AQA A Level Mathematics for A Level Year 1 and AS

Cover......Page 1
Book title......Page 3
Copyright......Page 4
Contents......Page 5
Getting the most from this book......Page 7
Prior knowledge......Page 9
1 Problem solving......Page 11
1.1 Solving problems......Page 12
1.2 Writing mathematics......Page 18
1.3 Proof......Page 22
Problem solving: Mountain modelling......Page 26
2 Surds and indices......Page 29
2.1 Using and manipulating surds......Page 30
2.2 Working with indices......Page 34
3 Quadratic functions......Page 42
3.1 Quadratic graphs and equations......Page 43
3.2 The completed square form......Page 52
3.3 The quadratic formula......Page 57
4 Equations and inequalities......Page 63
4.1 Simultaneous equations......Page 64
4.2 Inequalities......Page 69
5 Coordinate geometry......Page 75
5.1 Working with coordinates......Page 76
5.2 The equation of a straight line......Page 81
5.3 The intersection of two lines......Page 88
5.4 The circle......Page 90
5.5 The intersection of a line and a curve......Page 97
Problem solving: Integer point circles......Page 102
Practice questions: Pure mathematics 1......Page 106
6 Trigonometry......Page 109
6.1 Trigonometric functions......Page 110
6.2 Trigonometric functions for angles of any size......Page 114
6.3 Solving equations using graphs of trigonometric functions......Page 122
6.4 Triangles without right angles......Page 128
6.5 The area of a triangle......Page 136
7 Polynomials......Page 140
7.1 Polynomial expressions......Page 141
7.2 Dividing polynomials......Page 150
7.3 Polynomial equations......Page 152
8 Graphs and transformations......Page 158
8.1 The shapes of curves......Page 159
8.2 Using transformations to sketch curves......Page 165
8.3 Using transformations......Page 174
8.4 Transformations and graphs of trigonometric functions......Page 177
9 The binomial expansion......Page 182
9.1 Binomial expansions......Page 183
9.2 Selections......Page 190
Practice questions: Pure mathematics 2......Page 196
10 Differentiation......Page 200
10.1 The gradient of the tangent as a limit......Page 201
10.2 Differentiation using standard results......Page 204
10.3 Tangents and normals......Page 208
10.4 Increasing and decreasing functions, and turning points......Page 211
10.5 Sketching the graphs of gradient functions......Page 216
10.6 Extending the rule......Page 220
10.7 Higher order derivatives......Page 223
10.8 Practical problems......Page 228
10.9 Finding the gradient from first principles......Page 231
Problem solving: Proofs......Page 236
11 Integration......Page 239
11.1 Integration as the reverse of differentiation......Page 240
11.2 Finding areas......Page 244
11.3 Areas below the x axis......Page 248
11.4 Further integration......Page 251
12.1 Vectors......Page 257
12.2 Working with vectors......Page 263
12.3 Vector geometry......Page 269
13 Exponentials and logarithms......Page 274
13.1 Exponential functions......Page 275
13.2 Logarithms......Page 278
13.3 The exponential function......Page 283
13.4 The natural logarithm function......Page 288
13.5 Modelling curves......Page 290
Practice questions: Pure mathematics 3......Page 298
14 Data collection......Page 301
14.1 Using statistics to solve problems......Page 302
14.2 Sampling......Page 307
15 Data processing, presentation and interpretation......Page 316
15.1 Presenting different types of data......Page 318
15.2 Ranked data......Page 322
15.3 Discrete numerical data......Page 327
15.4 Continuous numerical data......Page 334
15.5 Bivariate data......Page 345
15.6 Standard deviation......Page 352
16 Probability......Page 360
16.1 Working with probability......Page 361
Problem solving: Alphabet puzzle......Page 378
Problem solving: Estimating minnows......Page 380
17 The binomial distribution......Page 382
17.1 Introduction to binomial distribution......Page 383
17.2 Using the binomial distribution......Page 387
18 Statistical hypothesis testing using the binomial distribution......Page 393
18.1 The principles and language of hypothesis testing......Page 395
18.2 Extending the language of hypothesis testing......Page 401
Practice questions: Statistics......Page 409
19.1 The language of motion......Page 413
19.2 Speed and velocity......Page 416
19.3 Acceleration......Page 421
19.4 Using areas to find distances and displacement......Page 425
19.5 The constant acceleration formulae......Page 431
19.6 Further examples......Page 436
20.1 Force diagrams......Page 444
20.2 Force and motion......Page 450
20.3 Types of forces......Page 452
20.4 Pulleys......Page 457
20.5 Applying Newton's second law along a line......Page 460
20.6 Newton's second law applied to connected objects......Page 467
Problem solving: Reviewing models for air resistance......Page 478
21 Variable acceleration......Page 482
21.1 Using differentiation......Page 483
21.2 Finding displacement from velocity......Page 485
21.3 The constant acceleration formulae revisited......Page 489
Problem solving: Human acceleration......Page 494
Practice questions: Mechanics......Page 497
Dataset......Page 500
Answers*......Page 502
E......Page 571
N......Page 572
S......Page 573
W......Page 574