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

(2016)

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.
PLUS Free LiveText CD-ROM, containing Solutionbank and Exam Café to support, motivate and inspire students to reach their potential for exam success.
• Solutionbank contains fully worked solutions with hints and tips for every question in the Student Books.
• Exam Café includes a revision planner and checklist as well as a fully worked examination-style paper with examiner commentary.

Section Title Page Action Price
Cover Cover
Contents ii
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