CHAPTER 1 - PLOTTING POINTS
TI-nspire
To plot the points below:
x (m)
0
5
10
15
20
25
30
y (m)
1:25
10
16:25
20
21:25
20
16:25
We first enter the x values into List A and label the list x, then enter the
y values into List B and label the list y.
Press ctrl
I
5 : Data & Statistics.
Move the cursor to the bottom of the screen until the “Click or enter to add
variable” box appears. Press enter , then select x.
Move the cursor to the left side of the screen, and select y for the variable
on the vertical axis.
CHAPTER 1 - SOLVING QUADRATIC EQUATIONS
TI-nspire
To solve the quadratic equation x2 ¡ 4x ¡ 3 = 0, press
ctrl
I
2 :
2
Graphs, and store x ¡ 4x ¡ 3 into f1 (x).
To find the x-intercepts, press menu , then select 6 : Analyze Graph
> 1 : Zero. Place the lower and upper bounds either side of the first
x-intercept.
The first x-intercept x ¼ ¡0:646 is given.
Repeat this process to find the remaining x-intercept x ¼ 4:65 .
So, the equation x2 ¡ 4x ¡ 3 = 0 has solutions x ¼ ¡0:646 or 4:65 .
CHAPTER 3 - EXPONENTIAL EQUATIONS
TI-nspire
To solve the equation 2x = 8, press
2x into f1 (x) and 8 into f2 (x).
ctrl
I
2 : Graphs, and store
Press menu , then select 6 : Analyze Graph > 4 : Intersection. Move
the cursor to the left of the intersection point and press enter , then move
the cursor to the other side and press enter .
The intersection point (3, 8) is displayed. So, the solution to 2x = 8 is
x = 3.
CHAPTER 5 - GRAPHING FUNCTIONS
TI-nspire
Open the Graphs application and store
2x
¡ 2 into f1 (x).
x
To find the y-intercept, press menu , then select 5 : Trace > 1 : Graph
Trace, and press 0 enter .
There is no y-intercept.
To find the x-intercepts, press menu , then select 6 : Analyze Graph > 1 :
Zero. Place the lower and upper bounds either side of the first x-intercept.
The first x-intercept x = 1 is given.
Repeat this process to find the second x-intercept x = 2.
So, the x-intercepts are 1 and 2.
To find the coordinates of the local minimum, press menu , then select 6 :
Analyze Graph > 2 : Minimum. Place the lower and upper bounds either
side of the minimum. The local minimum is at (1:44, ¡0:116).
Press menu , then select 5 : Trace > 1 : Graph Trace.
Press ¡5 enter . We can see that as x ! ¡1, y ! ¡2, so y = ¡2 is
a horizontal asymptote.
Press 0:001 enter . We can see that as x ! 0 from the right, y ! 1,
so x = 0 is a vertical asymptote.
CHAPTER 6 - EVALUATING SERIES
TI-nspire
We can write the series 4 + 7 + 10+ .... to 50 terms as
50
P
(3k + 1).
k=1
To evaluate
50
P
k=1
and select the
Press
So,
K
50
P
k=1
¤
X
¤ =¤
(3k + 1), from the Calculator application, press ctrl £ ,
¤
template.
tab 1 tab 50 tab 3 K
(3k + 1) = 3875.
+ 1 enter .
CHAPTER 6 - GENERATING SEQUENCES
TI-nspire
To find the first five terms of the sequence represented by f2ng, enter the
numbers 1, 2, 3, 4, 5 into List A.
Move the cursor to the second row of List B, and press
= 2 £
A
enter .
So, the first five terms of the sequence are 2, 4, 6, 8, 10.
CHAPTER 6 - SIGMA NOTATION
TI-nspire
To evaluate
7
P
k=1
and select the
Press
So,
K
7
P
k=1
¤
X
¤ =¤
(k + 1), from the Calculator application, press ctrl £ ,
¤
template.
tab 1 tab 7 tab
(k + 1) = 35.
K
+ 1 enter .
CHAPTER 7 - CALCULATING BINOMIAL COEFFICIENTS
TI-nspire
Step 1
To calculate
¡4¢
2 , from the Calculator application press menu , then
select 5 : Probability > 3 : Combinations. Press 4
The result is 6.
Step 2
,
2 enter .
To generate the entire 5th row of Pascal’s triangle, open the Lists and
Spreadsheet application, enter the numbers 0, 1, 2, 3, 4, 5 into List A
and label the list data. Move the cursor to the second row of List B,
press =
(Catalog), and select nCr( . Press 5
data enter .
,
CHAPTER 8 - CONVERTING DEGREES INTO MINUTES AND SECONDS
TI-nspire
To convert 0:63± into minutes and seconds, from the Calculator application
press 0:63, then press
, select I DMS, and press enter .
So, 0:63± is equivalent to 37 minutes and 48 seconds.
Note: Your calculator must be set to Degrees mode.
