Mathematics IB for the international student, Pre-Diploma SL and HL (MYP 5 plus) 2ed
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Entries: 226
Pamela Vollmar
Edward Kemp
Michael Haese
core math
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Mathematics IB for the international student, Pre-Diploma SL and HL (MYP 5 plus) 2ed
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226
0. Graphics Calculator Instructions
Theory
Page 9
0.1 Basic Calculations
Theory
Page 10
0.2 Basic Functions
Theory
Page 12
0.3 Secondary Function and Alpha Keys
Theory
Page 15
0.4 Memory
Theory
Page 15
0.5 Lists
Theory
Page 18
0.6 Statistical Graphs
Theory
Page 20
0.7 Working with Functions
Theory
Page 21
1. Sets and Venn Diagrams
Theory
Page 29
1.1 Number Sets
Theory
Page 30
1.2 Interval Notation
Theory
Page 32
1.3 Venn Diagrams
Theory
Page 33
1.4 Union and Intersection
Theory
Page 36
1.5 Problem Solving with Venn Diagrams
Theory
Page 40
1.6 The Algebra of Sets
Theory
Page 42
1.7 Review Set 1A
Theory
Page 43
1.8 Review Set 1B
Theory
Page 44
2. Algebraic Expansion and Factorisation
Theory
Page 45
2.1 Revision of Expansion Laws
Theory
Page 46
2.2 Revision of Factorisation
Theory
Page 48
2.3 Further Expansion
Theory
Page 50
2.4 The Binomial Expansion
Theory
Page 51
2.5 Factorising Expressions with Four Terms
Theory
Page 54
2.6 Factorising Quadratic Trinomials
Theory
Page 55
2.7 Factorisation by Splitting
Theory
Page 57
2.8 Miscellaneous Factorisation
Theory
Page 60
2.9 Review Set 2A
Theory
Page 61
2.10 Review Set 2B
Theory
Page 62
3. Radicals and Surds
Theory
Page 63
3.1 Basic Operations with Radicals
Theory
Page 65
3.2 Properties of Radicals
Theory
Page 67
3.3 Multiplication of Radicals
Theory
Page 70
3.4 Division by Radicals
Theory
Page 72
3.5 Equality of Surds
Theory
Page 74
3.6 Review Set 3A
Theory
Page 77
3.7 Review Set 3B
Theory
Page 78
4. Pythagoras’ Theorem
Theory
Page 79
4.1 Pythagoras’ Theorem
Theory
Page 81
4.2 The Converse of Pythagoras’ Theorem
Theory
Page 85
4.3 Problem Solving Using Pythagoras’ Theorem
Theory
Page 88
4.4 Circle Problems
Theory
Page 93
4.5 Three-Dimensional Problems
Theory
Page 96
4.6 More Difficult Problems
Theory
Page 98
4.7 Review Set 4A
Theory
Page 100
4.8 Review Set 4B
Theory
Page 101
5. Coordinate Geometry
Theory
Page 103
5.1 Distance Between Two Points
Theory
Page 105
5.2 Midpoints
Theory
Page 108
5.3 Gradient or Slope
Theory
Page 110
5.4 Using Coordinate Geometry
Theory
Page 116
5.5 Equations of Straight Lines
Theory
Page 118
5.6 Distance from a Point to a Line
Theory
Page 127
5.7 3-Dimensional Coordinate Geometry
Theory
Page 129
5.8 Review Set 5A
Theory
Page 130
5.9 Review Set 5B
Theory
Page 131
6. Congruence and Similarity
Theory
Page 133
6.1 Congruence of Figures
Theory
Page 134
6.2 Constructing Triangles
Theory
Page 135
6.3 Congruent Triangles
Theory
Page 137
6.4 Similarity
Theory
Page 146
6.5 Areas and Volumes of Similar Figures
Theory
Page 150
6.6 Review Set 6A
Theory
Page 152
6.7 Review Set 6B
Theory
Page 153
7. Transformation Geometry
Theory
Page 155
7.1 Translations
Theory
Page 157
7.2 Reflections
Theory
Page 158
7.3 Rotations
Theory
Page 160
7.4 Dilations
Theory
Page 162
7.5 Review Set 7A
Theory
Page 167
7.6 Review Set 7B
Theory
Page 168
8. Univariate Data Analysis
Theory
Page 169
8.1 Statistical Terminology
Theory
Page 171
