Cambridge additional mathematics IGCSE (0606)
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English
General book
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Entries: 160
Michael Haese
Sandra Haese
Mark Humphries
Chris Sangwin
igcse
O-level
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Cambridge additional mathematics IGCSE (0606)
Preparing book pages
1
Entries
160
Symbols and Notation Used in This Book
Other
Page 6
1. Sets and Venn Diagrams
Theory
Page 11
1A. Sets
Theory
Page 12
1B. Interval notation
Theory
Page 15
1C. Relations
Theory
Page 17
1D. Complements of sets
Theory
Page 18
1E. Properties of union and intersection
Theory
Page 20
1F. Venn diagrams
Theory
Page 21
1G. Numbers in regions
Theory
Page 26
1H. Problem solving with Venn diagrams
Theory
Page 28
Review set 1A
Problem
Page 31
Review set 1B
Problem
Page 33
2. Functions
Theory
Page 35
2A. Relations and functions
Theory
Page 36
2B. Function notation
Theory
Page 40
2C. Domain and range
Theory
Page 43
2D. The modulus function
Theory
Page 46
2E. Composite functions
Theory
Page 49
2F. Sign diagrams
Theory
Page 51
2G. Inverse functions
Theory
Page 54
Review set 2A
Problem
Page 60
Review set 2B
Problem
Page 61
3. Quadratics
Theory
Page 63
3A. Quadratic equations
Theory
Page 65
3B. Quadratic inequalities
Theory
Page 72
3C. The discriminant of a quadratic
Theory
Page 73
3D. Quadratic functions
Theory
Page 75
3E. Finding a quadratic from its graph
Theory
Page 87
3F. Where functions meet
Theory
Page 91
3G. Problem solving with quadratics
Theory
Page 93
3H. Quadratic optimisation
Theory
Page 95
Review set 3A
Problem
Page 98
Review set 3B
Problem
Page 99
4. Surds, Indices, and Exponentials
Theory
Page 101
4A. Surds
Theory
Page 102
4B. Indices
Theory
Page 107
4C. Index laws
Theory
Page 108
4D. Rational indices
Theory
Page 111
4E. Algebraic expansion and factorisation
Theory
Page 113
4F. Exponential equations
Theory
Page 116
4G. Exponential functions
Theory
Page 118
4H. The natural exponential e^x
Theory
Page 123
Review set 4A
Problem
Page 125
Review set 4B
Problem
Page 127
5. Logarithms
Theory
Page 129
5A. Logarithms in base 10
Theory
Page 130
5B. Logarithms in base a
Theory
Page 133
5C. Laws of logarithms
Theory
Page 135
5D. Logarithmic equations
Theory
Page 138
5E. Natural logarithms
Theory
Page 142
5F. Solving exponential equations using logarithms
Theory
Page 145
5G. The change of base rule
Theory
Page 147
5H. Graphs of logarithmic functions
Theory
Page 149
Review set 5A
Problem
Page 152
Review set 5B
Problem
Page 154
6. Polynomials
Theory
Page 155
6A. Real polynomials
Theory
Page 156
6B. Zeros, roots, and factors
Theory
Page 162
6C. The remainder theorem
Theory
Page 167
6D. The factor theorem
Theory
Page 169
Review set 6A
Problem
Page 173
Review set 6B
Problem
Page 173
7. Straight Line Graphs
Theory
Page 175
7A. Equations of straight lines
Theory
Page 177
7B. Intersection of straight lines
Theory
Page 183
7C. Intersection of a straight line and a curve
Theory
Page 186
7D. Transforming relationships to straight line form
Theory
Page 187
7E. Finding relationships from data
Theory
Page 192
Review set 7A
Problem
Page 197
Review set 7B
Problem
Page 199
8. The Unit Circle and Radian Measure
Theory
Page 201
8A. Radian measure
Theory
Page 202
8B. Arc length and sector area
Theory
Page 205
8C. The unit circle and the trigonometric ratios
Theory
Page 208
8D. Applications of the unit circle
Theory
Page 213
8E. Multiples of π/6 and π/4
