APPENDIX
TI-
Nspire
CAS
calculator
CAS calculators have the added advantage of performing algebraic tasks.
Example: Expand
(3x 2)(2x 1).
TI-Nspire CAS keystrokes
TI-Nspire CAS screens
From the Calculator screen select expand( from the
Algebra menu (X=).
Type in your expression, ensuring you include a
multiplication between the two sets of parentheses,
and press ¸.
Example: Factorise
From the Calculator screen select the Algebra menu
and choose factor( - or just type the command.
Type in your expression and press ¸.
5x
2
17x 6.
Using technology to expand and factorise
507
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Example: Write a program that will calculate the area of a rectangle given the length
and width.
TI-Nspire CAS keystrokes TI-Nspire CAS screens
While TI-Nspire has no programming facility as
such, it easily supports defining functions which will
serve the same purpose.
For example, defining the function ‘rect’ as shown
allows the area of any rectangle to be calculated by
simply typing the length and width into the function
argument.
CAS
Using technology to write simple programs for finding
areas of shapes
Graphics or CAS calculators can be used to solve linear equations.
Example: Solve the equation
3(2x 4)
2
3
TI-Nspire CAS keystrokes
TI-Nspire CAS screens
Create a Calculator page.
Choose Solve( from the Algebra menu (or just type it);
enter the equation , followed by ‘,x’
and press ¸.
The solution is x 3.
3(2x 4)>2 3
Using technology to solve linear equations
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CAS calculators can be used to solve linear equations.
Example: Solve the set of simultaneous equations below.
3 x 2y 4
2 x y 5
TI-Nspire CAS keystrokes
TI-Nspire CAS screens
Using the Calculator application, choose the Solve(
command from the Algebra (X=) menu (or type the
command).
From the Templates menu, (CTRL-MENU>7: Math
Templates . . .), choose the System of Equations option
shown.
Enter the two linear equations into the template, arrow
right to leave the template and type ‘{x, y}’.
Press ¸ and the solution will be given.
The solution is: and y 1.x 2
Using technology to solve simultaneous linear equations
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Example: For the rule use technology to:
a construct a table of values using
b draw a graph
3 x 3
y 2x 3
TI-Nspire CAS keystrokes
TI-Nspire CAS screens
Begin with a Graphs & Geometry page, and enter the
function 2x 3 into f1(x). Press ¸ to plot the
graph.
Press CTRL-T to show the table of values for this
function and scroll up to show values between 3 and 3.
Function table settings may be altered in the Function
Table menu.
Using technology to construct a table of values and draw a graph
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Example: Use technology to sketch a graph of and find the x- and y-intercepts.y 2x 4
TI-Nspire CAS keystrokes
TI-Nspire CAS screens
Within a Graphs and Geometry page, enter the
equation into the Graph Box at the bottom of the page
(or type it anywhere on the graph screen using the Text
tool, then drag it onto the axes).
To find the intercepts, choose the Trace menu and drag
to the required places along the x-axis (shown).
Alternatively, choose Point On from the Points &
Lines menu, place a point on the line and then edit the
coordinates to jump to the values where x 0 and
y 0. A zero marker (z) will appear to indicate the
zero on dragging.
Using technology to sketch straight lines and
find
x
- and
y
-intercepts
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Example: Use technology to sketch a graph of the following family of linear relations.
abc
de
y 2x 1y x 1
y 1y x 1y 2x 1
TI-Nspire CAS keystrokes
TI-Nspire CAS screens
On a Graphs and Geometry page, use the Points &
Lines menu to drop a Point On the x-axis, and then
Coordinates & Equations from the Tools menu to
show the coordinates of that point.
Use the Text tool from the Tools menu to enter the
equation ‘m*x 1’ on the screen, and then choose
Calculate also from the Tools menu.
Click on the equation, then on the x-coordinate of the
variable point for m. Finally click on the x-axis for x.
The line drawn will vary its gradient as you drag the
variable point along the x-axis.
Using technology to sketch the graph of a family of linear relations
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Example: Use technology to solve the following pair of simultaneous equations graphically.
y 5 2x
y 4 x
TI-Nspire CAS keystrokes
TI-Nspire CAS screens
Enter both functions into the Graph Box on
a Graphs and Geometry page.
Now select Point of Intersection from the Points &
Lines menu and click on each line.
Using technology to find intersections
Example: Use technology to sketch a graph of .y 2x 3
TI-Nspire CAS keystrokes
TI-Nspire CAS screens
In a Graphs and Geometry page, backspace to delete
the ‘’ in the Graph Box and enter ‘>2x+3’ as required.
Using technology to graph inequations (Extension material
8.11 on the Student CD-Rom)
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Example 9
The following is a program that simulates the tossing of a coin 100 times and counts the
number of heads tossed.
Comments
Number of heads starts at 0
Loop for 100 trials
Selection of 0 or 1 randomly
Tests if the number of heads increases by 1
End of loop
Displays number of heads counted
a Type this program into your graphics or CAS calculator and execute the program.
b Record the output of your program.
c Calculate the proportion of heads obtained and compare this with the expected value of 0.5.
Solution
A 1
TI-Nspire CAS keystrokes TI-Nspire CAS screens
a Statistical simulation is easy using the in-built
commands of TI-Nspire .
