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CONTENTS

1 Functions
2 Inverse Functions
3 Graphs of Inverse Functions
4 The function y equals e to the x
5 The Chain Rule
6 Differentiating lnx
7 Differentiating some Trig Functions
8 The Product Rule
8a The Product Rule (OCR)
9 Differentiating Harder Products
9a Differentiating Harder Products (OCR)
10 Reciprocal Trig Ratios
11 Proving Trig Identities
12 The Quotient Rule
12a The Quotient Rule (OCR)
13 Inverse Trig Functions
14 Differentiating Inverse Trig Functions
15 More Transformations
16 The Modulus Function
17 Iteration using x=g(x)
18 Iteration diagrams and convergence
19 Newton-Raphson Iteration
20 The Mid-Ordinate Rule
21 Simpson's Rule
22 Integrating the Simple Functions
22a Integrating the Simple Functions (OCR)
23 Integrating some Compound Functions
23a Integrating some Compound Functions (OCR)
24 Calculus using cosx and sinx (OCR)
25 Integration by Parts
26 Integration by Substitution Part 1
27 Integration by Substitution Part 2
28 Integration giving Logs
29 Volumes of Revolution
31 Double Angle Formulae
32 The function acosx + bsinx
33 The equation acosx + bsinx = c
34 More on the Factor and Remainder Theorems
35 Algebraic Fractions
36 More Algebraic Division
37 Proof
38 Implicit Differentiation
39 Connected Rates of Change
40 More on the Trapezium Rule
41 Parametric Equations
42 Differentiating Parametric Equations
43 Partial Fractions
44 More Binomial Expansions
45 Even More Binomial Expansions
46 Applications of Partial Fractions
47 Solving Differential Equations
48 Growth and Decay
49 Setting up and Solving Differential Equations
50 Vectors
51 The Vector Equation of a Line
52 The Intersection of Lines
53 The Scalar Product of 2 Vectors
54 Applications of the Scalar Product
55 The Vector Equation of a Plane

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