## Edexcel AS and A Level Modular Mathematics Core Mathematics 3 C3

(2016)

### Abstract

Edexcel and A Level Modular Mathematics C3 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: Algebraic fractions 1
1.1: Simplify algebraic fractions by cancelling common factors 2
1.2: Multiplying and dividing algebraic fractions 4
1.3: Adding and subtracting algebraic fractions 6
1.4: Dividing algebraic fractions and the remainder theorem 8
Summary of key points 11
Chapter 2: Functions 12
2.1: Mapping diagrams and graphs of operations 13
2.2: Functions and function notation 14
2.3: Range, mapping diagrams, graphs and definitions of functions 17
2.4: Using composite functions 20
2.5: Finding and using inverse functions 23
Summary of key points 30
Chapter 3: The exponential and log functions 31
3.1: Introducing exponential functions of the form y=ax 32
3.2: Graphs of exponential functions and modelling using y=ex 33
3.3: Using ex and the inverse of the exponential function logex 36
Summary of key points 44
Chapter 4: Numerical methods 45
4.1: Finding approximate roots of f(x)=0 graphically 46
4.2: Using iterative and algebraic methods to find approximate roots of f(x)=0 50
Summary of key points 57
Review Exercise 1 58
Chapter 5: Transforming graphs of functions 63
5.1: Sketching graphs of the modulus function y=|f(x)| 64
5.2: Sketching graphs of the function y=f(|x|) 67
5.3: Solving equations involving a modulus 69
5.4: Applying a combination of transformations to sketch curves 72
5.5: Sketching transformations and labelling the coordinates of given point 77
Summary of key points 82
Chapter 6: Trigonometry 83
6.1: The functions secant ϴ, cosecant ϴ, and cotangent ϴ 84
6.2: The graphs of secant ϴ, cosecant ϴ, and cotangent ϴ 87
6.3: Simplifying expressions, proving identities and solving equations using sec ϴ, cosec ϴ, and cot ϴ 90
6.4: Using the identities 1+tan2ϴ=sec2ϴ and 1+cot2ϴ=cosec2ϴ 93
6.5: Using inverse trigonometrical functions and their graphs 98
Summary of key points 104
Chapter 7: Further trigonometric identities and their applications 106
7.1: Using addition trigonometrical formulae 107
7.2: Using double angle trigonometrical formulae 113
7.3: Solving equations and proving identities using double angle formulae 117
7.4: Using the form acosϴ+bsinϴ in solving trigonometrical problems 120
7.5: The factor formulae 124
Summary of key points 131
Chapter 8: Differentiation 132
8.1: Differentiating using the chain rule 133
8.2: Differentiating using the product rule 135
8.3: Differentiating using the quotient rule 137
8.4: Differentiating the exponential function 138
8.5: Finding the differential of the logarithmic function 140
8.6: Differentiating sin x 141
8.7: Differentiating cos x 143
8.8: Differentiating tan x 144
8.9: Differentiating further trigonometrical functions 145
8.10: Differentiating functions formed by combining trigonometrical, exponential, logarithmic and polynomial functions 147
Summary of key points 151
Review Exercise 2 152
Practice paper 157
Examination style paper 159
Formulae you need to remember 161
List of symbols and notation 162