AQA A Level Further Maths: Year 1 + Year 2

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Description

Contents

Reviews

Language

English

ISBN

9781382017893

Contents

PURE

Chapter 1: Complex numbers 1

Introduction

1.1 Properties and arithmetic

1.2 Solving polynomial equations

1.3 Argand diagrams

1.4 Modulus-argument form and loci

Summary and review

Exploration

Assessment

Chapter 2: Algebra and series

Introduction

2.1 Roots of polynomials

2.2 Inequalities

2.3 Summing series and the method of differences

2.4 Proof by induction

2.5 Maclaurin series 1

Summary and review

Exploration

Assessment

Chapter 3: Curve sketching 1

Introduction

3.1 Linear rational functions

3.2 Quadratic rational functions

3.3 Polar coordinates

3.4 Parabolas, ellipses and hyperbolas

3.5 Hyperbolic functions 1

Summary and review

Exploration

Assessment

Chapter 4: Integration 1

Introduction

4.1 Mean values

4.2 Volumes of revolution

Summary and review

Exploration

Assessment

Chapter 5: Matrices 1

Introduction

5.1 Properties and arithmetic

5.2 Transformations

5.3 Systems of linear equations

Summary and review

Exploration

Assessment

Chapter 6: Vectors 1

Introduction

6.1 The vector equation of a line

6.2 The scalar product

6.3 Finding distances 1

Summary and review

Exploration

Assessment

MECHANICS

Chapter 7: Forces and energy

Introduction

7.1 Work, energy and power

7.2 Hooke’s law

7.3 Dimensional analysis

Summary and review

Exploration

Assessment

Chapter 8: Momentum

Introduction

8.1 Conservation of momentum

8.2 Collisions

8.3 Impulses

Summary and review

Exploration

Assessment

Chapter 9: Circular motion 1

Introduction

9.1 Kinematics of circular motion

9.2 Horizontal circular motion

Summary and review

Exploration

Assessment

STATISTICS

Chapter 10: Discrete and continuous random variables

Introduction

10.1 Discrete distributions and expectation

10.2 The Poisson distribution

10.3 Continuous distributions 1

Summary and review

Exploration

Assessment

Chapter 11: Hypothesis testing and contingency tables

Introduction

11.1 Hypothesis testing and errors

11.2 Contingency tables

11.3 Confidence intervals

Summary and review

Exploration

Assessment

DISCRETE

Chapter 12: Graphs and networks 1

Introduction

12.1 Graphs and networks

12.2 Traversing a graph

12.3 Minimum spanning trees and Kruskal’s algorithm

12.4 Minimum spanning trees and Prim’s algorithm

12.5 The route inspection problem

e

12.7 Network flows 1

Summary and review

Exploration

Assessment

Chapter 13: Critical path analysis 1

Introduction

13.1 Activity networks

13.2 Critical paths

Summary and review

Exploration

Assessment

Chapter 14: Linear programming and game theory 1

Introduction

14.1 Constrained optimisation

14.2 Zero-sum games

14.3 Mixed-strategy games

Summary and review

Exploration

Assessment

Chapter 15: Abstract algebra

Introduction

15.1 Binary operations

15.2 Modular arithmetic

Summary and review

Exploration

Assessment

PURE

Chapter 16: Complex numbers 2

Introduction

16.1 Exponential form

16.2 De Moivre’s theorem

16.3 Roots of unity

Summary and review

Exploration

Assessment

Chapter 17: Series

Introduction

17.1 Summing series using partial fractions

17.2 Maclaurin series 2

Summary and review

Exploration

Assessment

Chapter 18: Curve sketching 2

Introduction

18.1 Reciprocal and modulus graphs

18.2 Transformations

18.3 Hyperbolic functions 2

18.4 Rational functions with oblique asymptotes

Summary and review

Exploration

Assessment

Chapter 19: Integration 2

Introduction

19.1 Improper integrals

19.2 Inverse trigonometric functions

19.3 Hyperbolic functions

19.4 Partial fractions

19.5 Reduction formulae

19.6 Polar graphs and areas

19.7 Lengths and surface areas

Summary and review

Exploration

Assessment

Chapter 20: Differential equations

Introduction

20.1 First order equations

20.2 Second order equations

20.3 Simple harmonic motion

20.4 Damped and forced harmonic motion

20.5 Coupled equations

Summary and review

Exploration

Assessment

Chapter 21: Numerical methods

Introduction

21.1 Numerical integration

21.2 Euler’s method

Summary and review

Exploration

Assessment

Chapter 22: Matrices 2

Introduction

22.1 Determinants, inverse matrices and linear equations

22.2 Manipulating determinants

22.3 Eigenvalues and eigenvectors

Summary and review

Exploration

Assessment

Chapter 23: Vectors 2

Introduction

23.1 The vector product

23.2 The equation of a plane

23.3 Finding distances 2

Summary and review

Exploration

Assessment

MECHANICS

Chapter 24: Circular motion 2

Introduction

24.1 Kinematics of circular motion 2

24.2 The conical pendulum

24.3 Vertical circular motion

Summary and review

Exploration

Assessment

Chapter 25: Centres of mass and stability

Introduction

25.1 Moments and couples

25.2 Centre of mass for point masses and laminas

25.3 Centre of mass for laminas

25.4 Further topics with centres of mass

25.5 Equilibrium

Summary and review

Exploration

Assessment

STATISTICS

Chapter 26: Random processes

Introduction

26.1 Continuous distributions 2

26.2 Exponential distribution

Summary and review

Exploration

Assessment

Chapter 27: Hypothesis testing and the t-test

Introduction

27.1 Type II errors and power

27.2 The t-test

Summary and review

Exploration

Assessment

DISCRETE

Chapter 28: Graphs and networks 2

Introduction

28.1 Planar graphs and isomorphisms

28.2 Network flows 2

Summary and review

Exploration

Assessment

Chapter 29: Critical path analysis 2

Introduction

29.1 Gantt charts

29.2 Resourcing

Summary and review

Exploration

Assessment

Chapter 30: Linear programming and game theory 2

Introduction

30.1 Simplex algorithm

30.2 Games as linear programming problems

Summary and review

Exploration

Assessment

Chapter 31: Group theory

Introduction

31.1 Groups

31.2 Subgroups

31.3 Isomorphisms

Summary and review

Exploration

Assessment

Mathematical formulae to learn

Mathematical notation

Answers

Index

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