Topics for Year 2 Pure Mathematics

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2.1 The modulus function

2.2 Functions and mappings

2.3 Composite functions

2.4 Inverse functions

2.5 y = |f(x)| and y = f(|x|)

2.6 Combining transformations

2.7 Solving modulus problems

3.1 Arithmetic sequences

3.2 Arithmetic series

3.3 Geometric sequences

3.4 Geometric series

3.5 Sum to infinity

3.6 Sigma notation

3.7 Recurrence relations

3.8 Modelling with series

7.1 Addition formulae

7.2 Using the angle addition formulae

7.3 Double-angle formulae

7.3 The factor theorem

7.4 Solving trigonometric equations

7.5 Simplifying a cos x +/- b sin x

7.6 Proving trigonometric identities

7.7 Modelling with trigonometric functions

8.1 Parametric equations

8.2 Using trigonometric identities

8.3 Curve sketching

8.4 Points of intersection

8.5 Modelling with parametric equations

9.7 Parametric differentiation

9.1 Differentiating sin x and cos x

9.10 Rates of change

9.2 Differentiating exponentials and logarithms

9.3 The chain rule

9.4 The product rule

9.5 The quotient rule

9.6 Differentiating trigonometric functions

9.8 Implicit differentiation

9.9 Using second derivatives

11.10 Solving differential equations

11.1 Integrating standard functions

11.11 Modelling with differential equations

11.2 Integrating f(ax + b)

11.3 Using trigonometric identities

11.4 Reverse chain rule

11.5 Integration by substitution

11.6 Integration by parts

11.7 Partial fractions

11.8 Finding areas

11.9 The trapezium rule

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HOW2NERD PREMIUM

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1.1 Proof by contradiction

1.2 Algebraic fractions

1.3 Partial fractions

1.4 Repeated factors

1.5 Algebraic division

2.1 The modulus function

2.2 Functions and mappings

2.3 Composite functions

2.4 Inverse functions

2.5 y = |f(x)| and y = f(|x|)

2.6 Combining transformations

2.7 Solving modulus problems

3.1 Arithmetic sequences

3.2 Arithmetic series

3.3 Geometric sequences

3.4 Geometric series

3.5 Sum to infinity

3.6 Sigma notation

3.7 Recurrence relations

3.8 Modelling with series

4.1 Expanding (1 + x)^n

4.2 Expanding (a + bx)^n

4.3 Using partial fractions

5.1 Radian measure

5.2 Arc length

5.3 Areas of sectors and segments

5.4 Solving trigonometric equations

5.5 Small angle approximations

6.1 Secant, cosecant and cotangent

6.2 Graphs of sec x, cosec x and cot x

6.3 Using sec x, cosec x and cot x

6.4 Trigonometric identities

6.5 Inverse trigonometric functions

7.1 Addition formulae

7.2 Using the angle addition formulae

7.3 Double-angle formulae

7.3 The factor theorem

7.4 Solving trigonometric equations

7.5 Simplifying a cos x +/- b sin x

7.6 Proving trigonometric identities

7.7 Modelling with trigonometric functions

8.1 Parametric equations

8.2 Using trigonometric identities

8.3 Curve sketching

8.4 Points of intersection

8.5 Modelling with parametric equations

9.7 Parametric differentiation

9.1 Differentiating sin x and cos x

9.10 Rates of change

9.2 Differentiating exponentials and logarithms

9.3 The chain rule

9.4 The product rule

9.5 The quotient rule

9.6 Differentiating trigonometric functions

9.8 Implicit differentiation

9.9 Using second derivatives

10.1 Locating roots

10.2 Iteration

10.3 The Newton-Raphson method

10.4 Applications to modelling

11.10 Solving differential equations

11.1 Integrating standard functions

11.11 Modelling with differential equations

11.2 Integrating f(ax + b)

11.3 Using trigonometric identities

11.4 Reverse chain rule

11.5 Integration by substitution

11.6 Integration by parts

11.7 Partial fractions

11.8 Finding areas

11.9 The trapezium rule

12.1 3D coordinates

12.2 Vectors in 3D

12.3 Solving geometric problems

12.4 Application to mechanics

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