Using the TI-83 Plus/TI-84 Plus

370 Pages·2013·20.52 MB·English

by  Christopher R. Mitchell

MANNING
Using the TI-83
Plus/TI-84 Plus
CHRISTOPHER R. MITCHELL
MANNING
SHELTER ISLAND
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ISBN: 9781617290848
Printed in the United States of America
1 2 3 4 5 6 7 8 9 10 – MAL – 19 18 17 16 15 14 13
brief contents
PART 1 BASICS AND ALGEBRA ON THE TI-83 PLUS/TI-84 PLUS.....1
1 ■ What can your calculator do? 3
2 ■ Get started with your calculator 25
3 ■ Basic graphing 57
4 ■ Variables, matrices, and lists 83
PART 2 PRECALCULUS AND CALCULUS ...................................111
5 ■ Expanding your graphing skills 113
6 ■ Precalculus and your calculator 141
7 ■ Calculus on the TI-83 Plus/TI-84 Plus 158
PART 3 STATISTICS, PROBABILITY, AND FINANCE....................171
8 ■ Calculating and plotting statistics 173
9 ■ Working with probability and distributions 202
10 ■ Financial tools 223
PART 4 GOING FURTHER WITH THE TI-83 PLUS/TI-84 PLUS ...235
11 ■ Turbocharging math with programming 237
12 ■ The TI-84 Plus C Silver Edition 260
13 ■ Now what? 282
iii