8.2 Quantitative Numerical Data
Theory
Page 176
8.3 Grouped Discrete Data
Theory
Page 179
8.4 Continuous Data
Theory
Page 181
8.5 Measuring the Centre
Theory
Page 184
8.6 Cumulative Data
Theory
Page 191
8.7 Measuring the Spread
Theory
Page 194
8.8 Box-and-Whisker Plots
Theory
Page 196
8.9 Statistics from Technology
Theory
Page 200
8.10 Standard Deviation
Theory
Page 202
8.11 The Normal Distribution
Theory
Page 206
8.12 Review Set 8A
Theory
Page 209
8.13 Review Set 8B
Theory
Page 211
9. Quadratic Equations
Theory
Page 213
9.1 Quadratic Equations of the Form $x^2=k$
Theory
Page 215
9.2 Solution by Factorisation
Theory
Page 216
9.3 Completing the Square
Theory
Page 220
9.4 Problem Solving
Theory
Page 222
9.5 The Quadratic Formula
Theory
Page 227
9.6 Review Set 9A
Theory
Page 231
9.7 Review Set 9B
Theory
Page 232
10. Trigonometry
Theory
Page 233
10.1 Trigonometric Ratios
Theory
Page 235
10.2 Trigonometric Problem Solving
Theory
Page 240
10.3 3-Dimensional Problem Solving
Theory
Page 246
10.4 The Unit Circle
Theory
Page 250
10.5 Area of a Triangle Using Sine
Theory
Page 252
10.6 The Sine Rule
Theory
Page 255
10.7 The Cosine Rule
Theory
Page 257
10.8 Problem Solving with the Sine and Cosine Rules
Theory
Page 259
10.9 Trigonometric Identities
Theory
Page 261
10.10 Review Set 10A
Theory
Page 264
10.11 Review Set 10B
Theory
Page 265
11. Probability
Theory
Page 267
11.1 Experimental Probability
Theory
Page 269
11.2 Probabilities from Tabled Data
Theory
Page 271
11.3 Representing Combined Events
Theory
Page 272
11.4 Theoretical Probability
Theory
Page 274
11.5 Compound Events
Theory
Page 277
11.6 Using Tree Diagrams
Theory
Page 280
11.7 Sampling with and without Replacement
Theory
Page 283
11.8 Mutually Exclusive and Non-Mutually Exclusive Events
Theory
Page 285
11.9 Venn Diagrams and Conditional Probability
Theory
Page 287
11.10 Review Set 11A
Theory
Page 292
11.11 Review Set 11B
Theory
Page 293
12. Algebraic Fractions
Theory
Page 295
12.1 Simplifying Algebraic Fractions
Theory
Page 296
12.2 Multiplying and Dividing Algebraic Fractions
Theory
Page 300
12.3 Adding and Subtracting Algebraic Fractions
Theory
Page 302
12.4 More Complicated Fractions
Theory
Page 305
12.5 Review Set 12A
Theory
Page 307
12.6 Review Set 12B
Theory
Page 308
13. Formulae
Theory
Page 309
13.1 Formula Substitution
Theory
Page 310
13.2 Formula Rearrangement
Theory
Page 313
13.3 Formula Construction
Theory
Page 315
13.4 Formulae by Induction
Theory
Page 318
13.5 More Difficult Rearrangements
Theory
Page 320
13.6 Review Set 13A
Theory
Page 323
13.7 Review Set 13B
Theory
Page 324
14. Relations, Functions and Sequences
Theory
Page 325
14.1 Relations and Functions
Theory
Page 326
14.2 Functions
Theory
Page 329
14.3 Function Notation
Theory
Page 331
14.4 Composite Functions
Theory
Page 334
14.5 Transforming $y=f(x)$
Theory
Page 335
14.6 Inverse Functions
Theory
Page 337
14.7 The Modulus Function
Theory
Page 340
14.8 Where Functions Meet
Theory
Page 343
14.9 Number Sequences
Theory
Page 344
14.10 Recurrence Relationships
Theory
Page 350
14.11 Review Set 14A
Theory
Page 354
14.12 Review Set 14B
Theory
Page 355
15. Vectors
Theory
Page 357
15.1 Directed Line Segment Representation
Theory
Page 358
15.2 Vector Equality
Theory
Page 360
15.3 Vector Addition
Theory
Page 361
15.4 Vector Subtraction
Theory
Page 365
15.5 Vectors in Component Form
