Edexcel AS and A level Mathematics Pure Mathematics Year 1 AS

Cover......Page 1
Contents......Page 3
Overarching themes......Page 5
Extra online content......Page 7
Chapter 1: Algebraic expressions......Page 10
1.1: Index laws......Page 11
1.2: Expanding brackets......Page 13
1.3: Factorising......Page 15
1.4: Negative and fractional indices......Page 18
1.5: Surds......Page 21
1.6: Rationalising denominators......Page 22
Mixed exercise 1......Page 24
Chapter 2: Quadratics......Page 27
2.1: Solving quadratic equations......Page 28
2.2: Completing the square......Page 31
2.3: Functions......Page 34
2.4: Quadratic graphs......Page 36
2.5: The discriminant......Page 39
2.6: Modelling with quadratics......Page 41
Mixed exercise 2......Page 44
Chapter 3: Equations and inequalities......Page 47
3.1: Linear simultaneous equations......Page 48
3.2: Quadratic simultaneous equations......Page 50
3.3: Simultaneous equations on graphs......Page 51
3.4: Linear inequalities......Page 55
3.5: Quadratic inequalities......Page 57
3.6: Inequalities on graphs......Page 60
3.7: Regions......Page 62
Mixed exercise 3......Page 65
Chapter 4: Graphs and transformations......Page 68
4.1: Cubic graphs......Page 69
4.2: Quartic graphs......Page 73
4.3: Reciprocal graphs......Page 75
4.4: Points of intersection......Page 77
4.5: Translating graphs......Page 80
4.6: Stretching graphs......Page 84
4.7: Transforming functions......Page 88
Mixed exercise 4......Page 91
Review exercise 1......Page 94
Chapter 5: Straight line graphs......Page 98
5.1: y = mx + c......Page 99
5.2: Equations of straight lines......Page 102
5.3: Parallel and perpendicular lines......Page 106
5.4: Length and area......Page 109
5.5: Modelling with straight lines......Page 112
Mixed exercise 5......Page 117
Chapter 6: Circles......Page 122
6.1: Midpoints and perpendicular bisectors......Page 123
6.2: Equation of a circle......Page 126
6.3: Intersections of straight lines and circles......Page 130
6.4: Use tangent and chord properties......Page 132
6.5: Circles and triangles......Page 137
Mixed exercise 6......Page 141
Chapter 7: Algebraic methods......Page 146
7.1: Algebraic fractions......Page 147
7.2: Dividing polynomials......Page 148
7.3: The factor theorem......Page 152
7.4: Mathematical proof......Page 155
7.5: Methods of proof......Page 159
Mixed exercise 7......Page 163
Chapter 8: The binomial expansion......Page 167
8.1: Pascal’s triangle......Page 168
8.2: Factorial notation......Page 170
8.3: The binomial expansion......Page 172
8.4: Solving binomial problems......Page 174
8.5: Binomial estimation......Page 176
Mixed exercise 8......Page 178
Chapter 9: Trigonometric ratios......Page 182
9.1: The cosine rule......Page 183
9.2: The sine rule......Page 188
9.3: Areas of triangles......Page 194
9.4: Solving triangle problems......Page 196
9.5: Graphs of sine, cosine and tangent......Page 201
9.6: Transforming trigonometric graphs......Page 203
Mixed Exercise 9......Page 207
Chapter 10: Trigonometric identities and equations......Page 211
10.1: Angles in all four quadrants......Page 212
10.2: Exact values of trigonometrical ratios......Page 217
10.3: Trigonometric identities......Page 218
10.4: Simple trigonometric equations......Page 222
10.5: Harder trigonometric equations......Page 226
10.6: Equations and identities......Page 228
Mixed exercise 10......Page 231
Review exercise 2......Page 235
Chapter 11: Vectors......Page 239
11.1: Vectors......Page 240
11.2: Representing vectors......Page 244
11.3: Magnitude and direction......Page 248
11.4: Position vectors......Page 251
11.5: Solving geometric problems......Page 253
11.6: Modelling with vectors......Page 257
Mixed exercise 11......Page 260
Chapter 12: Differentiation......Page 264
12.1: Gradients of curves......Page 265
12.2: Finding the derivative......Page 268
12.3: Differentiating xn......Page 271
12.4: Differentiating quadratics......Page 273
12.5: Differentiating functions with two or more terms......Page 275
12.6: Gradients, tangents and normal......Page 277
12.7: Increasing and decreasing functions......Page 279
12.8: Second order derivatives......Page 280
12.9: Stationary points......Page 282
12.10: Sketching gradient functions......Page 286
12.11: Modelling with differentiation......Page 288
Mixed exercise 12......Page 291
Chapter 13: Integration......Page 296
13.1: Integrating xn......Page 297
13.2: Indefinite integrals......Page 299
13.3: Finding functions......Page 302
13.4: Definite integrals......Page 304
13.5: Areas under curves......Page 306
13.6: Areas under the x-axis......Page 309
13.7: Areas between curves and lines......Page 311
Mixed exercise 13......Page 315
Chapter 14: Exponentials and logarithms......Page 320
14.1: Exponential functions......Page 321
14.2: y = ex......Page 323
14.3: Exponential modelling......Page 326
14.4: Logarithms......Page 328
14.5: Laws of logarithms......Page 330
14.6: Solving equations using logarithms......Page 333
14.7: Working with natural logarithms......Page 335
14.8: Logarithms and non-linear data......Page 337
Mixed exercise 14......Page 343
Review exercise 3......Page 347
Practice exam paper......Page 351
Answers......Page 354
Index......Page 408