Roadmap
Number
Integer arithmetic
1.01a - Adding and subtracting integers
1.01a - Multiplying and dividing integers
1.04a - Undoing calculations
Factors and powers
1.02a - Factors, multiples and primes
3.01a, 3.01b - Integer powers and roots
1.02b - Prime factorisation
1.02c - Highest factors and lowest multiples
1.03a - Order of operations
3.01c - Laws of indices
Fractions
2.01a - Equivalent fractions and mixed numbers
2.01b - Adding and subtracting fractions
2.01b - Multiplying and dividing fractions
2.01c, 3.03a - Fractions of quantities
Decimals and percentages
2.02a - Decimals and fractions
2.02b, 2.02c - Calculating with decimals
2.03a, 2.03b - Percentages of quantities
2.04a, 2.04b - Comparing numbers
2.03c - Percentage change and original values
Accuracy and estimation
4.01a - Rounding to useful accuracy
4.01b - Estimating calculations
4.01c - Error intervals
4.01c - Bounds in calculations
Standard form and surds
3.02a, 3.02b - Standard form
3.01a, 3.01b - Fractional powers
3.03a, 3.03b - Exact answers with surds
Algebra
Expressions and formulae
6.01a, 6.01b - Writing and simplifying expressions
6.01c - Multiplying and dividing algebraic terms
6.02b, 6.02e - Substituting into formulae
6.02a - Building expressions from situations
Brackets and factorisation
6.01d, 6.01e - Expanding and factorising a bracket
6.01d, 6.01e - Quadratic expressions
6.01c–6.01e - More demanding algebraic products
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6.01f - Completing the square
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3.03b - Rationalising denominators
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6.01g - Algebraic fractions
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Equations and rearranging
6.03a - Solving linear equations
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2.02a - Recurring decimals as fractions
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6.02c - Changing the subject
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6.03b - Solving factorised quadratics
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6.02d, 6.03b - Solving general quadratics
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6.03c - Simultaneous linear equations
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6.02c, 6.03a - Equations with algebraic fractions
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6.03c - Simultaneous equations with quadratics
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Inequalities and reasoning
6.04a - Linear inequalities
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6.04a - Quadratic inequalities
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6.01a - Identities and algebraic arguments
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6.01a - Proof with algebra
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Functions and sequences
6.05a - Inputs and outputs
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6.05a - Inverse and composite functions
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6.06a, 6.06b - Rules for sequences
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6.06b - Fibonacci and geometric sequences
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6.06a, 6.06b - Quadratic and other sequence rules
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Ratio and proportion
Ratio calculations
5.01a, 5.01c - Ratios and fractions
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5.01b - Sharing in a ratio
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5.01d - Using ratios in problems
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Proportional relationships
5.02a - Direct proportion
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5.02b - Inverse proportion
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5.02a, 5.02b, 6.02a - Proportion with powers and roots
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Growth and decay
2.03c, 5.03a - Interest and repeated percentage change
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5.03a, 6.02a - Exponential growth models
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Geometry and measures
Shapes and angles
8.01a–8.01c, 8.01e, 8.01f - Geometrical language and measurement
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8.03a–8.03c - Angles on lines
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8.03d, 8.04a–8.04c - Angles and properties of polygons
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9.02a, 9.02b - Congruent triangles
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8.03a–8.03d, 8.04a, 8.04b - Proof with angles and shapes
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Constructions and scale
8.02a–8.02c - Ruler and compass constructions
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8.02d - Loci and equidistance
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10.01c - Scale drawings and bearings
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Measurement and area
10.01a - Converting units
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10.02a, 10.03a–10.03c - Perimeter and polygon area
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8.05a - Parts of a circle
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3.03a, 6.02d, 10.02b - Circumference and arc length
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6.02d, 10.03d - Circle and sector area
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10.02c, 10.03e - Composite perimeters and areas
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Solids and volume
8.01d, 8.06a, 8.06b - Solids, plans and elevations
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10.04a - Volume and surface area of prisms
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10.04b, 10.04c - Cones, spheres and pyramids
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10.01b - Speed, density and pressure
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Transformations and similarity
7.01a, 8.01g - Coordinates in four quadrants
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9.01a–9.01c - Reflection, rotation and translation
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9.01d - Combining transformations
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9.04b - Enlargement
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9.04b - Negative scale factors
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9.04a, 9.04c - Similar triangles and lengths
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9.04c - Area and volume scale factors
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Right-angled triangles
6.02d, 10.05a - Pythagoras' theorem
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6.02d, 10.05b - Right-angled trigonometry
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10.05c - Exact trigonometric values
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10.05a, 10.05b - Lengths and angles in three dimensions
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General triangles
6.02d, 10.05d - The sine rule
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6.02d, 10.05e - The cosine rule
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6.02d, 10.03a - Triangle area using sine
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Circle theorems
8.05b–8.05d - Angles at the centre and circumference
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8.05e–8.05g - Chords and tangents
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8.05h - Cyclic quadrilaterals
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Vectors
9.03a, 9.03b - Calculating with vectors
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9.03a - Geometric proof with vectors
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Graphs and functions
Straight lines
7.01b, 7.01c, 7.02a - Straight-line graphs
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7.02a, 7.02b - Finding equations of lines
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6.03d - Solving equations with graphs
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Curves and equations
6.03d, 7.01b, 7.01c - Quadratic graphs
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6.03d, 7.01c - Turning points and intersections
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7.01b, 7.01c - Cubic and reciprocal graphs
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7.01b, 7.01d - Exponential graphs
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6.03e - Approximating roots by sign changes
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Further graphs
7.01f, 7.02b - Circles and perpendicular tangents
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7.01e - Sine, cosine and tangent graphs
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7.03a - Translating and reflecting graphs
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6.04b, 7.02a - Regions defined by inequalities
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Graphs in context
7.04a, 7.04b - Real-world graphs and rates
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7.04b - Average and instantaneous rates
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7.04c - Areas under graphs
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Probability
Chance and experiments
11.01a, 11.01d - Probability and expected outcomes
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11.01b, 11.01c - Estimating probability from experiments
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Representing outcomes
11.02a, 11.02b - Systematic lists and sample spaces
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11.02a, 11.02b - Counting and choosing representations
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11.02c, 11.02e - Sets, Venn diagrams and addition
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Combined events
11.02d, 11.02f - Probability trees
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11.02c, 11.02f - Conditional probability
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Statistics
Data and sampling
12.01a - Populations, samples and bias
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12.02a - Tables and charts
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12.02a, 12.03b - Time series and misleading graphs
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Summarising data
12.03a - Averages and spread
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12.03a - Estimating from grouped data
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Grouped distributions
12.02b, 12.03a - Histograms
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12.02b, 12.03a - Cumulative frequency and box plots
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Relationships in data
12.03c, 12.03d - Scatter graphs and outliers
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