Theory
Page 367
15.6 Scalar Multiplication
Theory
Page 371
15.7 Vector Equations
Theory
Page 373
15.8 Parallelism of Vectors
Theory
Page 374
15.9 The Scalar Product of Two Vectors
Theory
Page 376
15.10 Vector Proof
Theory
Page 380
15.11 Review Set 15A
Theory
Page 382
15.12 Review Set 15B
Theory
Page 384
16. Exponential Functions and Logarithms
Theory
Page 385
16.1 Index Laws
Theory
Page 386
16.2 Rational Fractional Indices
Theory
Page 389
16.3 Exponential Functions
Theory
Page 391
16.4 Growth and Decay
Theory
Page 393
16.5 Compound Interest
Theory
Page 395
16.6 Depreciation
Theory
Page 398
16.7 Exponential Equations
Theory
Page 400
16.8 Expansion and Factorisation
Theory
Page 401
16.9 Logarithms
Theory
Page 404
16.10 Review Set 16A
Theory
Page 410
16.11 Review Set 16B
Theory
Page 411
17. Quadratic Functions
Theory
Page 413
17.1 Quadratic Functions
Theory
Page 414
17.2 Graphs of Quadratic Functions
Theory
Page 416
17.3 Axes Intercepts
Theory
Page 425
17.4 Axis of Symmetry and Vertex
Theory
Page 429
17.5 Quadratic Optimisation
Theory
Page 433
17.6 Review Set 17A
Theory
Page 435
17.7 Review Set 17B
Theory
Page 436
18. Advanced Trigonometry
Theory
Page 437
18.1 Radian Measure
Theory
Page 438
18.2 Trigonometric Ratios from the Unit Circle
Theory
Page 441
18.3 The Multiples of $30^\circ$ and $45^\circ$
Theory
Page 444
18.4 Graphing Trigonometric Functions
Theory
Page 448
18.5 Modelling with Sine Functions
Theory
Page 451
18.6 Trigonometric Equations
Theory
Page 454
18.7 Negative and Complementary Angle Formulae
Theory
Page 457
18.8 Addition Formulae
Theory
Page 458
18.9 Review Set 18A
Theory
Page 461
18.10 Review Set 18B
Theory
Page 462
19. Inequalities
Theory
Page 463
19.1 Sign Diagrams
Theory
Page 464
19.2 Interval Notation
Theory
Page 468
19.3 Inequalities
Theory
Page 471
19.4 The Arithmetic Mean - Geometric Mean Inequality
Theory
Page 473
19.5 Review Set 19A
Theory
Page 476
19.6 Review Set 19B
Theory
Page 476
20. Matrices and Linear Transformations
Theory
Page 477
20.1 Introduction to Matrices
Theory
Page 478
20.2 Operations with Matrices
Theory
Page 480
20.3 Matrix Multiplication
Theory
Page 484
20.4 The Determinant of a Matrix
Theory
Page 487
20.5 Multiplicative Identity and Inverse Matrices
Theory
Page 489
20.6 Simultaneous Equations
Theory
Page 491
20.7 Linear Transformations
Theory
Page 494
20.8 Proofs with $2\times2$ Matrices
Theory
Page 503
20.9 Review Set 20A
Theory
Page 504
20.10 Review Set 20B
Theory
Page 505
21. Deductive Geometry
Theory
Page 507
21.1 Circle Theorems
Theory
Page 509
21.2 Further Circle Theorems
Theory
Page 513
21.3 Geometric Proof
Theory
Page 517
21.4 Cyclic Quadrilaterals
Theory
Page 521
21.5 Review Set 21A
Theory
Page 526
21.6 Review Set 21B
Theory
Page 527
22. Introduction to Calculus
Theory
Page 529
22.1 Estimating Gradients of Tangents to Curves
Theory
Page 530
22.2 Gradients Using Quadratic Theory
Theory
Page 531
22.3 Gradients Using Limit Theory
Theory
Page 532
22.4 Differentiation
Theory
Page 535
22.5 Optimisation
Theory
Page 540
22.6 Areas Under Curves
Theory
Page 543
22.7 Integration
Theory
Page 545
22.8 The Definite Integral
Theory
Page 547
22.9 Review Set 22A
Theory
Page 549
22.10 Review Set 22B
Theory
Page 550
26. Answers
Theory
Page 555
27. Index
Theory
Page 606
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