TI- Nspire Testing Instructions

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1 TI- Nspire Testing Instructions

2 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

3 Constructing Scatterplots Box and Whisker Plots Solving Quadratics

4 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

5 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.

6 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.

7 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

8 How to use Graphs to Backward Factor Example: Factor 1) On graphs page enter expression 2) Hit Graph 3. Menu>Analyze>Zero 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.

9 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.

10 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)

11 How to do arithmetic sequences in your calculator Example: Find the 50 th 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*

12 ***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

13 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.

14 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.

15 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

16 Checking Expressions Example: 1) Store a number for variable 2) Enter expressions Example 2**

17 Finding Mean, Quartiles, Standard Deviation 1) Enter data in spreadsheet 2) Menu>Stat>Stat Calc>One Var 3. Number of Lists is always 1 4. Input your x list

18 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.

19 Converting degrees to radians 1) Enter the degree to be converted and include the degree symbol 2) Control Book to select the convert symbol

20 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 2) Menu>Stat>Stat calc>regression

21 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 2. Enter function to be graphed

22 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] 8. Menu > Window > Window Settings

23 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?

24 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

25 7. Change table step to Period divided by 4 For specific x values, change independent to ask then input x values ask requested

26 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

27 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 4. Enter the two equations your variables

28 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.

29 Plotting Points Example: Plot the point (-2, 3) 1. Add gridlines to a graph. 2. Menu, Geometry, Points & Lines 3. Point 4. Open parenthesis, type -2, enter, type 3, enter 5. The point (-2, 3) will be plotted.

30 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, 2. Geometry, Points & Lines Plot point A (2, 3) and B (-2, 1). 3. Segment 4. Click on the first point then click on the second point. 5. A segment will be plotted. 6. Geometry, Measurement, Length

31 7. Double click on the segment. The length of the line will appear.

32 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, 2. Geometry, Points & Lines plot point A (3, 4) and B (-3, 0). 3. Segment 4. Click on the first point, click on the second point 5. The segment will be plotted. 6. Menu, Geometry, Measurement, Slope

33 7. Double click on the segment and the measurement of the slope will appear.

34 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 2. Plot all six points. add gridlines. 2. Menu, Geometry, Shapes 3. Polygon 4. Click on each point in the order that it is 5. The L-Shaped Garden will be is listed. Double click on the last point. constructed.

35 6. Menu, Geometry, Measurement, Length 7. Double click on the figure. The measurement of the perimeter will appear.

36 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. 6. The figure will appear. Double click on the last point

37 7. Menu, Geometry Measurement, Area, 8. Double click on the figure and the area will appear.

38 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. Plot the two points A and B 2. Menu, Geometry, Points & Lines 3. Segment 4. Click on the first point, click on the 5. The segment AB will appear. second point.

39 6. Menu, Geometry, Construction 7. Midpoint 8. Double click on the line and the midpoint 9. Menu, Actions, Coordinates and Equations will be plotted. 10. Double click on the midpoint point and its coordinates will appear.

40 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 2. Menu, Geometry, Points & Lines gridlines to the graph. 3. Point 4. Plot the two points 5. Menu, Geometry, Points & Lines 6. Line

41 7. Click on the first point, click on the 8. The line will appear. second point. 9. Menu, Actions, Coordinates & Equations 10. Double click on the line and the equation will appear.

42 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 2. Type the equation of the given line. gridlines to the graph. 3.After the equation is typed in, click enter 4. Plot the point (1, 3) and the given line will appear. 5. Menu, Geometry, Points & Lines 6. Line

43 7. Draw a line over the line that you 8. Menu, Settings, Construction Already plotted. 9. Parallel 10. Click on the line 11. Click on the point 12. A line parallel to the original line and through the given point will appear.

44 13. Menu, Actions, Coordinates & Equations 14. Click on the line and the equation will appear.

45 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 2. Type the given equation gridlines to the graph. 3. Click enter and a line will appear. 4. Plot the given point (-1, 2) 5. Menu, Geometry, Points & Lines 6. Line

46 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.

47 13. Menu, Actions, Coordinates and Equations 14. Click on the line and the equation will appear.