CHAPTER 8 - GRAPHING PARAMETRIC EQUATIONS
TI-nspire
Draw the parametric equation: f(x, y) j x = cos t, y = sin t, 0 6 t 6 2¼g
Step 1
From the Graphs application, press menu , then select 3:Graph Type
> 2:Parametric.
Step 2
Enter cos t into x1 (t) and sin t into y1 (t), pressing tab after each entry.
Step 3
Press enter to draw the parametric equation.
CHAPTER 10 - THE BASIC COSINE CURVE
TI-nspire
Step 1
From the Graphs application, enter cos x into f1 (x). Press enter to draw
the graph.
Step 2
Press menu , then select 4 : Window/Zoom > 8 : Zoom-Trig to set
the window to an appropriate scale.
Note: 8 : Zoom-Trig will set the x-axis extents to ¡2¼ to 2¼ if the calculator is in radian mode, and ¡360 to
360 if the calculator is in degree mode.
CHAPTER 10 - MODELLING USING SINE FUNCTIONS
TI-nspire
Step 1
Enter the times in hours after midnight into List A and name the list x.
Enter the tide levels into List B and name the list y.
Step 2
Press ctrl
I
1 : Calculator to open the Calculator application.
Press menu , then select 6:Statistics > 1 : Stat Calculations > C :
Sinusoidal Regression.
Step 3
Select x from the X List drop-box and y from the Y List drop-box. The
average period of the graph is about 12:4 hours, so enter 12:4 as the
period guess.
Step 4
Press enter to find the equation of the sine model.
CHAPTER 10 - DRAWING SCATTER DIAGRAMS
TI-nspire
Draw a scatter diagram of the following data set:
x
y
0
0
1
1
2
1:4
3
1
4
0
5
¡1
6
¡1:4
7
¡1
8
0
9
1
10
1:4
11
1
12
0
Step 1
Enter the x values into List A and name the list x. Enter the y values
into List B and name the list y.
Step 2
Press ctrl I 5 to open the Data and Statistics application. Move the
cursor to the bottom of the screen until the “click to add variable” box
appears. Press enter , then select x.
Step 3
Move the cursor to the left side of the screen until the “Click to add
variable” box appears. Press enter , then select y. The scatter diagram
is formed.
The data appears to exhibit periodic behaviour.
CHAPTER 11 - SOLVING TRIGONOMETRIC EQUATIONS
TI-nspire
From the home screen, select 5 : Settings > 2 : Settings > 1 : General.
Scroll down to the Angle drop-box, press I , then select Radian and press
enter twice.
To solve the equation 2 sin x ¡ cos x = 4 ¡ x for 0 6 x 6 2¼, press
2 : Graphs, then press
Window Settings ....
ctrl
I
Set XMin = ¡ ¼6 , XMax =
13¼
6 ,
menu 4 :
Window/Zoom > 1 :
and XScale =
¼
6.
(¼ is entered by
pressing the ¼ button.) Press enter when you are done.
Store 2 sin x ¡ cos x into f1 (x), and 4 ¡ x into f2 (x).
To find where the graphs intersect, press menu , then select 6 : Analyze
Graph > 4 : Intersection. Place the lower and upper bounds either side
of the first intersection point. The intersection point (1:82, 2:18) is given.
Repeat this process to find the remaining intersection points.
So, the solutions to 2 sin x ¡ cos x = 4 ¡ x are x ¼ 1:82, 3:28, and 5:81 .
CHAPTER 18 - EVALUATING DEFINITE INTEGRALS
TI-nspire
R5
To find 2 xex dx, from the Calculator application press menu , then select
4 : Calculus > 2 : Numerical Integral.
Set up the screen as shown.
R5
So, 2 xex dx ¼ 586:3 .
CHAPTER 18 - EVALUATING DEFINITE INTEGRALS
TI-nspire
R5
To find 2 xex dx, from the Calculator application press menu , then select
4 : Calculus > 2 : Numerical Integral.
Set up the screen as shown.
R5
So, 2 xex dx ¼ 586:3 .
CHAPTER 18 - ESTIMATING AREA USING RECTANGLES
TI-nspire
To calculate the lower and upper sums for the area between the graph of y = x2 and the x-axis on the interval
0 6 x 6 1 using 4 equal subdivisions:
Step 1
From the Calculator application, press ctrl
template.
Step 2
We will first calculate the lower sum. Press
indicate that x ranges from 0 to 3.
X
X
, and select the
tab 0 tab 3 tab
¤
X
¤
¤ =¤
to
Enter the expression 1 ¥ 4 £ (x ¥ 4)2 .
Step 3
Press I ctrl var (sto I) L followed by ctrl enter
the lower sum and store it in the variable L.
Step 4
We can repeat this process to calculate the upper sum. The only
difference is that x ranges from 1 to 4 instead of 0 to 3, and we store
the result in a different variable, U .
Step 5
Finally, calculate the average of the upper and lower sums (U + L) ¥ 2
to obtain an estimate of the area.
to calculate
You should be able to adapt these instructions to calculate lower and upper sums for different values of n (the
number of subdivisions).
