TI- Nspire Testing
Instructions
Property of Joseph Perlman
Rye Neck UFSD
Mathematics Department
Table of Contents
How to Nsolve
How to Check Compositions of Functions
How to Verify Compositions of Functions
How to Check Factoring
How to Use Graphs to Backward Factor
How to do Recursive Sequences
How to do Bernoulli Trials
How to do Arithmetic Sequences
How to Store Variables to Check Multiple Choice Questions
How to find Domain and Range
How to check Arithmetic Expressions
How to check Sum, Difference, Product Quotient of Radicals
How to check Expressions
How to find Mean, Quartiles and Standard Deviations
Converting Radians to DMS
Converting Degrees to Radians in terms of Pi
Regressions
Graphing Trig Functions
Determining What Values are Undefined for Trig Functions
Graphing Inverse Trig Functions
Graphing Systems of Equations
Add Gridlines
Plotting Points
Finding the Length of a Segment
Finding the Slope of a Segment
Finding the Perimeter of a Figure
Finding the Area of a Figure
Finding the Midpoint of a Segment
Graphing Equations of Lines through Points
Graphing Equations of Lines through a Point and Parallel to a Line
Graphing Equations of Lines through a Point and Perpendicular to a Line
Graphing Equations of Perpendicular Bisectors
Graphing Equations of Lines in Standard Form
Graphing Circles in Center-Radius Form
Graphing Circles in Standard Form
Systems of Equations Involving Circles
Reflections
Rotations
Transformations
Finding Zeros on a Graph
Graphing Inequalities
Graphing Linear Equations that are NOT in the from y=mx+b
Solving Exponential Equations
Property of Joseph Perlman
Rye Neck UFSD
Mathematics Department
Constructing Scatterplots
Box and Whisker Plots
Solving Quadratics
Property of Joseph Perlman
Rye Neck UFSD
Mathematics Department
How to N-Solve:
Example:
Menu, Algebra, Numerical Solve…. Enter the equation and finish with
x =10. Repeat the equation and change to x = -10.
Example:
Menu, algebra, numerical solves and
enter the equation. When dealing
with a trig equation, you must test
for all values of x from 45 degrees to
360 degrees going by 45.
(i.e.: 45, 90, 135, 180, 225, 270, 315,
360
Property of Joseph Perlman
Rye Neck UFSD
Mathematics Department
How to check compositions of functions:
Example:
Find
Go to a graph page and enter f(x) into
F1 and hit enter. Enter g(x) into F2
and hit enter. Open a calculator page
using CTRL DOC and type the
composition in……F2(F1(-2)) and hit
enter.
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Rye Neck UFSD
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Verifying a Rule of a Composition of Functions is correct.
Go to a graph page and enter f(x) into
F1 and hit enter. Enter g(x) into F2
and hit enter. Open a calculator page
using CTRL DOC and type the
composition in……F1(F2(x))=the
expression you came up with and hit
enter. If what you did is correct the
calculator will say true.
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Rye Neck UFSD
Mathematics Department
How to check factoring
Example
1)Store any # as n
2) Enter expression and use = button
3) Enter each multiple choice to determine which is true
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Rye Neck UFSD
Mathematics Department
How to use Graphs to Backward Factor
Example:
Factor
1) On graphs page – enter expression
3. Menu>Analyze>Zero
2) Hit Graph
4. Click to the left of your x-intercept
Drag across point and repeat for
Each x intercept
***********************
X = -3 x = 3 x = 1
These are your zeros – to find the factors bring each set back to the “x” side.
(x+3)(x-3)(x-1) are the factors.
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Rye Neck UFSD
Mathematics Department
How to do Recursive Sequence:
Example: Find the first 5 terms of the recursive sequence defined by
Open a Lists and Spreadsheet page, click into the “forbidden grey area” and select
Menu, Data, Generate Sequence. Type the recursive equation in under Formula.
(**Note instead of the letter and subscript, we use U(n-1)). Enter Formula, Initial
Term and nMax. Skip all other tabs.
