enter todraw the tangent.



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To find the equation of the tangent, press esc to exit

the tangent command, and move the cursor over the

tangent until the word line appears. Press ctrl menu

and select 6 : Coordinates and Equations. The tangent

has gradient 2, and equation y = 2x¡ 1.


Suppose we invest $5000 at 7:2% compounded annually. To find the value of the investment

after 10 years, press menu from the Calculator

application and select 7:Finance > 1:Finance Solver.

Set up the screen as shown.

MATRICES

STORING MATRICES

To store the matrix

0@

2 31 45 0

1A, press ctrl £ from the

Calculator screen, then select the template. Press 3

tab 2 enter to define a 3£ 2 matrix.

Enter the elements of the matrix, pressing tab after each

entry. To define this matrix as matrix A, press ctrl var

(stoI) A enter .


Note: All money being invested is considered as

outgoings and is entered as a negative value.

There are no payments into the account during

the term of the investment, so Pmt is set to 0.

Move the cursor to the FV field and press enter to find

the future value of the investment.

The investment amounts to $10 021:16.


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Documents

Graphics calculator instructions - … calculator instructions Contents: A B C Casio fx-9860G Texas Instruments TI-84 Plus Texas Instruments TI- spiren IB_STSL-2ed cyan magenta yellow