Topics for A Level Year 2 Pure

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1.1 Proof by contradiction

$1.2 Algebraic fractions$

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1.2 Algebraic fractions

$1.3 Partial fractions$

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1.3 Partial fractions

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1.4 Repeated factors

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1.5 Algebraic division

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2.1 The modulus function

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2.2 Functions and mappings

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2.3 Composite functions

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2.4 Inverse functions

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

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2.6 Combining transformations

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2.7 Solving modulus problems

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3.1 Arithmetic sequences

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3.2 Arithmetic series

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3.3 Geometric sequences

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3.4 Geometric series

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3.5 Sum to infinity

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3.6 Sigma notation

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3.7 Recurrence relations

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3.8 Modelling with series

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4.1 Expanding (1 + x)^n

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4.2 Expanding (a + bx)^n

$4.3 Using partial fractions$

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4.3 Using partial fractions

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5.1 Radian measure

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5.2 Arc length

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5.3 Areas of sectors and segments

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5.4 Solving trigonometric equations

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5.5 Small angle approximations

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6.1 Secant, cosecant and cotangent

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6.2 Graphs of sec x, cosec x and cot x

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6.3 Using sec x, cosec x and cot x

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6.4 Trigonometric identities

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6.5 Inverse trigonometric functions

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7.1 Addition formulae

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7.2 Using the angle addition formulae

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7.3 The factor theorem

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7.3 Double-angle formulae

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7.4 Solving trigonometric equations

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7.5 Simplifying a cos x +/- b sin x

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7.6 Proving trigonometric identities

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7.7 Modelling with trigonometric functions

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8.1 Parametric equations

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8.2 Using trigonometric identities

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8.3 Curve sketching

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8.4 Points of intersection

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8.5 Modelling with parametric equations

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9.7 Parametric differentiation

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9.1 Differentiating sin x and cos x

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9.2 Differentiating exponentials and logarithms

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9.3 The chain rule

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9.4 The product rule

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9.5 The quotient rule

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9.6 Differentiating trigonometric functions

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9.8 Implicit differentiation

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9.9 Using second derivatives

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9.10 Rates of change

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10.1 Locating roots

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10.2 Iteration

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10.3 The Newton-Raphson method

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10.4 Applications to modelling

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11.1 Integrating standard functions

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11.2 Integrating f(ax + b)

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11.3 Using trigonometric identities

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11.4 Reverse chain rule

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11.5 Integration by substitution

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11.6 Integration by parts

$11.7 Partial fractions$

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11.7 Partial fractions

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11.8 Finding areas

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11.9 The trapezium rule

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11.10 Solving differential equations

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11.11 Modelling with differential equations

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12.1 3D coordinates

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12.2 Vectors in 3D

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12.3 Solving geometric problems

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👋 Welcome to How2Nerd

👋 Welcome to Nerd+

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 The factor theorem

7.3 Double-angle formulae

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

9.2 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

9.10 Rates of change

10.1 Locating roots

10.2 Iteration

10.3 The Newton-Raphson method

10.4 Applications to modelling

11.1 Integrating standard functions

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

11.10 Solving differential equations

11.11 Modelling with differential equations

12.1 3D coordinates

12.2 Vectors in 3D

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