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Rye Neck UFSD
Mathematics Department
How to do Probability “Bernoulli Trials”
Example
1) Menu > Prob > distribution > Binomial Pdf
2) Enter n, p, r
****If the problem asks for at least or at most***** Use binomialCDF (Choice E)
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Rye Neck UFSD
Mathematics Department
How to do arithmetic sequences in your calculator
Example: Find the 50th term of the sequence 5,9,13,17…
1) Open a Lists and Spreadsheet page 2) Enter data in table
3) Menu, Stats, Stat Calc, Linear Regression* equation is
*If given a geometric sequence, use exponential regression*
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***Geometric sequence with alternating signs enter without negatives and when
writing the equation, negate the base.***
Storing Variables to check multiple choice
Example:
1) Store any # for x and y
2) Enter the expression, use the = and set
equal to the multiple choice answers.
3. If you get this error, look at slide (2) 4) Once corrected, the calculator will
You need to indicate multiplication
indicate true or false.
Between the x and y in the Denominator
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Rye Neck UFSD
Mathematics Department
Finding domain and range using graphs
Example:
1) Enter function in graph line
2) Analyze graph to find x values
3. Go to table (ctrl T) and determine where the end points of the domain are based
on the y-values. Any values indicated by #ERR are equivalent to undefined.
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Rye Neck UFSD
Mathematics Department
How to check arithmetic expressions using the check feature
Example:
1) Store a # for x
2) Input the given question
3. Type in multiple choices and reveal which is true.
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Rye Neck UFSD
Mathematics Department
Find the sum, difference, product or quotient of radicals
Example:
1) Store values for variables
2) Enter question and use check feature
3. Error means you didn’t use the
4. Included symbol – results in true
multiplication symbol as needed between
variables and radicals
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Checking Expressions
Example:
1) Store a number for variable
2) Enter expressions
Example 2**
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Finding Mean, Quartiles, Standard Deviation
1) Enter data in spreadsheet
3. Number of Lists is always 1
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2) Menu>Stat>Stat Calc>One Var
4. Input your x list
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Interquartile Range is Q3 – Q1.
Converting Radians to Degrees Minutes Seconds
Example
1. Enter 3 Radians (r is under the )
2. Ctrl Book and select arrow from line 1
3 Command the conversion by typing DMS.
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Rye Neck UFSD
Mathematics Department
Converting degrees to radians
1) Enter the degree to be converted and include the degree symbol
2) Control Book to select the convert symbol
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3) Type the letters RAD
4) Bring down answer, remove the r
and divide by the pi symbol.
5 Approximate to fraction and put Pi
in numerator.
Regressions
1) Enter data in spreadsheet
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2) Menu>Stat>Stat calc>Regression
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3 Insert x list, y list and Save to F1
4) Be sure to look at cell 2 for how to
write the equation
Graphing Trig Functions
Example: Graph y =2sin3x in the interval [0,360]
1. Open graphs page
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2. Enter function to be graphed
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3. The graph may originally look linear
4. Go to menu > settings
5. Change graph angle to degrees.
6. Menu > Window > Zoom Trig
(This may be accessed through home 5,2,2 if older OS)
7. Your graph will show in [-360,360]
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8. Menu > Window > Window Settings
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9. Change window – set x-scale to the
Period divided by 4
Determining what values are undefined for a trig function
Example: For what values of x is f(x) = tan(x) undefined?
Property of Joseph Perlman
Rye Neck UFSD
Mathematics Department
1 Enter function to be graphed
2. Graph will look similar to a line
3. Menu > Window > Zoom Trig
4. Graph will show from [-360, 360]
5. Control T to show table of values
6. Menu > Table > Edit Table
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Mathematics Department
7. Change table step to Period divided by 4
For specific x values, change independent to ask – then input x values ask requested
Property of Joseph Perlman
Rye Neck UFSD
Mathematics Department
Graphing Inverse Trig Functions
1. Enter a graphs
2. Insert inverse sin(x)
3 More often than not, it will look like this
4. Go to settings for graphs and
change to radians
5 Your inverse graph should display
Property of Joseph Perlman
Rye Neck UFSD
Mathematics Department
Graphing Systems of Equations
Example: Solve the system of equations
1. Add Calculator Page
2. Menu, Algebra, Solve Systems
of Linear Equations
3. Specify the number of equations and
your variables
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4. Enter the two equations
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5. Enter the two equations, the solution
