AQA A Level Further Maths: Year 1 / AS Level

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Description

Contents

Reviews

Language

English

ISBN

9781382017909

Front Cover

Title Page

Contents

Chapter 1: Complex numbers

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

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

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

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

12.6 The travelling salesman problem

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

Mathematical formulae

Mathematical notation

Answers

Index

Back Cover

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