**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

30 Trig Addition Formulae

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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