set is {5, 7} where 5 is the x-value and
7 is the y-value
Add Gridlines
1. Add a graphs page
2. View, Grid, Lined Grid
3. A graph with gridlines should appear.
Property of Joseph Perlman
Rye Neck UFSD
Mathematics Department
Plotting Points
Example: Plot the point (-2, 3)
1. Add gridlines to a graph.
2. Menu, Geometry, Points & Lines
4. Open parenthesis, type “-2”, enter,
type “3”, enter
3. Point
5. The point (-2, 3) will be plotted.
Property of Joseph Perlman
Rye Neck UFSD
Mathematics Department
Finding the Length
Example: Find the length of segment AB if A (2, 3) and B (-2, 1).
1. Open a graphs page, add a gridline,
Plot point A (2, 3) and B (-2, 1).
2. Geometry, Points & Lines
3. Segment
4. Click on the first point then click
on the second point.
5. A segment will be plotted.
6. Geometry, Measurement, Length
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Rye Neck UFSD
Mathematics Department
7. Double click on the segment. The
length of the line will appear.
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Rye Neck UFSD
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Finding the Slope of a Segment
Example: Find the slope of segment AB if A (3, 4) and B (-3, 0).
1. Open a new graphs page, add a gridline,
plot point A (3, 4) and B (-3, 0).
2. Geometry, Points & Lines
3. Segment
5. The segment will be plotted.
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4. Click on the first point,
click on the second point
6. Menu, Geometry, Measurement, Slope
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7. Double click on the segment and the
measurement of the slope will appear.
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Finding the Perimeter of a Figure
Example: Find the perimeter of an “L shaped garden” whose vertices are as follows: (0, 0),
(10, 0), (10, 2), (2, 2), (2, 6), and (0, 6).
1. Add a new graphs page and
add gridlines.
2. Plot all six points.
2. Menu, Geometry, Shapes
3. Polygon
4. Click on each point in the order that it is
is listed. Double click on the last point.
5. The “L-Shaped Garden” will be
constructed.
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Mathematics Department
6. Menu, Geometry, Measurement, Length
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7. Double click on the figure. The
measurement of the perimeter
will appear.
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Finding the Area of a Figure:
Example: Find the area of a figure whose vertices are A (-4, -2), B (-5, 4), C (5, 5), and D (5, 6)
1. Add a graphs page, add gridlines.
2. Plot points A, B, C, and D.
3. Menu, Geometry, Shapes
4. Polygon
5. Click on each point in the order that it is listed.
Double click on the last point
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6. The figure will appear.
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7. Menu, Geometry Measurement, Area,
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8. Double click on the figure and the
area will appear.
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Finding the Midpoint of a Segment
Example: Find the midpoint of segment AB is A (2, 0) and B (-3, 5)
1. Add a new graphs page, add gridlines
2. Menu, Geometry, Points & Lines
3. Segment
4. Click on the first point, click on the
second point.
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2. Plot the two points A and B
5. The segment AB will appear.
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6. Menu, Geometry, Construction
7. Midpoint
8. Double click on the line and the midpoint
will be plotted.
9. Menu, Actions, Coordinates and Equations
10. Double click on the midpoint point and
its coordinates will appear.
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Rye Neck UFSD
Mathematics Department
Graphing Equations of Lines through Points
Example: Find the equation of a line that passes through the points (-2, 5) and (1, 3).
1. Open a new graphs page, add
gridlines to the graph.
3. Point
5. Menu, Geometry, Points & Lines
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2. Menu, Geometry, Points & Lines
4. Plot the two points
6. Line
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7. Click on the first point, click on the
second point.
8. The line will appear.
9. Menu, Actions, Coordinates & Equations
10. Double click on the line and the equation
will appear.
Property of Joseph Perlman
Rye Neck UFSD
Mathematics Department
Graphing Equations of Lines through a Point and Parallel to a Line
Example: What is the equation of line parallel to y = 3x + 5 and through the point (1, 3)
1. Open a new graphs page and add
gridlines to the graph.