CHAPTER 18 - ESTIMATING
TI-nspire
Z 3
¡3
e
2
¡ x2
dx
2
¡x
2
for ¡3 6 x 6 3 and n = 4500.
Find upper and lower rectangular sums for the area under y = e
2
¡x
2
Step 1
From the Graphs application, store the function f1 (x) = e
Step 2
We will now obtain upper and lower sums for 0 6 x 6 3 and n = 2250.
3
1
The width of each rectangle will therefore be 2250
= 750
units.
From the Calculator application, press ctrl
template.
Step 3
We will first calculate the upper sum. Press
to indicate that x ranges from 0 to 2249.
¡1
2
Enter the expression e
x
( 750
)2
£
X
X
.
, and select the
¤
X
¤
¤ =¤
tab 0 tab 2249 tab
1
750 .
Step 4
Press I ctrl var (sto I) U
followed by enter to calculate the
upper sum and store it in the variable U .
Step 5
We can repeat this process to calculate the lower sum. The only
difference is that x ranges from 1 to 2250 instead of 0 to 2249, and
we store the result in a different variable, L.
Step 6
Since y = e 2 is symmetrical, lower and upper estimates of the area
for ¡3 6 x 6 3 can now be easily found.
2
¡x
CHAPTER 19 - AREAS UNDER CURVES
TI-nspire
To find the area enclosed by y = x2 + 1, the x-axis, x = 1, and x = 2,
we first draw a graph of y = x2 + 1. Press menu , then select 6 : Analyze
Graph > 6 : Integral. Press
(
2 enter
( 1 enter
to specify the upper bound.
So, the area = 3 13 units2 .
to specify the lower bound, then
CHAPTER 19 - DEFINITE INTEGRALS USING MODULUS
TI-nspire
¯
R1 ¯
To find ¡3 ¯x3 + 2x2 ¡ 3x¯ dx, open the Graphs application, press
and select abs ( .
Enter the expression x3 + 2x2 ¡ 3x, then press enter to draw the graph.
Press menu , then select 6 : Analyze Graph > 6 : Integral. Press
¡3 enter to specify the lower bound, then
upper bound.
¯
R1 ¯
So, ¡3 ¯x3 + 2x2 ¡ 3x¯ dx = 11 56 .
(
1 enter
(
to specify the
CHAPTER 19 - VOLUMES OF REVOLUTION
TI-nspire
R5
To find ¼ 0 x4 dx, from the Calculator application press ¼
select 4 : Calculus > 2 : Numerical Integral.
Set up the screen as shown.
R5
So, ¼ 0 x4 dx = 625¼.
menu , then
CHAPTER 20 - BOXPLOTS
TI-nspire
Consider the data set 3, 5, 5, 7, 10, 9, 4, 7, 8, 6, 6, 5, 8, 6.
Enter the data into List A and name this list data.
To obtain the descriptive statistics, press
ctrl
I
1 : Add Calculator to
open the Calculator application, press menu , then select 6 : Statistics >
1 : Stat Calculations .... > 1 : One-Variable Statistics.
Press enter to choose 1 list.
Select data from the X1 List drop-box, and
press enter .
So, the 5-number summary is
8
Q1 = 5
< minimum = 3
median = 6
Q3 = 8
:
maximum = 10
To obtain a boxplot of the data, press ctrl I 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 data. The
points will order themselves into a dotplot along the horizontal axis.
Press menu , then select 1 : Plot Type > 2 : Box Plot.
The range = 10 ¡ 3 = 7, and the IQR = 8 ¡ 5 = 3.
CHAPTER 20 - ESTIMATING THE MEAN OF DATA IN CLASSES
TI-nspire
To estimate the mean of the data alongside,
enter the mid-interval values into List A,
and label the list score. Enter the frequency
values into List B, and label the list freq.
Score
Frequency
0-9
2
10 - 19
5
Press ctrl I 1 to open the Calculator application. Press menu , then
select 6 : Statistics > 1 : Stat Calculations > 1 : One-Variable Statistics.
Press enter to choose 1 list. Select score from the X1 List drop-box and
freq from the Frequency List drop-box, then press enter .
So, the mean score is approximately 31:7 .
20 - 29
7
30 - 39
27
40 - 49
9
CHAPTER 20 - FINDING THE MEASURES OF CENTRE
TI-nspire
To find the mean and median of 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9:
Enter the data into List A, and name the list data.
Press ctrl I 1 to open the Calculator application. Press menu , then select 6 : Statistics > 1 : Stat
Calculations > 1 : One-Variable Statistics.
Press enter to choose 1 list. Select data from the X1 List drop-box, and press enter .
So, the mean ¼ 5:61, and the median = 6.
CHAPTER 20 - FINDING THE MEASURES OF SPREAD
TI-nspire
To find the measures of spread of 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9:
Enter the data into List A, and name the list data.
Press ctrl I 1 to open the Calculator application. Press menu , then select 6 : Statistics > 1 : Stat
Calculations > 1 : One-Variable Statistics.
