CAS TI-Nspire User manual

Quick Start Guide
–
TI-NspireTM CAS
Software
by
Bernhard Kutzler
(V1.4)

Table of Contents
0 Introduction ................................................................................................................. 1
1 Starting TI-Nspire™ CAS ............................................................................................ 3
2 Introduction to the Calculator ....................................................................................... 7
3 Introduction to Graphing ........................................................................................... 33
4 Introduction to Interactive Geometry .......................................................................... 45
5 Introduction to Lists & Spreadsheet ........................................................................... 57
6 Introduction to Notes ................................................................................................. 69
7 Introduction to Data & Statistics ................................................................................. 77
8 Introduction to Combining TI-Nspire™ CAS Applications – Part 1 ............................ 83
- Basics ...................................................................................................................... 83
- Calculator and Graphing .......................................................................................... 95
- Calculator and Lists&Spreadsheet ............................................................................ 98
- Geometry and Lists&Spreadsheet .......................................................................... 100
9 Introduction to Combining TI-Nspire CAS Applications – Part 2 .............................. 103
- Data Collection ...................................................................................................... 103
10 Appendix: Factory Default TI-Nspire CAS ............................................................... 109
Preface
The purpose of this book is to make TI-Nspire CAS easily and quickly accessible, especially
for teachers and students. Many thanks to David Stoutemyer who polished the language of this
text and made valuable suggestions for improving the original manuscript.
Bernhard Kutzler, September 2007 & October 2008

Introduction
Question: Why should we use technology for teaching and learning mathematics?
Answer: Because it can help students.
Technology is for automating tasks. Instead of walking to the grocery shop, we can go
there by car. This saves us from having to walk between our home and the shop and from
having to carry the groceries. For some people, using a car for their shopping is a convenience
which saves them time and energy which they can use for other activities – such as reading a
book. For people who are physically challenged, using a car for their daily shopping may be a
matter of survival.
This example shows two types of technology use: Amplification and compensation. Here
is another example: Optical instruments such as telescopes and microscopes amplify our natu-
ral eye sight so that we can see things that we cannot see otherwise. Optical instruments such
as eye-glasses compensate poor eyesight so that people with poor eyesight can see things
which people with normal eyesight can see without glasses.
TI-Nspire CAS is a powerful mathematics tool suited for teaching and learning. It combi-
nes several applications under one roof: A Computer Algebra System (CAS), a graphing soft-
ware, an interactive geometry system, a spreadsheet, an interactive statistics system, a text
editor, a data collection interface, and a programming environment.
TI-Nspire™ CAS enables new approaches in teaching, learning, and understanding mathe-
matics by providing seamless integration of numeric, algebraic, graphic, geometric, and sta-
tistic capabilities enhanced with the support of data collection, programming, and text editing.
You will find that many topics can be treated more efficiently and effectively with TI-
Nspire™ CAS than by using traditional methods or isolated products. TI-Nspire™ CAS is
available in three compatible versions – as computer software under Windows™ and under
Mac OS™ and as a handheld.

2 Introduction
There are also three corresponding versions of the TI-Nspire™ technology without CAS
functionality published under the name TI-Nspire™.
This book gets you started with TI-Nspire™ CAS by independent study. First, install TI-
Nspire™ CAS on your computer. Then, starting with the first chapter you will learn step by
step how to use the program. Follow all instructions and examples. The text leads you through
several mathematical topics to learn how to use TI-Nspire™ CAS. Paragraphs starting with
the symbol
 give instructions about what you should do on your computer. Hundreds of
screen images ensure that you will not get lost on this journey. This book is written so that
each introduction to an individual application of TI-Nspire CAS can be used independently
(and most of them also with TI-Nspire™).
All you need to run TI-Nspire™ CAS is a PC compatible computer with Windows 2000
(with Service Pack 4), Windows XP (with Service Pack 2), or Windows Vista™; or a
PowerPC, G4 or G5 with Mac OS™ X 10.4 or 10.5.
It is assumed that you know how to use the computer and the Windows™ or Mac OS™
operating system. The screen shots in this book were produced from TI-Nspire™ CAS
running on Windows XP™. If you are running TI-Nspire™ CAS with a different version of
Windows™ or under Mac OS™, then some of the screens may appear slightly different.
This book gets you started. A complete reference to all features is included with the
software as online help.
This text was written for TI-Nspire™ CAS Version 1. 4.11654. If you use a
later version of TI-Nspire™ CAS, some of the screen images may be differ-
rent.
Have fun reading and discovering.
For users of TI-Nspire™ :
Most parts of this book do not use the CAS component of TI-Nspire ™ CAS. Therefore you can
use this text also with TI-Nspire™. Only part of the “Introduction to the Calculator” is CAS
specific. All chapters that refer to “TI-Nspire” (rather than “TI-Nspire CAS”) are equally
valid for TI-Nspire™ and TI-Nspire™ CAS.
TI-Nspire Resources
For resources about how to integrate TI-Nspire technology into the classroom visit the
following websites:
- www.timath.com
- compasstech.com.au/TNSINTRO/TI-NspireCD
- groups.google.com/group/tinspire
- education.ti.com/uk (choose Online Resources from the Professional Development menu)

