This book is an attempt to cover, in one volume, the content outlined in the Cambridge O Level Additional Mathematics (4037) and Cambridge IGCSE Additional Mathematics (0606) syllabuses. The book can be used as a preparation for GCE Advanced Level Mathematics. The book has been endorsed by Cambridge.
The book can be used as a scheme of work but it is expected that the teacher will choose the order of topics. Exercises in the book range from routine practice and consolidation of basic skills, to problem-solving exercises that are quite demanding.
Author(s): Michael Haese, Sandra Haese, Mark Humphries, Chris Sangwin
Edition: 1st
Publisher: Haese Mathematics
Year: 2014
Language: English
Pages: 504
Tags: IGCSE, O Levels, Pure Mathematics, Further Mathematics, Additional Mathematics, Haese
1 SETS AND VENN DIAGRAMS 11
A Sets 12
B Interval notation 15
C Relations 17
D Complements of sets 18
E Properties of union and intersection 20
F Venn diagrams 21
G Numbers in regions 26
H Problem solving with Venn diagrams 28
Review set 1A 31
Review set 1B 33
2 FUNCTIONS 35
A Relations and functions 36
B Function notation 40
C Domain and range 43
D The modulus function 46
E Composite functions 49
F Sign diagrams 51
G Inverse functions 54
Review set 2A 60
Review set 2B 61
3 QUADRATICS 63
A Quadratic equations 65
B Quadratic inequalities 72
C The discriminant of a quadratic 73
D Quadratic functions 75
E Finding a quadratic from its graph 87
F Where functions meet 91
G Problem solving with quadratics 93
H Quadratic optimisation 95
Review set 3A 98
Review set 3B 99
4 SURDS, INDICES, AND EXPONENTIALS 101
A Surds 102
B Indices 107
C Index laws 108
D Rational indices 111
E Algebraic expansion and factorisation 113
F Exponential equations 116
G Exponential functions 118
H The natural exponential e^x 123
Review set 4A 125
Review set 4B 127
5 LOGARITHMS 129
A Logarithms in base 10 130
B Logarithms in base a 133
C Laws of logarithms 135
D Logarithmic equations 138
E Natural logarithms 142
F Solving exponential equations using logarithms 145
G The change of base rule 147
H Graphs of logarithmic functions 149
Review set 5A 152
Review set 5B 154
6 POLYNOMIALS 155
A Real polynomials 156
B Zeros, roots, and factors 162
C The Remainder theorem 167
D The Factor theorem 169
E Cubic equations 171
Review set 6A 173
Review set 6B 173
7 STRAIGHT LINE GRAPHS 175
A Equations of straight lines 177
B Intersection of straight lines 183
C Intersection of a straight line and a curve 186
D Transforming relationships to straight line form 187
E Finding relationships from data 192
Review set 7A 197
Review set 7B 199
8 THE UNIT CIRCLE AND RADIAN MEASURE 201
A Radian measure 202
B Arc length and sector area 205
C The unit circle and the trigonometric ratios 208
D Applications of the unit circle 213
E Multiples of π/6 and π/4 217
F Reciprocal trigonometric ratios 221
Review set 8A 221
Review set 8B 222
9 TRIGONOMETRIC FUNCTIONS 225
A Periodic behaviour 226
B The sine function 230
C The cosine function 236
D The tangent function 238
E Trigonometric equations 240
F Trigonometric relationships 246
G Trigonometric equations in quadratic form 250
Review set 9A 251
Review set 9B 252
10 COUNTING AND THE BINOMIAL EXPANSION 255
A The product principle 256
B Counting paths 258
C Factorial notation 259
D Permutations 262
E Combinations 267
F Binomial expansions 270
G The Binomial Theorem 273
Review set 10A 277
Review set 10B 278
11 VECTORS 279
A Vectors and scalars 280
B The magnitude of a vector 284
C Operations with plane vectors 285
D The vector between two points 289
E Parallelism 292
F Problems involving vector operations 294
G Lines 296
H Constant velocity problems 298
Review set 11A 302
Review set 11B 303
12 MATRICES 305
A Matrix structure 307
B Matrix operations and definitions 309
C Matrix multiplication 315
D The inverse of a 2 × 2 matrix 323
E Simultaneous linear equations 328
Review set 12A 330
Review set 12B 331
13 INTRODUCTION TO DIFFERENTIAL CALCULUS 333
A Limits 335
B Rates of change 336
C The derivative function 340
D Differentiation from first principles 342
E Simple rules of differentiation 344
F The chain rule 348
G The product rule 351
H The quotient rule 353
I Derivatives of exponential functions 355
J Derivatives of logarithmic functions 359
K Derivatives of trigonometric functions 361
L Second derivatives 363
Review set 13A 365
Review set 13B 366
14 APPLICATIONS OF DIFFERENTIAL CALCULUS 367
A Tangents and normals 369
B Stationary points 375
C Kinematics 380
D Rates of change 388
E Optimisation 393
F Related rates 399
Review set 14A 402
Review set 14B 405
15 INTEGRATION 409
A The area under a curve 410
B Antidifferentiation 415
C The fundamental theorem of calculus 417
D Integration 422
E Rules for integration 424
F Integrating f(ax+b) 428
G Definite integrals 431
Review set 15A 434
Review set 15B 435
16 APPLICATIONS OF INTEGRATION 437
A The area under a curve 438
B The area between two functions 440
C Kinematics 444
Review set 16A 449
Review set 16B 450
ANSWERS 453
INDEX 503
