Mathematics IB for the international student (SL) 3rd ed,2012
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Robert Haese
Sandra Haese
Michael Haese
core math
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Mathematics IB for the international student (SL) 3rd ed,2012
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Entries
248
0.1 Symbols and Notation Used in This Book
Theory
Page 10
0.2 Background Knowledge
Theory
Page 16
0.3 Graphics Calculator Instructions
Theory
Page 16
1. Quadratics
Theory
Page 17
1.1 Quadratic Equations
Theory
Page 19
1.2 The Discriminant of a Quadratic
Theory
Page 25
1.3 Quadratic Functions
Theory
Page 28
1.4 Finding a Quadratic from Its Graph
Theory
Page 38
1.5 Where Functions Meet
Theory
Page 42
1.6 Problem Solving with Quadratics
Theory
Page 44
1.7 Quadratic Optimisation
Theory
Page 47
1.8 Review Set 1A
Theory
Page 49
1.9 Review Set 1B
Theory
Page 50
1.10 Review Set 1C
Theory
Page 51
2. Functions
Theory
Page 53
2.1 Relations and Functions
Theory
Page 54
2.2 Function Notation
Theory
Page 57
2.3 Domain and Range
Theory
Page 59
2.4 Composite Functions
Theory
Page 64
2.5 Sign Diagrams
Theory
Page 66
2.6 Rational Functions
Theory
Page 69
2.7 Inverse Functions
Theory
Page 73
2.8 Review Set 2A
Theory
Page 77
2.9 Review Set 2B
Theory
Page 78
2.10 Review Set 2C
Theory
Page 80
3. Exponentials
Theory
Page 81
3.1 Exponents
Theory
Page 82
3.2 Laws of Exponents
Theory
Page 84
3.3 Rational Exponents
Theory
Page 87
3.4 Algebraic Expansion and Factorisation
Theory
Page 90
3.5 Exponential Equations
Theory
Page 92
3.6 Exponential Functions
Theory
Page 94
3.7 Growth and Decay
Theory
Page 98
3.8 The Natural Exponential $e^x$
Theory
Page 101
3.9 Review Set 3A
Theory
Page 105
3.10 Review Set 3B
Theory
Page 106
3.11 Review Set 3C
Theory
Page 107
4. Logarithms
Theory
Page 109
4.1 Logarithms in Base 10
Theory
Page 110
4.2 Logarithms in Base $a$
Theory
Page 113
4.3 Laws of Logarithms
Theory
Page 116
4.4 Natural Logarithms
Theory
Page 120
4.5 Exponential Equations Using Logarithms
Theory
Page 123
4.6 The Change of Base Rule
Theory
Page 125
4.7 Graphing Logarithmic Functions
Theory
Page 126
4.8 Growth and Decay
Theory
Page 130
4.9 Review Set 4A
Theory
Page 132
4.10 Review Set 4B
Theory
Page 133
4.11 Review Set 4C
Theory
Page 134
5. Transforming Functions
Theory
Page 135
5.1 Graphing Functions
Theory
Page 136
5.2 Transformation of Graphs
Theory
Page 140
5.3 Translations $y=f(x)+b$ and $y=f(x-a)$
Theory
Page 141
5.4 Stretches $y=pf(x)$ and $y=f(qx)$
Theory
Page 143
5.5 Reflections $y=-f(x)$ and $y=f(-x)$
Theory
Page 144
5.6 Miscellaneous Transformations
Theory
Page 146
5.7 Review Set 5A
Theory
Page 148
5.8 Review Set 5B
Theory
Page 149
5.9 Review Set 5C
Theory
Page 150
6. Sequences and Series
Theory
Page 151
6.1 Number Sequences
Theory
Page 152
6.2 The General Term of a Number Sequence
Theory
Page 153
6.3 Arithmetic Sequences
Theory
Page 155
6.4 Geometric Sequences
Theory
Page 159
6.5 Series
Theory
Page 166
6.6 Arithmetic Series
Theory
Page 167
6.7 Geometric Series
Theory
Page 170
6.8 Review Set 6A
Theory
Page 176
6.9 Review Set 6B
Theory
Page 176
6.10 Review Set 6C
Theory
Page 177
7. The Binomial Expansion
Theory
Page 179
7.1 Binomial Expansions
Theory
Page 180
7.2 The Binomial Coefficient
Theory
Page 183
7.3 The Binomial Theorem
Theory
Page 185
7.4 Review Set 7A
Theory
Page 187
7.5 Review Set 7B
Theory
Page 188
8. The Unit Circle and Radian Measure
Theory
Page 189
8.1 Radian Measure
Theory
Page 190
8.2 Arc Length and Sector Area
Theory
Page 193
8.3 The Unit Circle and the Trigonometric Ratios
Theory
Page 196