Press enter to choose 1 list. Select data from the X1 List drop-box, and press enter .
The median = 6, the upper quartile is
Q3 = 7, and the lower quartile is Q1 = 4.
The range = max ¡ min = 9 ¡ 2 = 7, and
the IQR = Q3 ¡ Q1 = 7 ¡ 4 = 3.
CHAPTER 20 - THE MEAN AND MEDIAN
TI-nspire
Enter the data values into List A, and name the list data.
Press ctrl I 5 to open the Data and Statistics application. Move the
cursor to the “Click to add variable” box at the bottom of the screen. Press
enter , then select data.
Press menu , then select 1 : Plot Type > 3 : Histogram.
Press menu , then select 5 : Window/Zoom > 1 : Window Settings, and
set XMin = 240, XMax = 280, and YMax = 30.
Press menu , then select 2 : Plot Properties > 2 : Histogram Properties
> 2 : Bin Settings. Set Width to 5, and Alignment to 240.
Press ctrl I 1 to open the Calculator application. Press menu , then
select 6 : Statistics > 1 : Stat Calculations > 1 : One-Variable Statistics.
Press enter to choose 1 list. Select data from the X1 List drop-box, and
press enter .
The mean of the data is ¼ 260:8, and the median is 263.
Press ctrl J to return to the histogram. By moving the cursor across the
columns, we find that the modal class is 260 6 d < 265 m.
Press menu , then select 2 : Plot Properties > 2 : Histogram Properties
> 2 : Bin Settings, and change the Width to 2. The modal class in this case
is 264 6 d < 266 m.
J
to return to the data, and change the three shortest drives to 82:1 m, 103:2 m, and 111:1 m.
Press ctrl I
below.
to return to the histogram, and change the Window Settings and the Bin Settings to those shown
Press
ctrl
Press ctrl I to return to the Calculator application, and recalculate the
mean and median.
The mean has decreased to ¼ 246:1, but the median is still 263.
Press
ctrl
J
twice to return to the data, and change the three longest drives to 403:9 m, 415:5 m, and
420:0 m. Press ctrl I
those shown below.
to return to the histogram, and change the Window Settings and the Bin Settings to
Press ctrl I to return to the Calculator application, and recalculate the
mean and median.
The mean has increased to ¼ 259:8, but the median is still 263.
CHAPTER 20 - MEASURES OF CENTRE FROM GROUPED DATA
TI-nspire
To obtain the measures of centre 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
0
1
2
3
4
12
11
3
Press ctrl I 1 to open the Calculator application. Press menu , then
select 6 : 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 .
So, the mean ¼ 1:43, and the median = 1.
CHAPTER 20 - STANDARD DEVIATION
TI-nspire
To find the standard deviation of 3, 7, 6, 8, 11:
Enter the data into List A and name this list data.
Press
ctrl
I
1 : Add Calculator to open the Calculator application,
press menu , then select 6 : Statistics > 1 : Stat Calculations .... > 1 :
One-Variable Statistics.
Press enter to choose 1 list.
Select data from the X1 List drop-box, and
press enter .
So, the standard deviation is ¾X ¼ 2:61 .
CHAPTER 20 - STANDARD DEVIATION FOR GROUPED DATA
TI-nspire
To find the standard deviation of the data
alongside, enter the score values into
List A, and label the list score. Enter
the frequency values into List B, and
label the list freq.
Score
Frequency
1
1
2
2
3
4
4
2
Press ctrl I 1 to open the Calculator application. Press menu , then
select 6 : Statistics > 1 : Stat Calculations > 1 : One-Variable Statistics.
Press enter to choose 1 list. Select score from the X1 List drop-box and
freq from the Frequency List drop-box, then press enter .
So, the standard deviation is approximately 1:10 .
5
1
CHAPTER 21 - CALCULATING r
TI-nspire
To find the correlation coefficient r for the data alongside, enter the
x values into List A and label the list x, then enter the y values into
List B and label the list y.
Press ctrl I 1 : Calculator menu , then select 6 : Statistics > 1 : Stat
Calculations > 3 : Linear Regression (mx+b). Select x from the X List
drop-box and y from the Y List drop-box, then press enter .
So, r ¼ 0:969 .
x
y
1
3
2
3
4
6
5
8
CHAPTER 21 - LEAST SQUARES REGRESSION LINE
TI-nspire
To find the least squares regression line for the data
alongside, enter the x values into List A and label the
list x, then enter the y values into List B and label the
list y.
x
y
0
17:7
Press ctrl I 1 : Calculator menu , then select 6 : Statistics > 1 : Stat
Calculations > 3 : Linear Regression (mx+b). Select x from the X List
drop-box and y from the Y List drop-box, then press enter .
So, the least squares regression line is y ¼ 0:0402x + 18:1 .
50
20:4
100
22:0
150
25:0
200
26:0
250
27:8
CHAPTER 21 - CONSTRUCTING SCATTER DIAGRAMS
TI-nspire
To construct a scatter diagram of the data below:
x
y
40
11
53
15
20
2
65
20
35
4
60
22
85
30
49
16
35
27
76
25
We first enter the x values into List A and label the list x, then enter the
y values into List B and label the list y.
