BOOK

## Edexcel AS and A Level Modular Mathematics Further Pure Mathematics 1 FP1

(2016)

### Additional Information

#### Book Details

### Abstract

**Edexcel** **and A Level Modular Mathematics FP1** features:

**Student-friendly worked examples and solutions**, leading up to a wealth of practice questions.**Sample exam papers**for thorough exam preparation.**Regular review sections**consolidate learning.**Opportunities for stretch and challenge**presented throughout the course.**‘Escalator section’**to step up from GCSE.

**Solutionbank**and

**Exam Café**to support, motivate and inspire students to reach their potential for exam success.

contains fully worked solutions with hints and tips for every question in the Student Books.**Solutionbank**includes a revision planner and checklist as well as a fully worked examination-style paper with examiner commentary.**Exam Café**

### Table of Contents

Section Title | Page | Action | Price |
---|---|---|---|

Cover | Cover | ||

Contents | ii | ||

About this book | iv | ||

Chapter 1: Complex numbers | 1 | ||

1.1: Real and imaginary numbers | 2 | ||

1.2: Multiplying complex numbers and simplifying powers of i | 5 | ||

1.3: The complex conjugate of a complex number | 7 | ||

1.4: Representing complex numbers on an Argand diagram | 10 | ||

1.5: Finding the value of r, the modulus of a complex number z, and the value of ϴ, the argument of z | 14 | ||

1.6: The modulus-argument form of the complex number z | 19 | ||

1.7: Solving problems involving complex numbers | 21 | ||

1.8: Solving polynomial equations with real coefficients | 24 | ||

Summary of key points | 31 | ||

Chapter 2: Numerical solutions of equations | 32 | ||

2.1: Solving equations of the form f(x)=0 using interval bisection | 33 | ||

2.2: Solving equations of the form f(x)=0 using linear interpolation | 35 | ||

2.3: Solving equations of the form f(x)=0 using the Newton-Raphson process | 38 | ||

Summary of key points | 40 | ||

Chapter 3: Coordinate systems | 41 | ||

3.1: Introduction to parametric equations | 42 | ||

3.2: The general equation of a parabola | 45 | ||

3.3: The equation for a rectangular hyperbola and finding tangents and normals | 52 | ||

Summary of key points | 62 | ||

Review Exercise 1 | 63 | ||

Chapter 4: Matrix algebra | 72 | ||

4.1: Finding the dimension of a matrix | 73 | ||

4.2: Adding and subtracting matrices of the same dimension | 74 | ||

4.3: Multiplying a matrix by a scalar (number) | 76 | ||

4.4: Multiplying matrices together | 77 | ||

4.5: Using matrices to describe linear transformations | 82 | ||

4.6: Using matrices to represent rotations, reflections and enlargements | 86 | ||

4.7: Using matrix products to represent combinations of transformations | 90 | ||

4.8: Finding the inverse of a 2*2 matrix where it exists | 95 | ||

4.9: Using inverse matrices to reverse the effect of a linear transformation | 99 | ||

4.10: Using the determinant of a matrix to determine the area scale factor of the transformation | 101 | ||

4.11: Using matrices and their inverses to solve linear simultaneous equations | 103 | ||

Summary of key points | 106 | ||

Chapter 5: Series | 107 | ||

5.1: The Σ notation | 108 | ||

5.2: The formula for the sum of the first n natural numbers, Σr | 110 | ||

5.3: Formulae for the sum of the squares of the first n natural numbers, Σr2, and for the sum of the cubes of the first n natural numbers, Σr 3 | 114 | ||

5.4: Using known formulae to sum more complex series | 116 | ||

Summary of key points | 121 | ||

Chapter 6: Proof by mathematical induction | 122 | ||

6.1: Obtaining a proof for the summation of a series, using induction | 123 | ||

6.2: Using proof by induction to prove that an expression is divisible by a certain integer | 127 | ||

6.3: Using mathematical induction to produce a proof for the general terms of a recurrence relation | 130 | ||

6.4: Using proof by induction to prove general statements involving matrix multiplication | 133 | ||

Summary of key points | 136 | ||

Review Exercise 2 | 137 | ||

Examination style paper | 142 | ||

Answers | 144 | ||

Index | 155 |