Maths Quest Manual for the TI-Nspire CAS Calculator 4E & eBookPLUS

1 Navigating the TI-Nspire 1

How to …

1.1 Change System Settings 2

1.2 Use the Notes application 3

1.3 Navigate between documents and pages 6

1.4 Save and delete TNS files 8

1.5 Perform basic calculations 9

1.6 Use the Mathematical Expressions palette 11

1.7 Perform common numerical tasks 13

1.8 Transfer files between calculators 13

1.9 Transfer files between calculators and computers 15

2 Variables and expressions 16

How to …

2.1 Simplify algebraic expressions 16

2.2 Substitute values for pronumerals 18

2.3 Substitute values using function notation 20

2.4 Expand algebraic expressions 21

2.5 Factorise algebraic expressions using Highest Common Factor (HCF) 22

2.6 Add and subtract algebraic fractions 23

2.7 Multiply and divide algebraic fractions 24

2.8 Factorise over the complex number field 24

3 Linear functions 26

How to …

3.1 Plot linear graphs 26

3.2 Rearrange linear equations to make y the subject 30

3.3 Sketch linear graphs by pasting the rearranged equation into the graphing window 31

3.4 Sketch linear graphs in the graphing window 32

3.5 Alter the scale settings for graphs 34

3.6 Edit the equation of a graph on the Cartesian plane 35

3.7 Find the x-intercept of a graph 37

3.8 Graph linear inequations 38

4 Solving equations 39

How to …

4.1 Solve linear equations 39

4.2 Rearrange formulas 41

4.3 Solve linear inequations 41

4.4 Solve simultaneous equations graphically 42

4.5 Solve simultaneous equations algebraically 44

4.6 Solve quadratic equations 44

4.7 Solve linear simultaneous equations with three unknowns 45

4.8 Solve a quadratic equation and a linear equation simultaneously 47

4.9 Solve simultaneous inequations graphically 48

5 Quadratic functions 49

How to …

5.1 Plot parabolas 49

5.2 Apply transformations to quadratic functions 54

5.3 Find features of the parabola graphically 61

5.4 Solve quadratic equations to determine irrational xintercepts 64

6 Exponential and logarithmic functions 68

How to …

6.1 Simplify expressions involving indices and surds 68

6.2 Plot an exponential graph 70

6.3 Sketch exponential functions 74

6.4 Calculate logarithms 76

6.5 Solve exponential and logarithmic equations 76

6.6 Use the TI-Nspire CAS in applications of exponential and logarithmic functions 77

7 Advanced functions 82

How to …

7.1 Graph the absolute value function 82

7.2 Graph hybrid functions 86

7.3 Find an inverse algebraically 88

7.4 Find an inverse graphically 89

7.5 Find exact values on a graph 91

7.6 Lock variables 93

8 Geometry 96

How to …

8.1 Calculate the interior angle sum of a triangle 96

8.2 Illustrate a circle theorem (#1) 101

8.3 Illustrate a circle theorem (#2) 104

8.4 Optimise a rectangle inscribed in a circle 106

9 Trigonometry 116

How to …

9.1 Set the mode to radians or degrees 116

9.2 Work with exact values 120

9.3 Solve trigonometric equations 120

9.4 Convert between radians and degrees 122

9.5 Graph trigonometric functions 124

10 Financial mathematics 129

How to …

10.1 Calculate simple interest 129

10.2 Calculate compound interest 130

10.3 Calculate the interest rate 131

10.4 Calculate the monthly repayment on a reducing balance loan 132

10.5 Calculate the balance of the principal after any instalment 133

10.6 Calculate the number of days between dates 134

11 Sequences and series 135

How to …

11.1 Find the nth term of an arithmetic sequence 135

11.2 Find the sum of an arithmetic sequence 136

11.3 Find the nth term of a geometric sequence 137

11.4 Generate a list of terms from a difference equation 137

11.5 Generate a list of terms from a difference equation using an alternative method 138

11.6 Find the sum of a geometric sequence 140

12 Probability 141

How to …

12.1 Perform calculations using factorials, permutations and combinations 141

12.2 Graph the binomial probability distribution and calculate binomial probabilities 143

12.3 Calculate median, quantiles and the IQR 149

12.4 Calculate normal distribution probabilities 151

12.5 Calculate inverse normal distribution probabilities 153

12.6 Generate random numbers 154

13 Statistics 155

How to …

13.1 Calculate measures of centre and spread for univariate data 155

13.2 Draw boxplots 157

13.3 Draw histograms 160

13.4 Draw scatterplots using bivariate data 163

13.5 Construct lines of best fit and regression lines 164

13.6 Make predictions and calculate r and r 2 167

13.7 Display time-series plots and smoothed data 170

14 Matrices and vectors 172

How to …

14.1 Add, subtract and multiply matrices 172

14.2 Solve matrix equations 176

14.3 Solve linear simultaneous equations using matrices 177

14.4 Work with vectors 178

15 Differential calculus 181

How to …

15.1 Use a spreadsheet to demonstrate the limit of a function 181

15.2 Calculate the value of a limit 184

15.3 Differentiate from first principles 186

15.4 Draw a tangent to a curve and calculate its gradient 187

15.5 Find the derivative by rule 190

15.6 Sketch derivatives 193

15.7 Calculate implicit differentiation 195

16 Integral calculus 196

How to …

16.1 Find indefinite integrals 196

16.2 Find definite integrals 197

16.3 Graph a possible original function from a gradient function 199

16.4 Calculate the area under the curve 201

16.5 Find the general solution of a differential equation 203

16.6 Find the particular solution of a differential equation 204

16.7 Use Euler's method to tabulate the solution of a differential equation 205

16.8 Plot slope fields for a differential equation 206

16.9 Find the numerical solution of a differential equation 208

17 Vernier Dataquest 209

How to …

17.1 Set up, run and view experimental data 209

17.2 Store and analyse the collected data 212

18 Further graphing techniques 215

How to …

18.1 Plot families of functions 215

18.2 Plot parametric graphs 215

18.3 Plot polar graphs 217

18.4 Plot sequence graphs 218

18.5 Plot 3-dimensional surfaces 221

18.6 Insert images 223

18.7 Create a locus of points 224

19 Programming with the TI-Nspire

CAS calculator 229

How to …

19.1 Write a user-defined function 229

19.2 Create, write, edit and run a program 232

20 Problem solving 241

20.1 Matrices and simultaneous equations 241

20.2 Curve sketching 242

20.3 Calculus and function notation 242

20.4 Complex numbers 244

20.5 Binomial theorem 244

20.6 Probability 245

20.7 Linear regression 245

20.8 Differential equations 246