Core Math 4 (Edexcel AS and A level Modular Math)
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Keith Pledger
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Core Math 4 (Edexcel AS and A level Modular Math)
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1. Partial fractions
Theory
Page 9
1.1 Adding and subtracting algebraic fractions
Theory
Page 10
1.2 Partial fractions with two linear factors in the denominator
Theory
Page 11
1.3 Partial fractions with three or more linear factors in the denominator
Theory
Page 12
1.4 Partial fractions with repeated linear factors in the denominator
Theory
Page 14
1.5 Improper fractions into partial fractions
Theory
Page 15
2. Coordinate geometry in the $(x,y)$ plane
Theory
Page 18
2.1 Parametric equations used to define the coordinates of a point
Theory
Page 19
2.2 Using parametric equations in coordinate geometry
Theory
Page 21
2.3 Converting parametric equations into Cartesian equations
Theory
Page 24
2.4 Finding the area under a curve given by parametric equations
Theory
Page 26
3. The binomial expansion
Theory
Page 31
3.1 The binomial expansion for a positive integral index
Theory
Page 32
3.2 Using the binomial expansion to expand $(a+bx)^n$
Theory
Page 37
3.3 Using partial fractions with the binomial expansion
Theory
Page 39
4. Differentiation
Theory
Page 44
4.1 Differentiating functions given parametrically
Theory
Page 45
4.2 Differentiating relations which are implicit
Theory
Page 47
4.3 Differentiating the function $a^x$
Theory
Page 49
4.4 Differentiation and rates of change
Theory
Page 50
4.5 Simple differential equations
Theory
Page 51
5. Vectors
Theory
Page 59
5.1 Vector definitions and vector diagrams
Theory
Page 60
5.2 Vector arithmetic and the unit vector
Theory
Page 64
5.3 Using vectors to describe points in 2 or 3 dimensions
Theory
Page 68
5.4 Cartesian components of a vector in 2 dimensions
Theory
Page 69
5.5 Cartesian components of a vector in 3 dimensions
Theory
Page 72
5.6 Extending 2 dimensional vector results to 3 dimensions
Theory
Page 75
5.7 The scalar product of two vectors
Theory
Page 77
5.8 The vector equation of a straight line
Theory
Page 83
5.9 Intersecting straight line vector equations
Theory
Page 87
5.10 The angle between two straight lines
Theory
Page 89
6. Integration
Theory
Page 95
6.1 Integrating standard functions
Theory
Page 96
6.2 Integrating using the reverse chain rule
Theory
Page 98
6.3 Using trigonometric identities in integration
Theory
Page 100
6.4 Using partial fractions to integrate expressions
Theory
Page 103
6.5 Using standard patterns to integrate expressions
Theory
Page 106
6.6 Integration by substitution
Theory
Page 109
6.7 Integration by parts
Theory
Page 113
6.8 Numerical integration
Theory
Page 116
6.9 Integration to find areas and volumes
Theory
Page 119
6.10 Using integration to solve differential equations
Theory
Page 122
6.11 Differential equations in context
Theory
Page 125
Review exercise
Problem
Page 137
Practice paper
Test
Page 148
Examination style paper
Test
Page 150
Formulae you need to remember
Theory
Page 152
List of symbols and notation
Other
Page 153
Answers
Answer
Page 156
Index
Other
Page 168
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