2. Type the equation of the given line.
3 .After the equation is typed in, click enter
and the given line will appear.
5. Menu, Geometry, Points & Lines
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4. Plot the point (1, 3)
6. Line
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7. Draw a line over the line that you
Already plotted.
8. Menu, Settings, Construction
9. Parallel
11. Click on the point
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10. Click on the line
12. A line parallel to the original line and
through the given point will appear.
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13. Menu, Actions, Coordinates & Equations
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14. Click on the line and the equation
will appear.
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Graphing Equations of Lines Through a Point and Perpendicular to a Line
Example: Find the equation of the line that passes through the point A (−1, 2) and is perpendicular to the
line y=2x−3
1. Add a new graphs page and add
gridlines to the graph.
2. Type the given equation
3. Click enter and a line will appear.
5. Menu, Geometry, Points & Lines
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4. Plot the given point (-1, 2)
6. Line
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7. Draw a line over the existing line.
8. Menu Geometry, Construction,
9. Perpendicular
10. Click on the line
11. Click on the point
12. A perpendicular line through the
given point will appear.
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Rye Neck UFSD
Mathematics Department
13. Menu, Actions, Coordinates and Equations
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14. Click on the line and the equation
will appear.
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Graphing Equations of Perpendicular Bisectors
Example: Given points A (-4, 2) and B (3, 5), find the perpendicular bisector of line AB.
1. Open a new graphs page and
add gridlines to the graph.
2. Plot point A and B
3. Menu, Geometry, Points & Lines
4. Line
4. Click on the first point, click on the
second point. Line AB will appear.
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5. Menu, Geometry, Construction,
perpendicular bisector.
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6. Click on the first point, click on the second
point
8. Menu, Actions, Coordinates and Equations
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7. The perpendicular bisector will appear.
9. Click on the perpendicular bisector and
the equation will appear.
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Graphing Equations of Lines in Standard Form
Graph the equation of the line 2x+3y=1
1. Open a new graphs page and add
gridlines.
3. Line Standard
4. This screen will appear.
5. Type in the appropriate coefficients.
Click enter.
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2. Menu, Graph Entry/Edit, Equation
line
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6. The line 2x+3y= 1 will appear.
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Graphing Circles in Center-Radius Form
Example: Graph the circle whose equation is
1. Add a new graphs page, add gridlines
to the graph.
2.
+
2. Menu, Graph Entry/Edit, Equation, Circle
Center Form
radius equation will appear.
4. Type in the appropriate numbers.
Click enter.
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=25E
3. The center-
5. The circle will appear
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Graphing Circles in Standard Form
Example: Graph the circle whose equation is
+
+10x -2y-10=0
1. Open a new graphs page and add gridlines.
3. Standard Form
4. This screen will appear.
5. Type in the coefficients. Click enter.
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2. Menu, Graph Entry/Edit, Equation,
Circle
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6. The circle will appear.
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Systems of Equations Involving Circles
Example: Find the point of intersection between the parabola
1. Add a new graphs page and add
gridlines to the graph.
3. Standard Form
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+3 and the circle
+
= 16
2. Menu, Graph Entry/Edit , Equation,
Parabola
4. Type in the proper coefficients . Then
click enter.
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5. The graph of the parabola will appear.
6. Graph the circle (see instructions on how
to graph a circle above.)
7. Menu, Analyze Graph, Intersection
8. Create a box around point of intersection
and the coordinate where the two graphs
intersect will appear.
9. Repeat steps 7 and 8 to find the second
point of intersection.
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Reflections
Example: Given points A(-2, 3), B (1, 5), and C (4, 4), reflect triangle ABC over the x-axis
1. Open a new graphs page and add gridlines
to the graph.
2. Plot points A, B, and C. (See how to
plot a point instructions above.
3. Menu, Geometry, Shapes
4. Triangle
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5. Click on all three points. Double click on the
last point.
6. The triangle will appear.
7. Menu, Geometry, Reflection, Transformation,
Reflection
9. Click on the line of reflection, in this case
the x-axis.
