Mathematics for the IB Diploma_ Higher Level (2012).pdf
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Entries: 188
Paul Fannon
Vesna Kadelburg
Ben Woolley
Stephen Ward
higher level
Cambridge University Press
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Mathematics for the IB Diploma_ Higher Level (2012).pdf
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1. Counting principles
Theory
Page 12
1A. The product principle and the addition principle
Theory
Page 12
1B. Counting arrangements
Theory
Page 17
1C. Algebra of factorials
Theory
Page 20
1D. Counting selections
Theory
Page 22
1E. Exclusion principle
Theory
Page 26
1F. Counting ordered selections
Theory
Page 29
1G. Keeping objects together or separated
Theory
Page 32
2. Exponents and logarithms
Theory
Page 39
2A. Laws of exponents
Theory
Page 39
2B. Exponential functions
Theory
Page 44
2C. The value e
Theory
Page 50
2D. Introducing logarithms
Theory
Page 51
2E. Laws of logarithms
Theory
Page 55
2F. Graphs of logarithms
Theory
Page 60
2G. Solving exponential equations
Theory
Page 61
3. Polynomials
Theory
Page 69
3A. Working with polynomials
Theory
Page 69
3B. Remainder and factor theorems
Theory
Page 74
3C. Sketching polynomial functions
Theory
Page 79
3D. The quadratic formula and the discriminant
Theory
Page 87
4. Algebraic structures
Theory
Page 98
4A. Solving equations by factorising
Theory
Page 98
4B. Solving equations by substitution
Theory
Page 100
4C. Features of graphs
Theory
Page 102
4D. Using a graphical calculator to solve equations
Theory
Page 105
4E. Solving simultaneous equations by substitution
Theory
Page 108
4F. Systems of linear equations
Theory
Page 112
4G. Solving inequalities
Theory
Page 121
4H. Working with identities
Theory
Page 124
5. The theory of functions
Theory
Page 129
5A. Relations, functions and graphs
Theory
Page 129
5B. Function notation
Theory
Page 134
5C. Domain and range
Theory
Page 136
5D. Composite functions
Theory
Page 142
5E. Inverse functions
Theory
Page 144
5F. Rational functions
Theory
Page 152
6. Transformations of graphs
Theory
Page 165
6A. Translations
Theory
Page 166
6B. Stretches
Theory
Page 168
6C. Reflections
Theory
Page 172
6D. Modulus transformations
Theory
Page 174
6E. Consecutive transformations
Theory
Page 178
6F. Reciprocal transformations
Theory
Page 185
6G. Symmetries of graphs and functions
Theory
Page 189
7. Sequences and series
Theory
Page 201
7A. General sequences
Theory
Page 201
7B. General series and sigma notation
Theory
Page 204
7C. Arithmetic sequences
Theory
Page 206
7D. Arithmetic series
Theory
Page 210
7E. Geometric sequences
Theory
Page 212
7F. Geometric series
Theory
Page 216
7G. Infinite geometric series
Theory
Page 218
7H. Mixed questions
Problem
Page 222
8. Binomial expansion
Theory
Page 228
8A. Introducing the binomial theorem
Theory
Page 228
8B. Applying the binomial theorem
Theory
Page 230
8C. Products of binomial expansions
Theory
Page 234
8D. Binomial expansions as approximations
Theory
Page 237
9. Circular measure and trigonometric functions
Theory
Page 243
9A. Radian measure
Theory
Page 243
9B. Definitions and graphs of sine and cosine functions
Theory
Page 250
9C. Definition and graph of the tangent function
Theory
Page 259
9D. Exact values of trigonometric functions
Theory
Page 262
9E. Transformations of trigonometric graphs
Theory
Page 265
9F. Modelling using trigonometric functions
Theory
Page 272
9G. Inverse trigonometric functions
Theory
Page 275
10. Trigonometric equations and identities
Theory
Page 284
10A. Introducing trigonometric equations
Theory
Page 284
10B. Harder trigonometric equations
Theory
Page 292
10C. Trigonometric identities
Theory
Page 302
10D. Using identities to solve equations
Theory
Page 308
11. Geometry of triangles and circles
Theory
Page 315
11A. Right-angled triangles
Theory
Page 316
11B. The sine rule
Theory
Page 318
11C. The cosine rule
Theory
Page 323
11D. Area of a triangle
Theory
Page 329
11E. Trigonometry in three dimensions
Theory
Page 332
11F. Length of an arc
Theory
Page 337
11G. Area of a sector
Theory
Page 341
11H. Triangles and circles
Theory
Page 344
12. Further trigonometry
Theory
Page 357
12A. Double angle identities
Theory
Page 358
12B. Compound angle identities
Theory
Page 365
12C. Functions of the form a sin x + b cos x
Theory
Page 370
12D. Reciprocal trigonometric functions
Theory
Page 375
13. Vectors
Theory
Page 386
13A. Positions and displacements
Theory
Page 386
13B. Vector algebra
Theory
Page 395
13C. Distances
Theory
Page 400
13D. Angles
Theory
Page 404
13E. Properties of the scalar product
Theory
Page 408
13F. Areas
Theory
Page 413
13G. Properties of the vector product
Theory
Page 415
14. Lines and planes in space
Theory
Page 424
14A. Vector equation of a line
Theory