8.4 Applications of the Unit Circle
Theory
Page 201
8.5 Multiples of $\frac{\pi}{6}$ and $\frac{\pi}{4}$
Theory
Page 205
8.6 The Equation of a Straight Line
Theory
Page 209
8.7 Review Set 8A
Theory
Page 210
8.8 Review Set 8B
Theory
Page 211
8.9 Review Set 8C
Theory
Page 212
9. Non-Right Angled Triangle Trigonometry
Theory
Page 213
9.1 Areas of Triangles
Theory
Page 214
9.2 The Cosine Rule
Theory
Page 217
9.3 The Sine Rule
Theory
Page 220
9.4 Using the Sine and Cosine Rules
Theory
Page 224
9.5 Review Set 9A
Theory
Page 228
9.6 Review Set 9B
Theory
Page 229
9.7 Review Set 9C
Theory
Page 230
10. Trigonometric Functions
Theory
Page 231
10.1 Periodic Behaviour
Theory
Page 232
10.2 The Sine Function
Theory
Page 236
10.3 Modelling Using Sine Functions
Theory
Page 243
10.4 The Cosine Function
Theory
Page 246
10.5 The Tangent Function
Theory
Page 248
10.6 General Trigonometric Functions
Theory
Page 251
10.7 Review Set 10A
Theory
Page 253
10.8 Review Set 10B
Theory
Page 253
10.9 Review Set 10C
Theory
Page 254
11. Trigonometric Equations and Identities
Theory
Page 255
11.1 Trigonometric Equations
Theory
Page 256
11.2 Using Trigonometric Models
Theory
Page 263
11.3 Trigonometric Relationships
Theory
Page 265
11.4 Double Angle Formulae
Theory
Page 268
11.5 Trigonometric Equations in Quadratic Form
Theory
Page 271
11.6 Review Set 11A
Theory
Page 272
11.7 Review Set 11B
Theory
Page 273
11.8 Review Set 11C
Theory
Page 274
12. Vectors
Theory
Page 275
12.1 Vectors and Scalars
Theory
Page 276
12.2 Geometric Operations with Vectors
Theory
Page 279
12.3 Vectors in the Plane
Theory
Page 286
12.4 The Magnitude of a Vector
Theory
Page 288
12.5 Operations with Plane Vectors
Theory
Page 290
12.6 The Vector Between Two Points
Theory
Page 293
12.7 Vectors in Space
Theory
Page 296
12.8 Operations with Vectors in Space
Theory
Page 300
12.9 Parallelism
Theory
Page 304
12.10 The Scalar Product of Two Vectors
Theory
Page 307
12.11 Review Set 12A
Theory
Page 314
12.12 Review Set 12B
Theory
Page 315
12.13 Review Set 12C
Theory
Page 317
13. Vector Applications
Theory
Page 319
13.1 Problems Involving Vector Operations
Theory
Page 320
13.2 Lines in 2-D and 3-D
Theory
Page 322
13.3 The Angle Between Two Lines
Theory
Page 326
13.4 Constant Velocity Problems
Theory
Page 328
13.5 The Shortest Distance from a Line to a Point
Theory
Page 331
13.6 Intersecting Lines
Theory
Page 335
13.7 Relationships Between Lines
Theory
Page 337
13.8 Review Set 13A
Theory
Page 340
13.9 Review Set 13B
Theory
Page 341
13.10 Review Set 13C
Theory
Page 342
14. Introduction to Differential Calculus
Theory
Page 343
14.1 Limits
Theory
Page 345
14.2 Limits at Infinity
Theory
Page 347
14.3 Rates of Change
Theory
Page 350
14.4 The Derivative Function
Theory
Page 353
14.5 Differentiation from First Principles
Theory
Page 355
14.6 Review Set 14A
Theory
Page 357
14.7 Review Set 14B
Theory
Page 358
14.8 Review Set 14C
Theory
Page 358
15. Rules of Differentiation
Theory
Page 359
15.1 Simple Rules of Differentiation
Theory
Page 360
15.2 The Chain Rule
Theory
Page 364
15.3 The Product Rule
Theory
Page 367
15.4 The Quotient Rule
Theory
Page 369
15.5 Derivatives of Exponential Functions
Theory
Page 371
15.6 Derivatives of Logarithmic Functions
Theory
Page 375
15.7 Derivatives of Trigonometric Functions
Theory
Page 378
15.8 Second and Higher Derivatives
Theory
Page 381
15.9 Review Set 15A
Theory
Page 383
15.10 Review Set 15B
Theory
Page 383
15.11 Review Set 15C
Theory
Page 384
16. Properties of Curves
Theory
Page 385
16.1 Tangents and Normals
Theory
Page 386
16.2 Increasing and Decreasing Functions
Theory