Press ctrl
I
5 : Data & Statistics.
Move the cursor to the bottom of the screen until the “Click or enter to add
variable” box appears. Press enter , then select x.
Move the cursor to the left side of the screen, and select y for the variable
on the vertical axis.
CHAPTER 23 - THE MEAN AND STANDARD DEVIATION OF A BINOMIAL DISTRIBUTION
TI-nspire
Enter the values 0, 1, 2, ...., 30 into List A, and name this list one. Move
the cursor to the second row of List B, and press = menu , then select
4 : Statistics > 2 : Distributions > D : Binomial Pdf ....
Set up the screen as shown, then press enter twice.
This calculates P(X = x) for every value of x from 0 to 30, where
X » B(30, 0:25). Name this list two.
To draw a scatter diagram of the data, press ctrl I 5 to open the Data &
Statistics application. Move the cursor to the bottom of the screen until the
“Click or Enter to add variable” box appears. Press enter , then select one.
Similarly, select the variable two for the vertical axis.
To calculate the descriptive statistics, press ctrl
I 1 to open the Calculator
application. Press menu , then select 6 : Statistics > 1 : Stat Calculations
> 1 : One-Variable Statistics. Press enter to choose 1 list. Select one
from the X1 List drop-box, and two from the Frequency List drop-box, then
press enter .
So, ¹ = 7:5 and ¾ ¼ 2:3717 .
BINOMIAL PROBABILITIES
TI-nspire
To find P(X = 2) for X » B(10, 0:3), press
ctrl
I
1 to
open the Calculator application. Press menu then select
5 : Probability > 5 : Distributions > D : Binomial Pdf ... .
Press 10
tab
0:3
tab
2
tab
enter
. The result is 0:233 .
To find P(X 6 5) for X » B(10, 0:3), press menu from
the Calculator application and select 5 : Probability > 5 :
Distributions > E : Binomial Cdf ... .
Press 10
tab
0:3
tab
0
tab
5
tab
enter
. The result is 0:953 .
TI-Nspire
Calculator Instructions
Texas Instruments
TI-nspire
cyan
magenta
yellow
95
100
50
75
Basic functions
Memory
Lists
Statistics
Mathematical modelling
Probability
Working with functions
25
0
5
95
A
B
C
D
E
F
G
100
50
75
25
0
5
95
100
50
75
25
0
5
95
100
50
75
25
0
5
Contents:
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2
TEXAS INSTRUMENTS TI-NSPIRE
GETTING STARTED
takes you to the home screen, where you can choose which application you wish to use.
Pressing
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
ctrl
or
I
.
Press ctrl I 1 : Add Calculator 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.
A
BASIC FUNCTIONS
GROUPING SYMBOLS (BRACKETS)
(
The TI-nspire 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
)
enter
.
We also use brackets to make sure the calculator understands the expression we are typing in.
For example, to evaluate
2
we type
4+1
If we typed 2
1
¥
4
+
enter
2
¥
4
(
+
1
)
enter
.
the calculator would think we meant
2
+ 1.
4
In general, it is a good idea to place brackets around any complicated expressions which need to be
evaluated separately.
POWER KEYS
3
^
. We type the base first, press the power key, then
enter
.
Numbers can be squared on the TI-nspire using the special key
cyan
magenta
yellow
.
50
75
.
25
0
enter
5
95
x2
100
50
75
25
0
5
95
100
50
75
25
0
5
95
100
50
75
25
0
5
For example, to evaluate 252 we type 25
x2
95
For example, to evaluate 253 we type 25
^
100
The TI-nspire has a power key that looks like
enter the index or exponent.
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TEXAS INSTRUMENTS TI-NSPIRE
3
ROOTS
To enter roots on the TI-nspire we need to use the secondary function
x2
We enter square roots by pressing ctrl
p
For example, to evaluate 36 we press
You can press the right arrow key
p
evaluate 18 + 5 we type ctrl
ctrl
.
.
ctrl
36
x2
enter
.
I
to move the cursor out of the square root sign. For example, to
x2
18
5
+
I
enter
.
p
Higher roots are entered by pressing ctrl ^ , which creates the ¤ ¤ 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.
LOGARITHMS
We can perform operations involving logarithms using the log
function, which is accessed by pressing
10x
ctrl
.
Put the base number in the first entry, and the number you wish to
find the logarithm of in the second entry.
For example, to find log3 11 press
10x
ctrl
3
11
I
enter
.
ROUNDING OFF
You can instruct the TI-nspire to round off values to a fixed number
of decimal places.
For example, to round to 3 decimal places, from the home screen
select 5 : Settings > 2 : Settings > 1 : General . When the
Display Digits drop-box is highlighted, press
H
enter
key to select Fix 3, and press
I
, then use the
.
For most operations, the default setting of Float 6 is recommended.