Page 424
14B. Solving problems with lines
Theory
Page 431
14C. Other forms of equation of a line
Theory
Page 443
14D. Equation of a plane
Theory
Page 450
14E. Angles and intersections between lines and planes
Theory
Page 460
14F. Intersection of three planes
Theory
Page 468
14G. Strategies for solving problems with lines and planes
Theory
Page 474
15. Complex numbers
Theory
Page 487
15A. Definition and basic arithmetic of i
Theory
Page 487
15B. Geometric interpretation
Theory
Page 493
15C. Properties of complex conjugates
Theory
Page 498
15D. Complex solutions to polynomial equations
Theory
Page 504
15E. Sums and products of roots of polynomials
Theory
Page 509
15F. Operations in polar form
Theory
Page 515
15G. Complex exponents
Theory
Page 521
15H. Roots of complex numbers
Theory
Page 523
15I. Using complex numbers to derive trigonometric identities
Theory
Page 528
16. Basic differentiation and its applications
Theory
Page 538
16A. Sketching derivatives
Theory
Page 538
16B. Differentiation from first principles
Theory
Page 546
16C. Rules of differentiation
Theory
Page 549
16D. Interpreting derivatives and second derivatives
Theory
Page 552
16E. Trigonometric functions
Theory
Page 558
16F. The exponential and natural logarithm functions
Theory
Page 560
16G. Tangents and normals
Theory
Page 561
16H. Stationary points
Theory
Page 565
16I. General points of inflexion
Theory
Page 571
16J. Optimisation
Theory
Page 573
17. Basic integration and its applications
Theory
Page 580
17A. Reversing differentiation
Theory
Page 580
17B. Constant of integration
Theory
Page 582
17C. Rules of integration
Theory
Page 583
17D. Integrating x^-1 and e^x
Theory
Page 586
17E. Integrating trigonometric functions
Theory
Page 587
17F. Finding the equation of a curve
Theory
Page 588
17G. Definite integration
Theory
Page 590
17H. Geometrical significance of definite integration
Theory
Page 592
17I. The area between a curve and the y-axis
Theory
Page 599
17J. The area between two curves
Theory
Page 602
18. Further differentiation methods
Theory
Page 610
18A. Differentiating composite functions using the chain rule
Theory
Page 610
18B. Differentiating products using the product rule
Theory
Page 615
18C. Differentiating quotients using the quotient rule
Theory
Page 618
18D. Implicit differentiation
Theory
Page 622
18E. Differentiating inverse trigonometric functions
Theory
Page 627
19. Further integration methods
Theory
Page 633
19A. Reversing standard derivatives
Theory
Page 633
19B. Integration by substitution
Theory
Page 637
19C. Using trigonometric identities in integration
Theory
Page 645
19D. Integration using inverse trigonometric functions
Theory
Page 652
19E. Other strategies for integrating quotients
Theory
Page 655
19F. Integration by parts
Theory
Page 660
20. Further applications of calculus
Theory
Page 670
20A. Related rates of change
Theory
Page 670
20B. Kinematics
Theory
Page 674
20C. Volumes of revolution
Theory
Page 679
20D. Optimisation with constraints
Theory
Page 685
21. Summarising data
Theory
Page 700
21A. Some important concepts in statistics
Theory
Page 700
21B. Measures of spread
Theory
Page 702
21C. Frequency tables and grouped data
Theory
Page 706
22. Probability
Theory
Page 716
22A. Introduction to probability
Theory
Page 716
22B. Combined events and Venn diagrams
Theory
Page 722
22C. Tree diagrams and finding the intersection
Theory
Page 726
22D. Independent events
Theory
Page 731
22E. Counting principles in probability
Theory
Page 733
22F. Conditional probability
Theory
Page 735
22G. Further Venn diagrams
Theory
Page 738
22H. Bayes’ theorem
Theory
Page 743
23. Discrete probability distributions
Theory
Page 754
23A. Random variables
Theory
Page 754
23B. Expectation, median and variance of a discrete random variable
Theory
Page 758
23C. The binomial distribution
Theory
Page 762
23D. The Poisson distribution
Theory
Page 769
24. Continuous distributions
Theory
Page 780
24A. Continuous random variables
Theory
Page 780
24B. Expectation and variance of continuous random variables
Theory
Page 784
24C. The normal distribution
Theory
Page 788
24D. Inverse normal distribution
Theory
Page 794
25. Mathematical induction
Theory
Page 802
25A. The principle of mathematical induction
Theory
Page 802
25B. Induction and series
Theory
Page 804
25C. Induction and sequences
Theory
Page 806
25D. Induction and differentiation
Theory
Page 810
25E. Induction and divisibility
Theory
Page 812
25F. Induction and inequalities
Theory
Page 814
26. Questions crossing all chapters
Problem
Page 820
Examination tips
Other
Page 831
Answers
Answer
Page 832
Index
Other
Page 922
Acknowledgements
Other
Page 928
Terms and conditions of use for the CD-ROM
Other
Page 929
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