Roadmap

Number

1.1 - Fractions, percentages, ratio and proportion
1.2 - The product rule for counting
1.3 - Surds and rationalising denominators

Algebra

Algebraic manipulation

2.1 - Basic algebra skills
2.6 - Expanding and simplifying brackets
2.7 - Binomial expansion with Pascal's triangle
2.8 - Factorising fully
2.9 - Simplifying, multiplying and dividing algebraic fractions
2.9 - Adding and subtracting algebraic fractions
2.10 - Using and rearranging formulae
2.12 - Completing the square

Functions

2.2, 2.3 - Functions, domain and range
2.4, 2.5 - Composite and inverse functions
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Equations and graphs

2.14 - Solving linear and quadratic equations
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2.11 - The factor theorem for polynomials
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2.13 - Sketching linear and quadratic graphs
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2.15 - Solving simultaneous equations
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2.16 - Linear equations in three unknowns
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2.17 - Solving linear and quadratic inequalities
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2.18 - Index laws and index equations
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2.13 - Exponential and piecewise graphs
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Proof and sequences

2.21 - nth terms of linear sequences
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2.19 - Algebraic proof
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2.20 - Using nth terms and limiting values
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2.22 - nth terms of quadratic sequences
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Coordinate geometry

3.1–3.3 - Gradients, perpendicular lines and distance
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3.4 - Dividing a line in a ratio
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3.5, 3.6 - Equations of straight lines
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3.7, 3.8 - Equations of circles
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3.9 - Tangents to a circle
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Calculus

4.1, 4.2 - The gradient function of a curve
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4.3 - Differentiating sums of powers of x
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4.4 - Tangents and normals to curves
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4.5 - Increasing and decreasing functions
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4.6, 4.7 - Stationary points and the second derivative
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4.8 - Maximum and minimum problems
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4.9 - Sketching curves with known turning points
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Matrix transformations

5.1, 5.2 - Multiplying matrices and the identity matrix
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5.3 - Transformations of the unit square
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5.4 - Combining transformations with matrices
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Geometry

6.1 - Perimeter, area and volume
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6.1 - Angle facts and circle theorems
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6.2 - Geometric proof
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6.4 - Pythagoras' theorem in 2D and 3D
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6.6, 6.7 - Trigonometry for any angle
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6.8 - Exact trigonometric values
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6.3 - Sine rule, cosine rule and triangle area
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6.5 - Lengths and angles in 2D and 3D
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6.9 - Trigonometric identities
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6.10 - Solving trigonometric equations
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