Theory
Page 217
8F. Reciprocal trigonometric ratios
Theory
Page 221
Review set 8A
Problem
Page 221
Review set 8B
Problem
Page 222
9. Trigonometric Functions
Theory
Page 225
9A. Periodic behaviour
Theory
Page 226
9B. The sine function
Theory
Page 230
9C. The cosine function
Theory
Page 236
9D. The tangent function
Theory
Page 238
9E. Trigonometric equations
Theory
Page 240
9F. Trigonometric relationships
Theory
Page 246
9G. Trigonometric equations in quadratic form
Theory
Page 250
Review set 9A
Problem
Page 251
Review set 9B
Problem
Page 252
10. Counting and the Binomial Expansion
Theory
Page 255
10A. The product principle
Theory
Page 256
10B. Counting paths
Theory
Page 258
10C. Factorial notation
Theory
Page 259
10D. Permutations
Theory
Page 262
10E. Combinations
Theory
Page 267
10F. Binomial expansions
Theory
Page 270
10G. The Binomial Theorem
Theory
Page 273
Review set 10A
Problem
Page 277
Review set 10B
Problem
Page 278
11. Vectors
Theory
Page 279
11A. Vectors and scalars
Theory
Page 280
11B. The magnitude of a vector
Theory
Page 284
11C. Operations with plane vectors
Theory
Page 285
11D. The vector between two points
Theory
Page 289
11E. Parallelism
Theory
Page 292
11F. Problems involving vector operations
Theory
Page 294
11G. Lines
Theory
Page 296
11H. Constant velocity problems
Theory
Page 298
Review set 11A
Problem
Page 302
Review set 11B
Problem
Page 303
12. Matrices
Theory
Page 305
12A. Matrix structure
Theory
Page 307
12B. Matrix operations and definitions
Theory
Page 309
12C. Matrix multiplication
Theory
Page 315
12D. The inverse of a 2 × 2 matrix
Theory
Page 323
12E. Simultaneous linear equations
Theory
Page 328
Review set 12A
Problem
Page 330
Review set 12B
Problem
Page 331
13. Introduction to Differential Calculus
Theory
Page 333
13A. Limits
Theory
Page 335
13B. Rates of change
Theory
Page 336
13C. The derivative function
Theory
Page 340
13D. Differentiation from first principles
Theory
Page 342
13E. Simple rules of differentiation
Theory
Page 344
13F. The chain rule
Theory
Page 348
13G. The product rule
Theory
Page 351
13H. The quotient rule
Theory
Page 353
13I. Derivatives of exponential functions
Theory
Page 355
13J. Derivatives of logarithmic functions
Theory
Page 359
13K. Derivatives of trigonometric functions
Theory
Page 361
13L. Second derivatives
Theory
Page 363
Review set 13A
Problem
Page 365
Review set 13B
Problem
Page 366
14. Applications of Differential Calculus
Theory
Page 367
14A. Tangents and normals
Theory
Page 369
14B. Stationary points
Theory
Page 375
14C. Kinematics
Theory
Page 380
14D. Rates of change
Theory
Page 388
14E. Optimisation
Theory
Page 393
14F. Related rates
Theory
Page 399
Review set 14A
Problem
Page 402
Review set 14B
Problem
Page 405
15. Integration
Theory
Page 409
15A. The area under a curve
Theory
Page 410
15B. Antidifferentiation
Theory
Page 415
15C. The fundamental theorem of calculus
Theory
Page 417
15D. Integration
Theory
Page 422
15E. Rules for integration
Theory
Page 424
15F. Integrating ∫(ax + b)
Theory
Page 428
15G. Definite integrals
Theory
Page 431
Review set 15A
Problem
Page 434
Review set 15B
Problem
Page 435
16. Applications of Integration
Theory
Page 437
16A. The area under a curve
Theory
Page 438
16B. The area between two functions
Theory
Page 440
16C. Kinematics
Theory
Page 444
Review set 16A
Problem
Page 449
Review set 16B
Problem
Page 450
Answers
Answer
Page 453
Index
Other
Page 503
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