Starting TI-Nspire CAS
This text assumes that you use a factory default TI-Nspire CAS. Only then (and when you use
WINDOWS XP) will your screen images fully match those in this book. If you just installed TI-
Nspire CAS, it is a factory default version. If you use a version of TI-Nspire CAS that was
used by someone else earlier, we recommend that you turn it into an almost factory default
version now. The Appendix gives instructions on how to do this.
 Start TI-Nspire CAS by double clicking on the TI-Nspire CAS icon. If there is no such
icon on your computer’s desktop or task bar, you probably will find TI-Nspire CAS on the
Start menu or via Start>All Programs in the TI Tools folder.
The following screen appears after a few seconds:
The TI-Nspire CAS screen comprises (from top to bottom):
• the Titlebar
• the Menubar
• the Command Toolbar
• a thumbnail preview pane at the left and a work area at the right
See what applications are available:

4 Starting TI-Nspire CAS
 Move the mouse pointer into the work area, and then click the right mouse button.
= =
These are the five main applications of TI-Nspire CAS.
 If you move the mouse button over the Insert menu button in the Command Toolbar, and
then click the left mouse button, …
=
… you will see two more applications to choose from.
The Calculator application is a computer algebra system (CAS) as known from programs such
as Derive or from handhelds such as the TI-89, TI-92, or Voyage200.
The Graphs & Geometry application is a double application. It is a graphing application as
known from graphing calculators such as the TI-83 or TI-84. It is also an interactive geometry
application as known from interactive geometry programs such as Cabri Geometry. Having
both applications integrated with each other creates a powerful “geo-graphical” environment
which goes far beyond what the individual applications usually offer.
The Lists & Spreadsheet application is a spreadsheet as known from programs such as Micro-
soft Excel. In addition to the usual cell-based logic it also offers column-based logic as known
from the list editor in a TI-89, TI-92, or Voyage200.
The Notes application is an easy-to-use word processor, which allows modes and styles parti-
cularly useful for annotating mathematical and educational work.
The Data & Statistics application is an easy-to-use package for statistical analysis as known
from programs such as Fathom.
The Program Editor application is an easy-to-use and very convenient environment for writing
and updating user defined programs and functions.
The Data Collection application is an interface for collecting real world data. It supports 34
sensors manufactured by Vernier.

Quick Start Guide – TI-Nspire CAS (Software) 5
The following chapters provide independent introductions to the five main applications. The
two applications contained in the Graphs&Geometry application are treated separately.
A major strength of TI-Nspire CAS is the “roof” that connects the individual applications. The
first part of the “Introduction to Combining TI-Nspire CAS Applications” introduces you to
this “roof”. The second part introduces you to the collecting of real world data.
The Program Editor is not treated in this book.
TI-Nspire CAS Teacher Edition
There are two versions of the TI-Nspire CAS Software: the standard edition and the teacher
edition. In this section we describe the specific features of the teacher edition.
 If available, then start the TI-Nspire CAS Teacher Edition.
The teacher edition offers an emulation of the handheld. You can choose between two views.
 Open the View menu and from therein open the TI-SmartView Emulator submenu.