contents
preface xi
acknowledgments xiii
about this book xv
PART 1 BASICS AND ALGEBRA ON THE
TI-83 PLUS/TI-84 PLUS.....................................1
1 What can your calculator do? 3
1.1 Five examples of what your calculator can do 4
Calculating the volume of a cube 5 ■ Solving the
Quadratic Formula 7 ■ Graphing sine and cosine 10
Calculating the area under a curve 12 ■ Fitting a line
to data 14
1.2 This book and your calculator 17
Your calculator, a multipurpose tool 17 ■ What you’ll need 19
1.3 MathPrint vs. non-MathPrint calculators 20
1.4 Summary 23
v
vi CONTENTS
2 Get started with your calculator 25
2.1 Before you begin 26
2.2 Performing basic calculations 29
Simple arithmetic 30 ■ Dividing sums: demonstrating
the importance of parentheses 30 ■ Using exponents 32
Roots of numbers 33 ■ Continuing a calculation: Ans 34
2.3 More homescreen skills 36
More on 2nd and ALPHA 36 ■ Editing an equation 37
Repeating a calculation 38 ■ MathPrint focus: entering
and displaying fractions 39
2.4 Finding functions 41
Examples of homescreen math functions 42 ■ A guide
to finding functions 45
2.5 Setting modes 47
2.6 Solving equations and checking your answers 51
Using the Equation Solver tool 51 ■ Boolean algebra
with the Test/Logic menu 54
2.7 Summary 56
3 Basic graphing 57
3.1 Getting started with graphing 58
3.2 Visualizing solutions and examining graphs 61
A ball is thrown: maximum and minimum of a function 61
Two trains: intersection of two functions 67
3.3 Manipulating graphs 71
Viewing different parts of the graph 71 ■ Modifying graph
format settings 74 ■ Graph styles, shading, and inequalities 77
3.4 Using the Table 78
Examining graph values 79 ■ G-T and Horiz split screen 80
3.5 Summary 81
4 Variables, matrices, and lists 83
4.1 What are variables? Why do I need them? 84
Plugging x into a polynomial 86 ■ Finding the volume
of a box 87 ■ Testing the Pythagorean Theorem 89
4.2 Using sequences of numbers: lists 91
Typing lists 92 ■ Storing lists into list variables 93
Isolating a single list element 94
CONTENTS vii
4.3 List operations and functions 95
List-wise algebra operations 95 ■ List-wise math functions 97
Element-wise list operations 99
4.4 Exploring 2D matrices 101
Typing matrices on the homescreen 102 ■ Creating and using
matrix variables 102 ■ Typing matrices in the matrix editor 103
4.5 Matrix operations and functions 104
Matrix-wise algebraic operations 104
Single-matrix operations 106
4.6 Summary 109
PART 2 PRECALCULUS AND CALCULUS........................111
5 Expanding your graphing skills 113
5.1 Parametric mode 114
Parametric example: graphing a circle 116
Parametric example: throwing a baseball 118
Parametric example: a Lissajous curve 120
5.2 Graphing polar functions 121
Polar example: a spiral 123 ■ Polar example: polar rose 124
5.3 Graphing sequences 125
Sequence example: a sequence of squares 126
Sequence example: the Fibonacci series 127
5.4 Drawing on graphs 130
Graphscreen drawing tools 131 ■ Using drawing tools
on the homescreen 133 ■ Drawing graphlike functions:
DrawInv, DrawF, and Shade 136
5.5 Saving graph settings and pictures 137
Saving and recalling picture variables 138
Saving and recalling graph databases 139
5.6 Summary 140
6 Precalculus and your calculator 141
6.1 Imaginary and complex numbers 142
Complex number functions and symbols 142
Complex roots with the Quadratic Formula 144
6.2 Experimenting with trigonometry 145
Trig functions 146 ■ Trigonometry and the unit circle 149
viii CONTENTS
6.3 Understanding limits 151
6.4 Exponents and logarithms 154
6.5 Summary 156
7 Calculus on the TI-83 Plus/TI-84 Plus 158
7.1 Derivatives and slope 159
Calculating derivatives on the graphscreen 160
Calculating derivatives on the homescreen 161
7.2 Finding minima, maxima, and inflection points 162
7.3 Integrals and area under a curve 165
Computing integrals on the graphscreen 166
Computing integrals on the homescreen 168
7.4 Summary 170
PART 3 STATISTICS, PROBABILITY, AND FINANCE.........171
8 Calculating and plotting statistics 173
8.1 Working with data lists 174
8.2 Calculating properties of data 178
Summarizing data 179 ■ 1-Var Stats and 2-Var Stats 180
8.3 Statistical plots 184
Using Scatter and XYLine 185 ■ Plotting a histogram 188
Understanding Box plots 189 ■ Normal probability plots 192
8.4 Regression: fitting lines to data 193
Linear regression 194 ■ Exponential regression 197
More regression: the many options 199
8.5 Summary 200
9 Working with probability and distributions 202
9.1 Calculating PDFs and CDFs 203
Probability distribution functions 204 ■ Cumulative
distribution functions 208 ■ Inverse CDFs 212
9.2 Drawing distributions 213
9.3 Combinatorics 216
9.4 Generating random numbers 219
9.5 Summary 222
CONTENTS ix
10 Financial tools 223
10.1 Financial variables and tools 224
10.2 Solving finance problems 225
Investments and interest 226 ■ Mortgages and loans 228
Other finance tools 231
10.3 Summary 233
PART 4 GOING FURTHER WITH THE
TI-83 PLUS/TI-84 PLUS.................................235
11 Turbocharging math with programming 237
11.1 Hello World, your first program 238
What’s a program? 239 ■ Creating and writing a program 239
Testing the Hello World program 241
11.2 Writing a Quadratic Formula solver 242
Coding and testing the Quadratic Formula solver 243
Understanding the Quadratic Formula solver 244
11.3 A crash course in programming commands 246
Input and output 247 ■ Conditional statements 249
Menus, labels, and jumps 252 ■ Loops 254
11.4 Putting it all together: programming, SATs, math, and
more 257
11.5 Summary: taking programming further 259
12 The TI-84 Plus C Silver Edition 260
12.1 Arithmetic and algebra 262
The homescreen and the Mode menu 263
MathPrint features 264 ■ OS-wide Catalog Help 265
The Equation Solver 266
12.2 Graphing features 267
Your first graph in color 268 ■ TI-84 Plus C Silver Edition
graphing features 270
12.3 Drawing in color 274
12.4 Statistics features 276
Using QuickPlot & Fit-EQ 277 ■ Using manual Stat Plots 279
12.5 Summary 280