## Edexcel AS and A Level Modular Mathematics Core Mathematics 1 C1

(2016)

### Abstract

Edexcel and A Level Modular Mathematics C1 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: Algebra and functions 1
1.1: Simplifying expressions by collecting like terms 2
1.2: The rules of indices 3
1.3: Expanding an expression 4
1.4: Factorising expressions 5
1.6: The rules of indices for all rational exponents 8
1.7: The use and manipulation of surds 10
1.8: Rationalising the denominator of a fraction when it is a surd 11
Summary of key points 14
2.1: Plotting the graphs of quadratic functions 16
2.2: Solving quadratic equations by factorisation 17
2.3: Completing the square 19
2.4: Solving quadratic equations by completing the square 20
2.5: Solving quadratic equations by using the formula 22
2.6: Sketching graphs of quadratic equations 23
Summary of key points 26
Chapter 3: Equations and inequalities 27
3.1: Solving simultaneous linear equations by elimination 28
3.2: Solving simultaneous linear equations by substitution 29
3.3: Using substitution when one equation is linear and the other is quadratic 30
3.4: Solving linear inequalities 31
Summary of key points 40
Chapter 4: Sketching curves 41
4.1: Sketching the graphs of cubic functions 42
4.2: Interpreting graphs of cubic functions 47
4.3: Sketching the reciprocal function 49
4.4: Using the intersection points of graphs of functions to solve equations 52
4.5: The effect of the transformations f(x+a), f(x-a), and f(x)+a 55
4.6: The effect of the transformations f(ax) and af(x) 60
4.7: Performing transformations on the sketches of curves 64
Summary of key points 68
Review Exercise 1 69
Chapter 5: Coordinate geometry in the (x , y) plane 73
5.1: The equation of a straight line in the form y=mx+c or ax+by+c=0 74
5.2: The gradient of a straight line 77
5.3: The equation of a straight line of the form y-y1=m(x-x1) 79
5.4: The formula for finding the equation of a straight line 81
5.5: The conditions for two straight lines to be parallel or perpendicular 84
Summary of key points 90
Chapter 6: Sequences and series 91
6.1: Introduction to sequences 92
6.2: The nth term of a sequence 93
6.3: Sequences generated by a recurrence relationship 95
6.4: Arithmetic sequences 98
6.5: Arithmetic series 100
6.6: The sum to n of an arithmetic series 103
6.7: Using ∑ notation 107
Summary of key points 111
Chapter 7: Differentiation 112
7.1: The derivative of f(x) as the gradient of the tangent to the graph y=f(x) 113
7.2: Finding the formula for the gradient of xn 116
7.3: Finding the gradient formula of simple functions 120
7.4: The gradient formula for a function where the powers of x are real numbers 124
7.5: Expanding or simplifying functions to make them easier to differentiate 125
7.6: Finding second order derivatives 126
7.7: Finding the rate of change of a function at a particular point 127
7.8: Finding the equation of the tangent and normal to a curve at a point 128
Summary of key points 132
Chapter 8: Integration 133
8.1: Integrating xn 134
8.2: Integrating simple expressions 136
8.3: Using the integral sign 137
8.4: Simplifying expressions before integrating 138
8.5: Finding the constant of integration 140
Summary of key points 142
Review Exercise 2 143
Practice paper 147
Examination style paper 149
Formulae you need to remember 152
List of symbols and notation 153