48 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 2. Plot point A and B add gridlines to the graph. 3. Menu, Geometry, Points & Lines 4. Line 4. Click on the first point, click on the 5. Menu, Geometry, Construction, second point. Line AB will appear. perpendicular bisector.

49 6. Click on the first point, click on the second 7. The perpendicular bisector will appear. point 8. Menu, Actions, Coordinates and Equations 9. Click on the perpendicular bisector and the equation will appear.

50 Graphing Equations of Lines in Standard Form Graph the equation of the line 2x+3y=1 1. Open a new graphs page and add 2. Menu, Graph Entry/Edit, Equation gridlines. line 3. Line Standard 4. This screen will appear. 5. Type in the appropriate coefficients. 6. The line 2x+3y= 1 will appear. Click enter.

51 Graphing Circles in Center-Radius Form Example: Graph the circle whose equation is + =25E 1. Add a new graphs page, add gridlines 2. Menu, Graph Entry/Edit, Equation, Circle to the graph. 2. Center Form 3. The centerradius equation will appear. 4. Type in the appropriate numbers. 5. The circle will appear Click enter.

52 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. 2. Menu, Graph Entry/Edit, Equation, Circle 3. Standard Form 4. This screen will appear. 5. Type in the coefficients. Click enter. 6. The circle will appear.

53 Systems of Equations Involving Circles Example: Find the point of intersection between the parabola +3 and the circle + = Add a new graphs page and add 2. Menu, Graph Entry/Edit, Equation, gridlines to the graph. Parabola 3. Standard Form 4. Type in the proper coefficients. Then click enter.

54 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.

55 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 2. Plot points A, B, and C. (See how to to the graph. plot a point instructions above. 3. Menu, Geometry, Shapes 4. Triangle

56 5. Click on all three points. Double click on the 6. The triangle will appear. last point. 7. Menu, Geometry, Reflection, Transformation, 8. Click on triangle Reflection 9. Click on the line of reflection, in this case 10. The reflection, A B C will appear. the x-axis.

57 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 2. Plot points A, B, and C. (See instructions gridlines to the graph. above on how to plot points.) 3. Menu, Geometry, Shapes 4. Triangle

58 5. Click on each point. Double click on the 6. The triangle will appear. last point. 7. Menu, Geometry, Transformation, Rotation 8. Click on the figure. 9. Click on the origin. 10. Type in the degree of rotation, Click Enter

59 11. The rotated figure will appear.

60 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 2. Plot points A, B, and C. (See instructions gridlines to the graph. above on how to plot points) 3. Menu, Geometry, Shapes 4. Triangle 5. Click on all three points. Double click on 6. The triangle will appear. the last point.

61 Finding Zeros on a Graph Example: Find the roots of the equation -2x-2=0 1. Open a new graphs page and add 2. Menu, Graph Entry/Edit, Equation gridlines. 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)

62 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 9. The coordinates for the second root will appear. The roots for this equation are ( , 0) and ( , 0)

63 Graphing Linear Inequalities Example: Graph y 2x Open a new graphs page and 2. Menu, Graph Entry/Edit, Function add gridlines. 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

64 7. The graphed inequality will appear.

65 Graphing Inequalities that are NOT in the form y=mx+b Example: Graph the equation of the line 3x+y= Open a new graphs page and add 2. Menu, Graph Entry/Edit, Equation gridlines. line 3. Line Standard 4. Type in the proper coefficients. Click enter. 6. The graphed line will appear.

66 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?

67 1. Add a Lists & Spreadsheet page 2. This page will appear. 3. Type in the data. The independent 4. Be sure to label both columns. variables go in the first column, the dependent variables go in the second column. 5. Ctrl, doc, Add Data & Statistics 6. This screen will appear. 7. Click click to add variable and 8. This scatterplot represents the label your axis. Repeat for the y-axis. solution.

68 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, Add Lists & Spreasheet 2. Type in the data in the first column. Be sure to label the column. 3. Ctrl, doc, Add Data & Statistics 4. Click on/ label the x-axis. 5. A screen similar to this will appear. 6. Menu, Plot Type, Box Plot

69 7. A box and whiskers plot will appear.

70 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

71 7. The roots of the quadratic equation will appear. Standard Form

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