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A P P E N D I X
TI-Nspire CAS calculator
CAS calculators have the added advantage of performing algebraic tasks. Example: Expand (3 x 2)(2 x 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 ¸.
5 x^2 17 x 6.
Using technology to expand and factorise
Appendix — TI-Nspire CAS calculator 507
508 Essential Mathematics VELS Edition Year 9
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(2 x 4) 2
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(2 x 4)> 2 3
Using technology to solve 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 2 x 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
Appendix — TI-Nspire CAS calculator 511
Example: Use technology to sketch a graph of y 2 x 4 and find the x- and y- intercepts. 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
findx- andy-intercepts
Appendix — TI-Nspire CAS calculator 513
Example: Use technology to solve the following pair of simultaneous equations graphically.
y 5 2 x
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 2 x 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)
514 Essential Mathematics VELS Edition Year 9
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.
516 Essential Mathematics VELS Edition Year 9
c Press TAN 89 (hold down CTRL for a decimal result).
This gives the answer which rounds up to 57.2900.
Appendix — TI-Nspire CAS calculator 517
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
Appendix — TI-Nspire CAS calculator 519
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 7 x 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
520 Essential Mathematics VELS Edition Year 9
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 4 x 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 findx-intercepts
A graphics or CAS calculator can be used to solve quadratic equations. Example: Use technology to solve x^2 8 x 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
522 Essential Mathematics VELS Edition Year 9
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.
x f 15 7 20 12 25 14 30 8 35 5
Appendix — TI-Nspire CAS calculator 523
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!