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8. Click on triangle
10. The reflection, A’B’C’ will appear.
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Rotations
Example: Rotate the triangle A (2, 1), B (5, 4) and C (5, 5) 90 counterclockwise about the
origin.
1. Open a new graphs page and add
gridlines to the graph.
2. Plot points A, B, and C. (See instructions
above on how to plot points.)
3. Menu, Geometry, Shapes
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4. Triangle
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5. Click on each point. Double click on the
last point.
6. The triangle will appear.
7. Menu, Geometry, Transformation, Rotation
8. Click on the figure.
9. Click on the origin.
10. Type in the degree of rotation, Click
Enter
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11. The rotated figure will appear.
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Transformation
Example: Transform the triangle whose vertices are A (-2, 3), B (1, 0), and C (3, 2) along the
vector
.
1. Open a new graphs page and add
gridlines to the graph.
3. Menu, Geometry, Shapes
4. Triangle
5. Click on all three points. Double click on
the last point.
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2. Plot points A, B, and C. (See instructions
above on how to plot points)
6. The triangle will appear.
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Finding Zeros on a Graph
Example: Find the roots of the equation
-2x-2=0
1. Open a new graphs page and add
gridlines.
2. Menu, Graph Entry/Edit, Equation
Parabola
3. Type in the coefficients. Click enter.
4. The graph of the parabola will appear.
5. Menu, Analyze Graph, Zero
6. Click to the left of the first zero (where
the parabola intersects the x-axis)
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7. Click to the right of the first zero.
8. The coordinates of the first root will
appear.
9. Repeat steps 5, 6, and 7 for the second zero
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9. The coordinates for the second root will
appear. The roots for this equation are
(-.732051, 0) and (2.73205, 0)
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Graphing Linear Inequalities
Example: Graph y 2x +1
1. Open a new graphs page and
add gridlines.
2. Menu, Graph Entry/Edit, Function
3. This screen will appear. Click the “del” button
4. This screen will appear. Click on “5
5. This screen will appear.
6. Type in the inequality. Click enter
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”
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7. The graphed inequality will appear.
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Graphing Inequalities that are NOT in the form y=mx+b
Example: Graph the equation of the line 3x+y= -2
1. Open a new graphs page and add
gridlines.
3. Line Standard
2. Menu, Graph Entry/Edit, Equation
line
4. Type in the proper coefficients.
Click enter.
6. The graphed line will appear.
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Solving Exponential Equations
Example:
=
1. On, add calculators page
2. Menu, Algebra, Numerical Solve
3. Type in the equation then add “,x=10”
4. Repeat but type “x= -10” at the
in the parenthesis. Click enter. A
end. Click enter. A value for x
value for x will appear.
will appear.
Constructing Scatterplots
Example: For 10 days, Romero kept a record of the number of hours he spent listening to
music. The information is shown in the table below. Which scatter plot shows Romero’s
data graphically?
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1. Add a Lists & Spreadsheet page
2. This page will appear.
3. Type in the data. The independent
variables go in the first column, the
dependent variables go in the second
column.
5. Ctrl, doc, Add Data & Statistics
7. Click “click to add variable” and
label your axis. Repeat for the y-axis.
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4. Be sure to label both columns.
6. This screen will appear.
8. This scatterplot represents the
solution.
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Box and Whisker Plots
Example: Construct a box and whisker plot for the following math test scores: 80, 75, 90, 95, 65,
65, 80, 85, 70, 100
1. Add Lists & Spreasheet
2. Type in the data in the first column.
Be sure to label the column.
3. Ctrl, doc, Add Data & Statistics
5. A screen similar to this will appear.
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4. Click on/ label the x-axis.
6. Menu, Plot Type, Box Plot
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7. A box and whiskers plot will appear.
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Solving Quadratics
Example: Find the roots of the equation 3
1. Add a calculator page.
2. Menu, Algebra, Polynomial Tools
3. Find Roots of Polynomial
4. Type in the degree of the polynomial.
Click OK.
5. Type in the coefficients. Click OK
6. This screen will appear. Click enter
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7. The roots of the quadratic equation
will appear.
Standard Form
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