You can return to the application you were working on by pressing 4 : Current from the home screen.
DECIMAL EXPANSION OF FRACTIONS
, the calculator will simply return the fraction
cyan
magenta
yellow
5
8.
To find the decimal
95
100
50
.
75
enter
25
50
75
25
0
5
95
100
50
75
25
0
5
95
100
50
75
25
0
5
5
expansion of , press 5 ¥ 8 ctrl
8
0
enter
5
8
95
¥
100
If you press 5
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4
TEXAS INSTRUMENTS TI-NSPIRE
INVERSE TRIGONOMETRIC FUNCTIONS
The inverse trigonometric functions sin¡1 , cos¡1 , and tan¡1 are the secondary functions of
cos
, and
tan
respectively. They are accessed by using the secondary function key
³ ´
3
3
For example, if cos x = , then x = cos¡1
.
5
,
.
5
ctrl
To calculate this, press
ctrl
sin
3
cos
¥
5
)
enter
.
SCIENTIFIC NOTATION
Very large and very small numbers can be expressed in scientific
notation, which is in the form a £ 10k where 1 6 a 6 10 and
k is an integer.
To evaluate 23003 , press 2300
scientific notation, press
ctrl
^
3
enter
enter
. To express this in
. The answer displayed is
1:2167e10, which means 1:2167 £ 1010 .
³
´4
3
To express
in scientific notation, press
20 000
)
^
4
ctrl
You can enter values in scientific notation using the
enter
¥
. The answer is 5:0625 £ 10¡16 .
enter
2:6 £ 1014
, press 2:6
13
For example, to evaluate
3
(
20 000
key.
EE
14
EE
¥
13
. The answer is 2 £ 1013 .
B
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
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.
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
enter
.
cyan
magenta
10
enter
yellow
or
95
100
50
50
+
.
95
enter
100
3
75
0
^
5
95
100
50
75
25
0
5
95
100
50
75
25
0
5
cube this value by pressing A
25
We can now add 10 to this value by pressing A
75
(stoI) A
25
var
0
ctrl
5
number then press
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5
TEXAS INSTRUMENTS TI-NSPIRE
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
.
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
£
.
RECALLING PREVIOUS EXPRESSIONS
N
Pressing the
key allows you to recall and edit previously evaluated expressions.
To recall a previous expression, press the
enter
N
key until the desired expression is highlighted, and press
. The expression then appears in the current entry line, where it can be edited.
C
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
Pressing ctrl
editor screen.
4 : Lists & Spreadsheet takes you to the list
I
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
so on until all the data is entered.
enter
5
enter
.... and
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
magenta
yellow
95
100
50
75
to delete the list.
25
0
J
5
95
100
50
75
25
0
5
95
100
50
75
0
cyan
25
to highlight the whole column. Press
5
95
N
100
50
75
25
0
5
To delete a list of data from the list editor screen, move the cursor to the heading of that list, and press
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6
TEXAS INSTRUMENTS TI-NSPIRE
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 second row of List B, and press
+
2
enter
=
data
.
D
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: 5 2 3 3 6 4 5 3 7 5 7 1 8 9 5.
Enter the data into List A and name this list one.
I
ctrl
To obtain the descriptive statistics, press
1 : Add
Calculator to open the Calculator application, press menu , then
select 6 : Statistics > 1 : Stat Calculations ... > 1 : OneVariable 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
cyan
magenta
yellow
95
100
50
75
25
0
5
95
100
50
75
25
0
5
95
100
50
75
25
0
5
95
100
50
75
25
0
5
ctrl
I 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.
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TEXAS INSTRUMENTS TI-NSPIRE
7
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
list of data.
J
command to return to the page containing the
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.
To view boxplots of both data sets, press menu , then select 2 :
Plot Properties > 5 : Add X Variable. Select two from the box.
STATISTICS FROM GROUPED DATA
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.
Press
menu
I
ctrl
1
Data
Frequency
2
3
4
5
3
4
8
5
to open the Calculator application.
Press
, then select 6 : 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
cyan
magenta
yellow
95
100
50
75
25
0
5
95
100
50
75
.
25
0
5
95
enter
100
50
75
25
0
5
95
100
50
75
25
0
5
drop-box, then press
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8
TEXAS INSTRUMENTS TI-NSPIRE
E
MATHEMATICAL MODELLING
Given a set of bivariate data, we can use our calculator to draw a scatter diagram of the data, find
Pearson’s correlation coefficient r, and find the line of best fit for the data.
Consider the bivariate data:
x
y
1
5
2
8
3
10
4
13
5
16
6
18
7
20
We first 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.
DRAWING A SCATTER DIAGRAM
I 5 : Data
ctrl
To produce a scatter diagram for the data, press
& Statistics.
Move the cursor to the bottom of the screen until the “Click or
enter to add variable” box appears. Press enter , then select one.
Move the cursor to the left side of the screen, and select two for
the variable on the vertical axis.
FINDING r AND THE LINE OF BEST FIT
We will now find r and the line of best fit.