Page 392
16.3 Stationary Points
Theory
Page 397
16.4 Inflections and Shape
Theory
Page 401
16.5 Review Set 16A
Theory
Page 409
16.6 Review Set 16B
Theory
Page 410
16.7 Review Set 16C
Theory
Page 411
17. Applications of Differential Calculus
Theory
Page 413
17.1 Kinematics
Theory
Page 414
17.2 Rates of Change
Theory
Page 423
17.3 Optimisation
Theory
Page 428
17.4 Review Set 17A
Theory
Page 437
17.5 Review Set 17B
Theory
Page 438
17.6 Review Set 17C
Theory
Page 439
18. Integration
Theory
Page 441
18.1 The Area Under a Curve
Theory
Page 442
18.2 Antidifferentiation
Theory
Page 448
18.3 The Fundamental Theorem of Calculus
Theory
Page 449
18.4 Integration
Theory
Page 454
18.5 Rules for Integration
Theory
Page 457
18.6 Integrating $f(ax+b)$
Theory
Page 462
18.7 Integration by Substitution
Theory
Page 465
18.8 Definite Integrals
Theory
Page 468
18.9 Review Set 18A
Theory
Page 472
18.10 Review Set 18B
Theory
Page 473
18.11 Review Set 18C
Theory
Page 473
19. Applications of Integration
Theory
Page 475
19.1 The Area Under a Curve
Theory
Page 476
19.2 The Area Between Two Functions
Theory
Page 479
19.3 Kinematics
Theory
Page 483
19.4 Solids of Revolution
Theory
Page 489
19.5 Review Set 19A
Theory
Page 494
19.6 Review Set 19B
Theory
Page 496
19.7 Review Set 19C
Theory
Page 497
20. Descriptive Statistics
Theory
Page 499
20.1 Key Statistical Concepts
Theory
Page 500
20.2 Measuring the Centre of Data
Theory
Page 505
20.3 Measuring the Spread of Data
Theory
Page 517
20.4 Boxplots
Theory
Page 521
20.5 Cumulative Frequency Graphs
Theory
Page 526
20.6 Variance and Standard Deviation
Theory
Page 531
20.7 Review Set 20A
Theory
Page 539
20.8 Review Set 20B
Theory
Page 541
20.9 Review Set 20C
Theory
Page 542
21. Linear Modelling
Theory
Page 545
21.1 Correlation
Theory
Page 546
21.2 Pearson's Correlation Coefficient
Theory
Page 550
21.3 Line of Best Fit
Theory
Page 554
21.4 The Least Squares Regression Line
Theory
Page 557
21.5 Interpolation and Extrapolation
Theory
Page 558
21.6 Review Set 21A
Theory
Page 562
21.7 Review Set 21B
Theory
Page 563
21.8 Review Set 21C
Theory
Page 565
22. Probability
Theory
Page 567
22.1 Experimental Probability
Theory
Page 569
22.2 Sample Space
Theory
Page 574
22.3 Theoretical Probability
Theory
Page 575
22.4 Tables of Outcomes
Theory
Page 579
22.5 Compound Events
Theory
Page 581
22.6 Tree Diagrams
Theory
Page 585
22.7 Sampling With and Without Replacement
Theory
Page 588
22.8 Sets and Venn Diagrams
Theory
Page 591
22.9 Laws of Probability
Theory
Page 597
22.10 Independent Events
Theory
Page 601
22.11 Review Set 22A
Theory
Page 604
22.12 Review Set 22B
Theory
Page 604
22.13 Review Set 22C
Theory
Page 606
23. Discrete Random Variables
Theory
Page 607
23.1 Discrete Random Variables
Theory
Page 608
23.2 Discrete Probability Distributions
Theory
Page 610
23.3 Expectation
Theory
Page 614
23.4 The Binomial Distribution
Theory
Page 618
23.5 Review Set 23A
Theory
Page 626
23.6 Review Set 23B
Theory
Page 627
23.7 Review Set 23C
Theory
Page 628
24. The Normal Distribution
Theory
Page 629
24.1 The Normal Distribution
Theory
Page 631
24.2 Probabilities Using a Calculator
Theory
Page 636
24.3 The Standard Normal Distribution
Theory
Page 639
24.4 Quantiles or $k$-Values
Theory
Page 644
24.5 Review Set 24A
Theory
Page 648
24.6 Review Set 24B
Theory
Page 649
24.7 Review Set 24C
Theory
Page 650
25. Miscellaneous Questions
Theory
Page 651
25.1 Non-Calculator Questions
Theory
Page 652
25.2 Calculator Questions
Theory
Page 665
26. Answers
Theory
Page 679
27. Index
Theory
Page 755
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