Using ‘randInt(’and ‘sum’ commands readily produces
the total of 100 tosses of a coin, as shown.
CAS
b Since the program selects random numbers, the program will deliver different results
each time.
c Divide the number of heads by 100 to evaluate your proportion.
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It is difficult to determine trigonometric ratios accurately just by measuring the sides and
angles of a triangle. A scientific, graphics or CAS calculator can be used to obtain the
accurate values. Before entering angles you need to make sure that the calculator is in
degree mode.
Example: Use a calculator to find the value of each of the following, correct to four decimal
places.
abc
tan 89sin 54cos 30
Scientific calculator
TI-Nspire CAS calculator
a Set Document Settings to Degrees, press SIN 30.
This gives the answer 0.5 or
1
2
.
b Press cos 54.
Press COS 54.
Use CTRL-ENTER to force a
decimal approximation.
Using technology to determine trigonometric ratios
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c Press TAN 89 (hold down CTRL for a decimal
result).
This gives the answer which rounds up
to 57.2900.
57.28996
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Example: For the quadratic relation use technology to:
a construct a table of values for
b draw a graph
3 x 3
y x
2
TI-Nspire CAS keystrokes
TI-Nspire CAS screens
In a Graphs & Geometry page, enter x
2
into the Entry
Line. You may adjust the x-axis limits to –3 and 3 if
desired.
Press CTRL-T to show the Function Table.
Axis settings may be adjusted using the Window
Settings menu if desired.
Define column b as ‘a
2
’.
Scroll up to the value x 3.
Using technology to construct tables of values and draw graphs
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Example:
a Use technology to sketch the quadratic equations on
the same axes.
b Describe how each graph transforms the graph of y x
2
.
y
1
2
x
2
y 3x
2
,y 2x
2
,y x
2
,
TI-Nspire CAS keystrokes
TI-Nspire CAS screens
In a Graphs and Geometry page, type x^2 into the
Graph Box (or use the Symbol Palette).
Other functions may be entered into subsequent graph
definitions or the ‘arms’ of the parabola may be
dragged to give the required graphs.
The graph of is narrower than the graph of
The graph of is wider than the graph of y x
2
.y
1
2
x
2
y x
2
.
y 2x
2
Using technology to compare graphs of the form
y
ax
2
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A graphics or CAS calculator can be used to find the turning point of the graph of
a quadratic relation.
Example: For use technology to find the turning point correct to two
decimal places.
y x
2
7x 4
TI-Nspire CAS keystrokes TI-Nspire CAS screens
Turning points may be found in several ways. Using the
Calculator, define the function, and then use the
template to solve for the zero of the derivative, or just
use the fMin( command.
Graphically, use the Text tool to type f(x) onto the
graph screen and drag it over the axes to graph the
function. Then select Graph Trace or Point On to
identify the turning point.
The turning point is (3.5, 8.25).
Using technology to find turning points
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A graphics or CAS calculator can be used to solve quadratic equations or find x-intercepts of
graphs.
Example: For use technology to find the x-intercepts correct to two
decimal places.
y x
2
4x 6
TI-Nspire CAS keystrokes TI-Nspire CAS screens
Enter the function into the Graph Box of a Graphs and
Geometry page. Choose Graph Trace or Point On
from the Points & Lines menu to read off the required
intercept points.
The decimal display may be adjusted by hovering over
the value and pressing plus or minus keys to increase
or decrease the accuracy.
The first x-intercept is Repeat the process
to find the second x-intercept, x 5.16.
x 1.16.
Using technology to find
x
-intercepts
A graphics or CAS calculator can be used to solve quadratic equations.
Example: Use technology to solve x
2
8x 20 0.
TI-Nspire CAS keystrokes
TI-Nspire CAS screens
In the Calculator application, choose the Solve(
command from the Algebra menu (X=) (or simply
type it) and enter the equation as shown.
Using technology to solve quadratic equations
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Example: Determine the mean for this set of numbers: 246810
TI-Nspire CAS keystrokes TI-Nspire CAS screens
Statistical operations may be carried out using either the
Lists and Spreadsheet tool or the Calculator tool
(where the operation may be chosen from the Statistics
menu or simply typed, and may act upon a list already
defined—as shown—or on a set of numbers entered as
a list using braces—as shown.
Within the Lists and Spreadsheet page, the list may be
named and the data entered, and then the One-variable
statistics command chosen.
Following the steps as shown drops one-variable
statistics data into the page, as specified.
Using technology to find the mean
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Using technology to determine the mean of a frequency distribution
Example: Determine the mean for the following set of data.
TI-Nspire CAS keystrokes TI-Nspire CAS screens
In a Lists and Spreadsheet page, data may be entered
and the lists named, as shown.
Note that spreadsheet features may be used if desired:
after entering 15 into cell, a1, a2 is defined as ‘=a1+5’
and this formula is copied into subsequent cells by
dragging from the bottom right corner.
Using the Statistics menu, select One-variable
statistics (as shown), complete the floating menus
as required.
xf
15 7
20 12
25 14
30 8
35 5
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The results are placed on the page.
Of course, once the lists have been named, the mean
may be found using the Calculator page as well!
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