Roadmap
Number
Structure and calculation
N1, N2 - Place value, ordering and inequality symbols
N2 - Written methods for the four operations
N3 - Inverse operations and order of operations
N4 - Factors, multiples, primes and prime factorisation
N1, N2 - Equivalent fractions, mixed numbers and ordering
N2 - Calculating with fractions and mixed numbers
N5 - Systematic listing and the product rule
N6 - Powers and roots
N7 - Calculating with roots and indices
N7 - Fractional indices (Higher)
N8 - Exact answers with pi and surds
N9 - Standard form
Fractions, decimals and percentages
N10 - Converting fractions and decimals
N12 - Fractions and percentages of amounts
Measures and accuracy
N13 - Metric units and conversions
N14, N15 - Rounding, significant figures and estimation
N15, N16 - Error intervals and limits of accuracy
N16 - Upper and lower bounds (Higher)
Algebra
Notation, vocabulary and manipulation
A1–A3 - Algebraic notation, substitution and vocabulary
A4 - Simplifying, expanding single brackets and factorising
A4 - Expanding double brackets and factorising quadratics
A4 - Three brackets and harder factorising (Higher)
A4 - Algebraic fractions (Higher)
A5 - Using and rearranging formulae
A6 - Algebraic arguments and proof
Locked
A7 - Functions, composites and inverses
Locked
Graphs
A8–A10 - Coordinates and straight-line graphs
Locked
A9 - Equations of straight lines
Locked
A11, A12 - Quadratic graphs, roots and turning points
Locked
A11 - Turning points by completing the square (Higher)
Locked
A12 - Cubic, reciprocal and exponential graphs
Locked
A13 - Translating and reflecting graphs (Higher)
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A14 - Real-life graphs
Locked
A15, R15 - Gradients and areas under graphs (Higher)
Locked
Solving equations and inequalities
A17 - Solving linear equations
Locked
A18 - Solving quadratic equations by factorising
Locked
A18 - Quadratic formula and completing the square (Higher)
Locked
A19 - Simultaneous linear equations
Locked
A19 - Linear and quadratic simultaneous equations (Higher)
Locked
A20 - Approximate solutions by iteration (Higher)
Locked
A21 - Forming and solving equations
Locked
A22 - Solving linear inequalities
Locked
A22 - Quadratic inequalities, set notation and regions (Higher)
Locked
Sequences
A23, A24 - Sequence rules and special sequences
Locked
A25 - The nth term of a linear sequence
Locked
A24, A25 - Quadratic nth term and harder sequences (Higher)
Locked
Ratio, proportion and rates of change
Units, scale and ratio
R1 - Converting standard and compound units
Locked
R3, R4 - Comparing quantities as fractions and ratios
Locked
R2 - Scale diagrams and maps
Locked
R5 - Sharing in a ratio
Locked
R5 - Ratio problems and best buys
Locked
R6–R8, N11 - Ratios, fractions and proportion
Locked
Percentages
R9 - Percentages and percentage change
Locked
R9 - Reverse percentages and simple interest
Locked
Proportion, rates and growth
R10 - Direct and inverse proportion
Locked
R11 - Speed, density and other compound units
Locked
R13, R14 - Proportion equations and graphs
Locked
R13 - Forming proportion equations (Higher)
Locked
R16 - Compound interest, growth and decay
Locked
Geometry and measures
Properties and constructions
G1, G2 - Geometric terms and constructions
Locked
G2 - Loci and shortest distances
Locked
G3 - Angle facts and parallel lines
Locked
G3 - Angles in triangles and polygons
Locked
G4 - Properties of triangles and quadrilaterals
Locked
G5, G6 - Congruent triangles and geometric proof
Locked
G7 - Reflections, rotations and translations
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G7 - Enlargement and scale factors
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G8 - Combined transformations and invariant points (Higher)
Locked
G9, G10 - Circle parts and angle theorems
Locked
G10 - Circle theorems about tangents and chords (Higher)
Locked
G11 - Geometry problems on coordinate axes
Locked
G12, G13 - 3D shapes, plans and elevations
Locked
Measurement and calculation
G14, G15 - Measuring, scale drawings and bearings
Locked
G16, G17 - Perimeter and area of 2D shapes
Locked
G17 - Circumference and area of circles
Locked
G16, G17 - Volume and surface area of prisms
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G18 - Arc length and sector area
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G19, R12 - Congruence and similar shapes
Locked
G20 - Pythagoras' theorem
Locked
G17 - Spheres, pyramids, cones and composite solids
Locked
G19 - Similar areas and volumes (Higher)
Locked
G20, G21 - Right-angled trigonometry and exact values
Locked
G20 - Pythagoras and trigonometry in 3D (Higher)
Locked
G22, G23 - Sine rule, cosine rule and triangle area (Higher)
Locked
A12 - Graphs of sin, cos and tan (Higher)
Locked
A16 - Equation of a circle and tangents (Higher)
Locked
Vectors
G24, G25 - Column vectors and vector arithmetic
Locked
G25 - Vector geometry proofs (Higher)
Locked
Probability
P1–P5 - Probability, relative frequency and expected outcomes
Locked
P6, P7 - Sample spaces and Venn diagrams
Locked
P8 - Tree diagrams and combined events
Locked
P9 - Conditional probability (Higher)
Locked
Statistics
S1, S2 - Samples, tables and charts
Locked
S4 - Averages and range
Locked
S4, S5 - Frequency tables and comparing distributions
Locked
S3 - Histograms (Higher)
Locked
S3, S4 - Cumulative frequency and box plots (Higher)
Locked
S6 - Scatter graphs and correlation
Locked