AQA A Level Mathematics Year 2

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 Proof......Page 11
1.1 Problem solving......Page 12
1.2 Methods of proof......Page 15
2.1 Radians......Page 22
2.2 Circular measure......Page 27
2.3 Small-angle approximations......Page 32
R.1 Surds and indices......Page 37
R.2 Exponentials and logarithms......Page 39
3 Sequences and series......Page 45
3.1 Definitions and notation......Page 46
3.2 Arithmetic sequences and series......Page 53
3.3 Geometric sequences and series......Page 57
R.1 Equations and inequalities......Page 66
R.2 Polynomials......Page 71
Review: Graphs and transformations......Page 74
4.1 The language of functions......Page 81
4.2 Composite functions......Page 90
4.3 The modulus function......Page 100
5 Differentiation......Page 106
Review: Differentiation......Page 107
5.1 The shape of curves......Page 112
5.2 The chain rule......Page 120
5.3 Connected rates of change......Page 126
5.4 The product and quotient rules......Page 128
Practice questions: Pure mathematics 1......Page 137
1 Working with triangles......Page 140
Problem solving: Triples......Page 144
6.1 Reciprocal trigonometric functions......Page 147
6.2 Working with trigonometric equations and identities......Page 152
6.3 Solving equations involving radians......Page 157
7 Further algebra......Page 160
Review: Pascal’s triangle and the binomial expansion......Page 161
7.1 The general binomial expansion......Page 163
7.2 Simplifying algebraic expressions......Page 168
7.3 Partial fractions......Page 173
8 Trigonometric identities......Page 179
8.1 Compound angle formulae......Page 180
8.2 Double angle formulae......Page 184
8.3 The forms rcos (θ ± α), rsin (θ ± α)......Page 187
9 Further differentiation......Page 194
9.1 Differentiating exponentials and logarithms......Page 195
9.2 Differentiating trigonometric functions......Page 199
9.3 Implicit differentiation......Page 203
10 Integration......Page 207
Review: Integration......Page 208
10.1 Finding areas......Page 212
10.2 Integration by substitution......Page 221
10.3 Integrating other functions......Page 226
10.4 Integration involving the natural logarithmic function......Page 230
10.5 Further integration by substitution......Page 237
10.6 Integration by parts......Page 239
Practice questions: Pure mathematics 2......Page 247
R.1 Line segments......Page 250
R.2 Circles......Page 253
Problem solving: Eggs......Page 258
11 Parametric equations......Page 260
11.1 Graphs from parametric equations......Page 262
11.2 Finding the equation by eliminating the parameter......Page 265
11.3 Parametric differentiation......Page 271
12.1 Vectors......Page 276
12.2 Using vectors to solve problems......Page 283
13 Differential equations......Page 288
13.1 First order differential equations......Page 289
13.2 Solving differential equations by separating the variables......Page 294
14 Numerical methods......Page 301
14.1 Solving equations numerically......Page 302
14.2 The Newton–Raphson method......Page 314
14.3 Numerical integration......Page 318
Problem solving: Numerical integration......Page 326
Practice questions: Pure mathematics 3......Page 329
R.1 Statistical problem solving......Page 331
Problem solving: Trains......Page 342
Review: Probability......Page 344
15.1 The probability of events from two experiments......Page 349
15.2 Conditional probability......Page 354
Review: The binomial distribution......Page 363
16.1 Discrete random variables......Page 365
16.2 The Normal distribution......Page 372
Review......Page 388
17.1 Interpreting sample data using the Normal distribution......Page 394
17.2 Bivariate data: correlation and association......Page 404
Practice questions: Statistics......Page 420
Review: Motion in one dimension......Page 424
18.1 Motion in two or three dimensions......Page 433
Review: Forces and motion......Page 448
19.1 Forces in equilibrium......Page 456
19.2 Finding resultant forces......Page 466
19.3 Newton’s second law in two dimensions......Page 472
20 Moments of forces......Page 480
20.1 Rigid bodies......Page 481
21 Projectiles......Page 492
21.1 Equations for projectile motion......Page 493
21.2 Projectile problems......Page 496
21.3 Further examples......Page 500
21.4 The path of a projectile......Page 508
21.5 General equations......Page 509
Problem solving: Fireworks and aeroplanes......Page 514
22 A model for friction......Page 516
22.1 A model for friction......Page 517
Practice questions: Mechanics......Page 528
Data set......Page 531
Answers......Page 533
E......Page 595
P......Page 596
U......Page 597
W......Page 598