Press ctrl I 1 : Calculator menu , then select 6 : 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 r ¼ 0:998, and the line of best fit is
y ¼ 2:54x + 2:71 .
To graph the line of best fit, press
ctrl
J
to return to the scatter
cyan
magenta
yellow
95
100
50
75
25
0
5
95
100
50
75
25
0
5
95
100
50
75
25
0
5
95
100
50
75
25
0
5
diagram, press menu , then select 4 : Analyze > 6 : Regression
> 1 : Show Linear (mx+b). The line of best fit will appear.
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TEXAS INSTRUMENTS TI-NSPIRE
F
9
PROBABILITY
BINOMIAL PROBABILITIES
To find P(X = 2) for X » B(10, 0:3), press
I
ctrl
1 to
open the Calculator application. Press menu then select
5 : Probability > 5 : Distributions > D : Binomial Pdf ... .
Press 10
0:3
tab
tab
2
tab
enter
. The result is 0:233 .
To find P(X 6 5) for X » B(10, 0:3), press menu from
the Calculator application and select 5 : Probability > 5 :
Distributions > E : Binomial Cdf ... .
Press 10
0:3
tab
tab
0
tab
5
tab
enter
. The result is 0:953 .
NORMAL PROBABILITIES
Suppose X is normally distributed with mean 10 and standard
deviation 2.
To find P(8 6 X 6 11), press menu from the Calculator
application and select
5 : Probability > 5 : Distributions > 2 : Normal Cdf ... .
Press 8
tab
11
tab
10
tab
2
tab
enter
. The result is 0:533 .
To find P(X > 7), press menu from the Calculator application
and select
5 : Probability > 5 : Distributions > 2 : Normal Cdf ... .
cyan
magenta
yellow
95
100
50
75
25
0
5
95
100
50
75
25
0
5
95
100
50
75
25
0
5
95
100
50
75
25
0
5
Set up the screen as shown, and select OK. The result is 0:933 .
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10
TEXAS INSTRUMENTS TI-NSPIRE
To find a such that P(X 6 a) = 0:479, press menu from the
Calculator application and select
5 : Probability > 5 : Distributions > 3 : Inverse Normal ... .
Press 0:479
tab
10
tab
2
tab
. The solution is a ¼ 9:89 .
enter
G
WORKING WITH FUNCTIONS
GRAPHING FUNCTIONS
Pressing ctrl I 2 : Graphs opens the Graphing application,
where you can graph functions.
To graph the function y = x2 ¡ 3x ¡ 2, press
X
2
¡
enter
X
x2
¡
3
.
You can delete the functions you have graphed by pressing
menu
, then selecting 1 : Actions > 5 : Delete all.
ctrl
To view a table of values for the function, press
T .
The page splits into two, with the graph on one side and the table
of values on the other side.
You can delete the table by pressing ctrl
5 : Page Layout > 5 : Delete Application.
, then selecting
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.
To adjust the viewing window, press
are:
menu
then select 4 : Window/Zoom . The most useful options
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
20
6y6 .
3
3
cyan
magenta
yellow
95
100
50
75
25
0
5
95
100
50
75
25
0
5
95
100
50
75
25
0
5
95
100
50
75
25
0
5
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.
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TEXAS INSTRUMENTS TI-NSPIRE
Pressing
Press
11
G removes the function entry line, allowing you to use the full screen to view the graph.
ctrl
G again to bring the function entry line back.
ctrl
FINDING POINTS OF INTERSECTION
To find the intersection point of y = 11 ¡ 3x and y =
store y = 11 ¡ 3x into f1 (x) and y =
Press
menu
12 ¡ x
2
12 ¡ x
,
2
into f2 (x).
, then select 6 : Analyze Graph > 4 : Intersection.
Move the cursor to the left of the intersection point and press
enter
, then move the cursor to the other side and press
The intersection point (2, 5) is displayed.
enter
.
FINDING x-INTERCEPTS
To find the x-intercepts of f (x) = x3 ¡ 3x2 + x + 1, store
x3 ¡ 3x2 + x + 1 into f1 (x).
To find the x-intercepts, press menu , then select 6 : Analyze
Graph > 1 : Zero. Place the lower and upper bounds either side
of the first x-intercept.
The first x-intercept x ¼ ¡0:414 is given. Repeat this process to
find the remaining x-intercepts 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).
From the graph, the vertex is clearly a maximum, so press
menu
, then select 6 : Analyze Graph > 3 : Maximum.
cyan
magenta
yellow
95
100
50
75
25
0
5
95
100
50
75
25
0
5
95
100
50
75
25
0
5
95
100
50
75
25
0
5
Place the lower and upper bounds either side of the vertex. The
vertex is at (1, 4).
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12
TEXAS INSTRUMENTS TI-NSPIRE
THE TANGENT TO A FUNCTION
To find the gradient of the tangent to y = x2 when x = 1, we
first draw the graph of y = x2 . Press
Analyze Graph > 5 : dy/dx. Press
has a gradient of 2 at this point.