6 Starting TI-Nspire CAS
 Invoke the Handheld command.
Now you see a picture of the TI-Nspire CAS handheld. You could go through the exercises of
this book in this mode. Press a key by moving the mouse pointer above the key, and then
clicking the left mouse button. You can enter numbers, letters, and special symbols also via
the computer keyboard.
 Invoke the View>TI-SmartView Emulator>Handheld + Side Screen command.
In addition to the handheld you now see also an enlarged version of the handheld screen. This
view is particularly useful when a teacher teaches students using handhelds. This view is ideal
to show how to operate the handheld.
 Go back to standard software view with View>Normal.

Introduction to the Calculator
This chapter is an introduction to using the Calculator application of TI-Nspire CAS. It will
get you started and you will learn the routine use of this application independent of any other
TI-Nspire applications.
 Start TI-Nspire CAS. Move the mouse pointer into the work area, and then click any of
the two mouse buttons.
 Select Add Calculator by clicking the left mouse button on that text line.
This changes the appearance of the work area, which now shows a blinking cursor in the upper
left corner, a (currently dimmed) scroll bar at the right side and a counter in the lower right
corner (currently showing “
0/99 ”). Above the work area there are eight buttons in the
Calculator Toolbar.

8 Introduction to the Calculator
Start with the simple addition of two rational numbers.
 Input through the keyboard: 1/2+1/3
As you type them the symbols appear on the screen.
 End the input with the ‘Enter’-key E¿F .
The entry is displayed in “2-dimensional” output format, as opposed to the “1-dimensional” or
linear input format that was used for entering. The result of this computation is computed
automatically and displayed at the right end of the Calculator window. Entry and answer
together make the first history pair. The blinking cursor below the entry indicates that the
Calculator is ready to accept the next input. The counter in the lower right corner changed to
“
1/99 ” for “1 history pair out of 99”. (99 is the maximum number of history pairs a Calculator
page can store. If you add expressions beyond that, the oldest pair(s) are discarded.
Repeat the last input with an intentional typographical error:
 1/2+1’3 E¿F
An error message is displayed when the Calculator cannot understand an input string.
 Quit the error message by clicking E|lh|F or using the ‘Enter’-key E¿F .
The faulty input remains in input mode (though displayed 2-dimensionally where applicable)
with the cursor blinking at the position where the problem was detected. This gives you a
chance to correct the input.
 Delete the digit ‘3’ right of the cursor with the computer keyboard’s EabiF key or by
using the Command Toolbar’s Delete button .

Quick Start Guide – TI-Nspire CAS Software 9
 Delete the two symbols left of the cursor using the backspace key E‹|F two times.
An alternative to entering a fraction as a linear input string is using the “2-dimensional” frac-
tion template, which is similar to what equation editors offer. It is particularly useful for
entering more complicated fractions.
 Move the mouse pointer above the fifth button from the right in the Command Toolbar.
Observe the tool tip saying Shows the Math Templates , which appears under the mouse
pointer for about 3-4 seconds. Such tool tips are available for all buttons.
 With the mouse pointer pointing on the button , click the left mouse button to open the
Math Templates Toolbar.
The Math Templates Toolbar offers templates for many standard mathematical expressions
such as fractions, radicals, logarithms, matrices, vectors, limits, derivatives, integrals, etc.
 Insert a fraction template at the current cursor position by clicking on the fraction template
in the upper left corner.
= =
The cursor is positioned in the dashed box above the fraction bar so that you can input the
numerator.
 Type ‘ 3+4 ’. Use the tab key EˆF to move the cursor into the denominator input field.
= =
 Type ‘ 5 ’, and then conclude the input with E¿F .
=

Enter the next expression,
24
. There are several methods to enter the square root symbol,
one of them is to use the Math Templates Toolbar.1
1Alternative methods include entering the square root of 24 via the keyboard as SQRT(24) or 24^(1/2).

