AQA A Level Maths: Year 1 and 2: Bridging Edition

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Description

Contents

Reviews

Language

English

ISBN

9781382017954

Front Cover

IFC

Title Page

Imprint

Contents

About this book

Year 1/AS Level

PURE

Chapter 1: Algebra 1

Introduction

Bridging Unit 1

Topic A: Indices and surds

Topic B: Solving linear equations and rearranging formulae

Topic C: Factorising quadratics and simple cubics

Topic D: Completing the square

Topic E: The quadratic formula

Topic F: Line graphs

Topic G: Circles

1.1 Argument and proof

1.2 Index laws

1.3 Surds

1.4 Quadratic functions

1.5 Lines and circles

1.6 Simultaneous equations

1.7 Inequalities

Summary and review

Exploration

Assessment

Chapter 2: Polynomials and the binomial theorem

Introduction

Bridging Unit 2

Topic A: Expanding brackets

Topic B: Algebraic division

Topic C: Cubic, quartic and reciprocal graphs

2.1 Expanding and factorising

2.2 The binomial theorem

2.3 Algebraic division

2.4 Curve sketching

Summary and review

Exploration

Assessment

Chapter 3: Trigonometry

Introduction

Bridging Unit 3

Topic A: Trigonometry 1

Topic B: Trigonometry 2

3.1 Sine, cosine and tangent

3.2 The sine and cosine rules

Summary and review

Exploration

Assessment

Chapter 4: Differentiation and integration

Introduction

Bridging Unit 4

Topic A: Coordinate geometry

4.1 Differentiation from first principles

4.2 Differentiating axn and Leibniz notation

4.3 Rates of change

4.4 Tangents and normals

4.5 Turning points

4.6 Integration

4.7 Area under a curve

Summary and review

Exploration

Assessment

Chapter 5: Exponentials and logarithms

Introduction

Bridging Unit 5

Topic A: Exponentials and logarithms

5.1 The laws of logarithms

5.2 Exponential functions

5.3 Exponential processes

5.4 Curve fitting

Summary and review

Exploration

Assessment

Chapter 6: Vectors

Introduction

6.1 Definitions and properties

6.2 Components of a vector

Summary and review

Exploration

Assessment

Assessment, chapters 1–6: Pure

MECHANICS

Chapter 7: Units and kinematics

Introduction

Bridging Unit 7

Topic A: Kinematics

7.1 Standard units and basic dimensions

7.2 Motion in a straight line – definitions and graphs

7.3 Equations of motion for constant acceleration

7.4 Motion with variable acceleration

Summary and review

Exploration

Assessment

Chapter 8: Forces and Newton’s laws

Introduction

Bridging Unit 8

Topic A: Forces and Newton's laws

8.1 Forces 1

8.2 Dynamics 1

8.3 Motion under gravity

8.4 Systems of forces

Summary and review

Exploration

Assessment

Assessment, chapters 7–8: Mechanics

STATISTICS

Chapter 9: Collecting, representing and interpreting data

Introduction

Bridging Unit 9

Topic A: Averages

Topic B: Measures of spread

Topic C: Histograms

9.1 Sampling

9.2 Central tendency and spread

9.3 Single-variable data

9.4 Bivariate data

Summary and review

Exploration

Assessment

Chapter 10: Probability and discrete random variables

Introduction

10.1 Probability

10.2 Binomial distribution

Summary and review

Exploration

Assessment

Chapter 11: Hypothesis testing 1

Introduction

Bridging Unit 11

Topic A: Hypothesis testing

11.1 Formulating a test

11.2 The critical region

Summary and review

Exploration

Assesment

Assessment, chapters 9–11: Statistics

Year 2

PURE

Chapter 12: Algebra 2

Introduction

12.1 Further mathematical proof

12.2 Functions

12.3 Parametric equations

12.4 Algebraic fractions

12.5 Partial fractions

12.6 Vectors in 3D

Summary and review

Exploration

Assessment

Chapter 13: Sequences

Introduction

13.1 The binomial series

13.2 Introduction to sequences

13.3 Arithmetic sequences

13.4 Geometric sequences

Summary and review

Exploration

Assessment

Chapter 14: Trigonometric identities

Introduction

14.1 Radians

14.2 Reciprocal and inverse trigonometric functions

14.3 Compound angles

14.4 Equivalent forms for a cos θ + b sin θ

Summary and review

Exploration

Assessment

Chapter 15: Differentiation 2

Introduction

15.1 The shapes of functions

15.2 Trigonometric function

15.3 Exponential and logarithmic functions

15.4 The product and quotient rules

15.5 The chain rule

15.6 Inverse functions

15.7 Implicit differentiation

15.8 Parametric functions

Summary and review

Exploration

Assessment

Chapter 16: Integration and differential equations

Introduction

16.1 Standard integrals

16.2 Integration by substitution

16.3 Integration by parts

16.4 Integrating rational functions

16.5 Integrating parametric functions

16.6 Differential equations

Summary and review

Exploration

Assessment

Chapter 17: Numerical methods

Introduction

17.1 Simple root finding

17.2 Iterative root finding

17.3 Newton-Raphson root finding

17.4 Numerical integration

Summary and review

Exploration

Assessment

Assessment, chapters 12–17: Pure

MECHANICS

Chapter 18: Motion in two dimensions

Introduction

18.1 Two-dimensional motion with constant acceleration

18.2 Two-dimensional motion with variable acceleration

18.3 Motion under gravity 2

18.4 Motion under forces

Summary and review

Exploration

Assessment

Chapter 19: Forces 2

Introduction

19.1 Statics

19.2 Dynamics 2

19.3 Moments

Summary and review

Exploration

Assessment

Assessment, chapters 18–19: Mechanics

STATISTICS

Chapter 20 Probability and continuous random variables

Introduction

20.1 Conditional probability

20.2 Modelling with probability

20.3 The Normal distribution

20.4 Using the Normal distribution as an approximation to the binomial

Summary and review

Exploration

Assessment

Chapter 21: Hypothesis testing 2

Introduction

21.1 Testing correlation

21.2 Testing a Normal distribution

Summary and review

Exploration

Assessment

Assessment, chapters 20–21: Statistics

Mathematical formulae

Statistical tables

Mathematical formulae – to learn

Mathematical notation

Answers

Index

IBC

Back Cover

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