(
, then select 6 :
menu
1
enter
. The tangent
Press menu , then select 7 : Points & Lines > 7 : Tangent.
Move the cursor towards the point (1, 1) until the phrase point on
appears, then press
enter
to draw the tangent.
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 7 : Coordinates and
Equations. The tangent has equation y = 2x ¡ 1.
DEFINITE INTEGRALS
To calculate
menu
R3
1
x2 dx, we first draw a graph of y = x2 . Press
, then select 6 : Analyze Graph > 6 : Integral. Press
1 enter to specify the lower bound, then
the upper bound.
R3
So, 1 x2 dx = 8 23 .
3
(
enter
(
to specify
cyan
magenta
yellow
95
100
50
75
25
0
5
95
100
50
75
25
0
5
95
100
50
75
25
0
5
95
100
50
75
25
0
5
Alternatively, you can press menu from the Calculator application,
select 4 : Calculus > 2 : Numerical Integral, then set up the
screen as shown.
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LOGARITHMS
TI-nspire
We can perform operations involving logarithms using the log
function, which is accessed by pressing
ctrl
10x
.
Put the base number in the first entry, and the number you wish to
find the logarithm of in the second entry.
For example, to find log3 11 press
ctrl
10x
3
I
11
enter
.
NORMAL PROBABILITIES
TI-nspire
Suppose X is normally distributed with mean 10 and standard
deviation 2.
To find P(8 6 X 6 11), press menu from the Calculator
application and select
5 : Probability > 5 : Distributions > 2 : Normal Cdf ... .
Press 8
tab
11
tab
10
tab
2
tab
enter
. The result is 0:533 .
To find P(X > 7), press menu from the Calculator application
and select
5 : Probability > 5 : Distributions > 2 : Normal Cdf ... .
Set up the screen as shown, and select OK. The result is 0:933 .
To find a such that P(X 6 a) = 0:479, press menu from the
Calculator application and select
5 : Probability > 5 : Distributions > 3 : Inverse Normal ... .
Press 0:479
tab
10
tab
2
tab
enter
. The solution is a ¼ 9:89 .
NORMAL PROBABILITIES
TI-nspire
Suppose X is normally distributed with mean 10 and standard
deviation 2.
To find P(8 6 X 6 11), press menu from the Calculator
application and select
5 : Probability > 5 : Distributions > 2 : Normal Cdf ... .
Press 8
tab
11
tab
10
tab
2
tab
enter
. The result is 0:533 .
To find P(X > 7), press menu from the Calculator application
and select
5 : Probability > 5 : Distributions > 2 : Normal Cdf ... .
Set up the screen as shown, and select OK. The result is 0:933 .
To find a such that P(X 6 a) = 0:479, press menu from the
Calculator application and select
5 : Probability > 5 : Distributions > 3 : Inverse Normal ... .
Press 0:479
tab
10
tab
2
tab
enter
. The solution is a ¼ 9:89 .
POWER KEYS
TI-nspire
The TI-nspire has a power key that looks like
enter the index or exponent.
For example, to evaluate 253 we type 25
^
^
3
. We type the base first, press the power key, then
enter
.
Numbers can be squared on the TI-nspire using the special key
For example, to evaluate 252 we type 25
x2
enter
.
x2
.
THE TANGENT TO A FUNCTION
TI-nspire
To find the gradient of the tangent to y = x2 when x = 1, we
first draw the graph of y = x2 . Press
Analyze Graph > 5 : dy/dx. Press
has a gradient of 2 at this point.
(
menu
1
, then select 6 :
enter
. The tangent
Press menu , then select 7 : Points & Lines > 7 : Tangent.
Move the cursor towards the point (1, 1) until the phrase point on
appears, then press
enter
to draw the tangent.
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 7 : Coordinates and
Equations. The tangent has equation y = 2x ¡ 1.
THE TANGENT TO A FUNCTION
TI-nspire
To find the gradient of the tangent to y = x2 when x = 1, we
first draw the graph of y = x2 . Press
Analyze Graph > 5 : dy/dx. Press
has a gradient of 2 at this point.
(
menu
1
, then select 6 :
enter
. The tangent
Press menu , then select 7 : Points & Lines > 7 : Tangent.
Move the cursor towards the point (1, 1) until the phrase point on
appears, then press
enter
to draw the tangent.
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 7 : Coordinates and
Equations. The tangent has equation y = 2x ¡ 1.
THE TANGENT TO A FUNCTION
TI-nspire
To find the gradient of the tangent to y = x2 when x = 1, we
first draw the graph of y = x2 . Press
Analyze Graph > 5 : dy/dx. Press
has a gradient of 2 at this point.
(
menu
1
, then select 6 :
enter
. The tangent
Press menu , then select 7 : Points & Lines > 7 : Tangent.
Move the cursor towards the point (1, 1) until the phrase point on
appears, then press
enter
to draw the tangent.
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 7 : Coordinates and
Equations. The tangent has equation y = 2x ¡ 1.