10 Introduction to the Calculator
 Display the Math Templates Toolbar by clicking on . Enter
24
as follows:
Click on the Math Template Toolbar button . (You need to click twice – one time to
select the button, one more time to use it.) Type:
24
= =
 Conclude the input with E¿F .
=
This is different from what many calculators would produce. A mathematician once asked:
“How do you recognize a mathematician?” and suggested the following answer: “A mathe-
matician considers
26
⋅a beautiful result.” Most students strive to replace such an expres-
sion by the corresponding floating point approximation 4.8989…. As explained later TI-
Nspire CAS can do this as well.
Any expression in the history area can be highlighted then auto-pasted into the entry line to be
used to help build a new entry.
Press the upward key to shift the highlighting from the entry line to the last answer. Pressing
the upward key again moves the highlighting back in the history area: from the last answer to
the last entry, then to the penultimate answer, then to the penultimate entry, and so on.
 Use the up arrow key E½F . E½F
=
 E½F Use the down arrow key E¼F .
=
 Auto-paste the highlighted expression into the entry line with E¿F .
Alternatively one can highlight any expression (or a part thereof) using the standard Windows
technique with the mouse. (Click on one end of the string you want to select; hold the mouse
button, and then drag the mouse pointer to the other end of the string.) You can also use the
standard Windows hotkeys for copy (
E`íêäF + E`F ) and paste ( E`íêäF + EsF ).

Quick Start Guide – TI-Nspire CAS Software 11
The symbols on the Calculator Toolbar’s second button, , indicate a conversion from an
exact number to a floating point number (which may be an approximation).
 Open the Number menu by clicking the button with the left mouse button.
This menu offers several commands. The first command, Convert to Decimal, seems appro-
priate for obtaining a decimal approximation. Try it:
 Move the mouse pointer into the text line Convert to Decimal.
 Invoke the command by clicking on it with the left mouse button.
 Conclude the input with E¿F .
This is a six digit approximation. For a different number of digits use the File>Settings>
Document Settings command:
 Open the File menu, from therein open the Settings submenu, and then choose the
Document Settings command.

12 Introduction to the Calculator
The first input field in this dialog, Display Digits, is set to Float6, which stands for “floating
point number with six digits”.
 Open the selection menu of the Display Digits input field by clicking the down arrow
button at the right end of the input field.
 Change to ten digits: Move the mouse pointer into the text line Float10, …
 … and then click on it.
 Apply the new setting to the current document by exiting the dialog with E|lh|F .
Test the change by repeating the last example:
 Highlight the last entry by pressing E½F twice.
Try an alternative to auto-pasting with the ‘Enter’-key:
 Copy the highlighted expression into the Windows clipboard with E`íêäF + E`F .
Return control to the entry line with Ebp`F , and then paste the clipboard contents with
E`íêäF
+ EsF . Conclude the input with E¿F .
This is a ten digit approximation of the square root of 24.

Quick Start Guide – TI-Nspire CAS Software 13
Enter
24
again, this time using the built-in function sqrt :
 Type: sqr
As you type these letters, they appear in italics. TI-Nspire CAS displays variables in italics,
i.e. the input string entered so far is interpreted as a variable named sqr.
 Type: t
Once the letter ‘t’ is added, TI-Nspire CAS recognizes the input string as the name of the
built-in function
sqrt and does not display it in italics any longer. This feature helps avoiding
name conflicts.
 Type an opening parenthesis: (
A matching closing parenthesis automatically is inserted after the cursor.
 Type: 24
Now you can optionally type a closing parenthesis, it makes no difference.
 Conclude the input with E¿F .
See what happens if you apply the Convert to Decimal command from the Number menu
without having an expression in the entry line:
 Open the Number menu ( ), and then click on the Convert to Decimal command.
The string ‘
Ans ’ left of the black triangle is a reference to the most recent answer (which is
26
⋅).
 Conclude the input.
When this entry is displayed in the history pair, the first argument, ‘
Ans ’, got replaced by the
expression it stood for. Using ‘
Ans ’ indirectly such as in the previous example or directly by
typing it is a standard technique for using, in the next computation, the expression that was
just entered or produced.
A history pair can be deleted by highlighting the entry or the answer, and then using the key-
board’s
EabiF key or the Command Toolbar’s button .

