Roadmap
Papers 1, 2 and 3
1 Number
N1, N2 - Integers, decimals and written arithmetic
N1, N2, N3 - Fractions, mixed numbers and cancellation
N3, N6, N7 - Powers, roots and the order of operations
N4, N5 - Primes, factors, multiples and systematic lists
N5, N6 - The product rule and estimates of roots
N7, N8, A4 - Fractional indices and exact surd calculations
N8, N9 - Exact multiples of pi and standard form
N10, N12 - Fractions, decimals and percentage operators
N10 - Recurring decimals and fractions
N14, N15, N16 - Estimation, rounding and simple error intervals
N16 - Upper and lower bounds in calculations
2 Algebra
A1, A2, A3 - Algebraic notation, vocabulary and substitution
A4 - Simplifying, expanding and common factors
A4, A18 - Quadratic expansion, factorisation and roots
A4 - Advanced factorisation and algebraic fractions
A5 - Rearranging formulae
A6 - Equivalence, identities and algebraic arguments
A6 - Algebraic proof
A7 - Functions as inputs and outputs
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A7 - Inverse and composite functions
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A8, A9, A10 - Coordinates, straight lines and gradients
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A9, A16 - Perpendicular lines, circles and tangents
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A11, A12, A18 - Quadratic graphs and approximate roots
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A11, A18 - Completing the square and the quadratic formula
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A12, A14 - Cubic, reciprocal and real-context graphs
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A12, A13, A14 - Exponential, trigonometric and transformed graphs
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A15, R15 - Gradients, areas and rates on curved graphs
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A17, A21 - Linear equations and mathematical models
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A19, A21 - Simultaneous linear equations
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A19 - Linear and quadratic simultaneous equations
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A20 - Numerical solutions by iteration
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A22 - Linear inequalities and number lines
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A22 - Regions and quadratic inequalities
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A23, A24, A25 - Sequence rules and linear nth terms
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A24, A25 - Quadratic and surd sequences
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3 Ratio, proportion and rates of change
N11, R3, R4, R5, R6, R7, R8 - Ratios, fractions and proportional sharing
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N13, R1, R11, G14 - Standard units and compound measures
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R2, G15 - Scale drawings, maps and bearings
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R9 - Percentage changes and financial mathematics
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R10, R13, R14 - Direct and inverse proportion
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R10, R13 - Constructing proportional relationships
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R16 - Compound interest, growth and decay
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R16 - General iterative processes
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R12, G19 - Similarity ratios for lengths, areas and volumes
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4 Geometry and measures
G1, G4 - Geometrical language, triangles and quadrilaterals
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G3 - Angle facts, parallel lines and polygons
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G2 - Ruler and compass constructions and loci
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G5, G6 - Triangle congruence and geometrical arguments
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G7, G24 - Reflections, rotations, translations and enlargements
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G7, G8 - Negative enlargements and combined transformations
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G9, G17, G18 - Circles, circumference, arcs and sectors
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G10 - Circle theorems and their proofs
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G11 - Geometrical problems on coordinate axes
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G12, G13 - Three-dimensional shapes, plans and elevations
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G16, G17 - Perimeters, areas and composite shapes
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G16, G17 - Volumes and surface areas of solids
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G19, R12 - Congruence and similarity of lengths
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G6, G20 - Pythagoras theorem in two dimensions
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G20, G21 - Right-angle trigonometry and exact values
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G22, G23 - Sine rule, cosine rule and triangle area
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G20 - Pythagoras and trigonometry in three dimensions
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G25 - Vector notation and arithmetic
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G25 - Vector arguments and proofs
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5 Probability
P1, P2, P3, P4, P5 - Probability, relative frequency and expected outcomes
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P6, P7 - Sample spaces, sets and Venn diagrams
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P8 - Combined events and probability trees
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P9 - Conditional probability
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6 Statistics
S1, S5 - Samples, populations and statistical inference
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S2 - Tables, charts and time-series data
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S4 - Averages, range and grouped-data estimates
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S6 - Scatter graphs, correlation and prediction
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S3 - Histograms and frequency density
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S3, S4 - Cumulative frequency, quartiles and box plots
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