14 Introduction to the Calculator
 Highlight the most recent answer.
 Delete this history pair with the keyboard’s EabiF key.
A virtual version of the handheld’s keypad is an alternative to the computer keyboard.
 Display the handheld’s keypad by clicking on the Command Toolbar button (or by
using the View>Keypad command).
This keypad is resizable and floatable, hence it can be placed wherever wanted or needed.
Clicking on any of these keys is equivalent to making the respective input via the computer
keyboard. The keypad offers some keys that are not on a computer keyboard. Therefore it can
serve as a source for “hot keys” for entries that are more difficult to enter using a computer
keyboard.
 Click on the handheld keypad’s ‘Enter’-key · .
This repeated the last example. Note that no expression was entered. If there is no expression
in the entry line, TI-Nspire CAS uses the most recent entry.
The keypad’s ‘Enter’-key shows the approximation symbol ≈in blue color above the word
‘Enter’. This indicates that this function of the key can be accessed via the keypad’s blue
control key
/ .
 Click on the keypad’s control key / followed by the ‘Enter’-key · .

Quick Start Guide – TI-Nspire CAS Software 15
This produces the same result as the Convert to Decimal command. The key combination
E`íêäF + E¿F works the same on the computer keyboard.
 Turn off the keypad by clicking on in its upper right corner.
Using the computer keyboard type:
1/3 E`íêäF + E¿F

TI-Nspire CAS uses two types of numbers: exact (symbolic) numbers and floating point num-
bers. Exact numbers are integers, symbolic constants such as πand e, and expressions built
from these, such as 3+4, 1/2,
5
,
s
in( /2
)
π . Floating point numbers are numbers with a deci-
mal point such as 1., 2.5, and 0.33333, or ones that have an E representing ‘*10^’.
While
E`íêäF + E¿F always gives floating point results, the behavior of E¿F is determined by
a mode that is controlled via the Auto or Approximate input field in the Document Settings
dialog.
=
The default mode is Auto, in which E¿F gives exact (symbolic) results if an algorithm for
computing the exact result is implemented and if all numbers in the entry are exact numbers. If
at least one number in the entry is a floating point number, the result will be a floating point
number or, if the result is non-numeric, corresponding coefficients will be floating point num-
bers. This yields another method to enforce a floating point (approximate) result: Simply add a
decimal point to an integer in the input – or add a floating point zero (+0.) or multiply with a
floating point one (*1.).
 Enter: 1+1/2
Enter:
1.+1/2
In Approximate mode
E¿F always gives floating point results. In Exact mode E¿F always
gives exact answers or echoes the input if no exact answer can be given. This is where the
difference lies: While Exact mode will not give any result when a symbolic result cannot be
found, such as when solving the equation 2
s
in( )
0
xx−=, Auto mode in this case will try to
find an approximate answer. If it does not find an approximate
answer either, the input is echoed. The mode is displayed at the
right end of the command toolbar, see AUTO between RAD (mode
for angles in radian) and REAL (mode for real numbers).

16 Introduction to the Calculator

Symbolic constants such as πand ecan be entered via the Symbol Toolbar.
 Display the Symbol Toolbar by clicking the Command Toolbar’s button .
 Input πby clicking on in the upper left corner of the Symbol Toolbar.
 Type a plus (‘+’) for addition, and then input the number e: display the Symbol Toolbar,
and then use (which is next to ). Conclude the input.

TI-Nspire CAS can handle very large numbers.
 Enter 123 factorial: 123!
The result is larger than the width of this application window. Therefore the answer appears
cut off, as is indicated by the small black triangle just before the window’s right end.
Decompose this number into prime factors. This is done using the built-in
factor function:
 Auto-paste the factor function into the entry line by opening the Number menu ( ), and
then clicking on the Factor command (in the sequel denoted as Number>Factor).
The
factor function name comes with an opening and a closing parenthesis with the cursor in
between waiting for an argument to be inserted. You could highlight, and then auto-paste the
last answer – or the previous entry, or any other expression. Enter a reference to the last
answer:
 Type: ans
 Conclude the input by pressing E¿F .
Proceed as follows to see the rest of the answer:
 Highlight the answer.