Roadmap
Number
Factors and number types
C1.1; E1.1 - Factors, multiples and primes
C1.1, C1.5, C1.6; E1.1, E1.5, E1.6 - Integers and place value
C1.1, C1.3; E1.1, E1.3 - Squares, cubes and roots
C1.1; E1.1 - Highest common factor and lowest common multiple
C1.1; E1.1 - Rational numbers and reciprocals
Fractions and calculations
C1.4; E1.4 - Equivalent fractions and mixed numbers
C1.6; E1.6 - Adding and subtracting fractions
C1.6; E1.6 - Multiplying and dividing fractions
C1.4, C1.6; E1.4, E1.6 - Decimal calculations
C1.4; E1.4 - Fractions, decimals and percentages
C1.5; E1.5 - Comparing quantities
C1.6; E1.6 - Order of operations
Indices and accuracy
C1.7; E1.7 - Integer index laws
E1.7 - Fractional indices (Extended)
C1.8; E1.8 - Standard form
C1.9; E1.9 - Rounding and significant figures
C1.9; E1.9 - Estimation and sensible accuracy
C1.13; E1.13 - Using a graphic display calculator
Ratio, percentages and rates
C1.10; E1.10 - Ratio and sharing
C1.10; E1.10 - Proportional reasoning
C1.12; E1.12 - Percentage amounts and comparisons
C1.12; E1.12 - Percentage multipliers
C1.12; E1.12 - Simple and compound interest
E1.12 - Reverse percentages (Extended)
E1.16 - Exponential growth and decay (Extended)
C1.14; E1.14 - Time, clocks and timetables
C1.15, C1.11; E1.15, E1.11 - Money and currency conversion
C1.11; E1.11 - Rates and average speed
Sets and exact values
C1.2; E1.2 - Sets and Venn diagrams
E1.2 - Three sets and subset notation (Extended)
E1.17 - Simplifying surds (Extended)
E1.17 - Rationalising denominators (Extended)
Algebra
Expressions and manipulation
C2.1, C2.5; E2.1, E2.5 - Letters and substitution
C2.2; E2.2 - Collecting like terms
C2.2; E2.2 - Expanding brackets
E2.2 - Several brackets and variables (Extended)
C2.2; E2.2 - Factorising common factors
E2.2 - Factorising quadratics (Extended)
E2.2 - Special factorisations (Extended)
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Equations and formulas
C2.5; E2.5 - Forming and solving linear equations
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C2.5; E2.5 - Simultaneous linear equations and modelling
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C2.5; E2.5 - Changing the subject
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E2.5 - Rearranging harder formulas (Extended)
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E2.5 - Solving quadratic equations (Extended)
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Fractions and indices
C2.3; E2.3 - Simplifying algebraic fractions
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E2.3 - Calculating with algebraic fractions (Extended)
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E2.5 - Solving fractional equations (Extended)
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C2.4; E2.4 - Algebraic index laws
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E2.4 - Fractional algebraic indices (Extended)
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Inequalities and sequences
C2.6; E2.6 - Inequalities on a number line
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E2.6 - Solving linear inequalities (Extended)
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C2.7; E2.7 - Sequences and term rules
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C2.7; E2.7 - The nth term of a linear sequence
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C2.7; E2.7 - Simple quadratic and cubic sequences
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E2.7 - Quadratic, cubic and exponential sequences (Extended)
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E2.8 - Direct and inverse proportion (Extended)
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E2.8 - Choosing a variation model (Extended)
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Geometry
Shapes, angles and bearings
C5.1; E5.1 - Geometrical language
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C5.1; E5.1 - Solid shapes and circle vocabulary
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E5.1 - Planes and further solids (Extended)
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C5.2; E5.2 - Measuring lines and angles
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C5.5; E5.5 - Angles at points and in triangles
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C5.5; E5.5 - Angles in parallel lines
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C5.5; E5.5 - Angles in polygons
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E5.5 - Irregular polygons (Extended)
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C5.2; E5.2 - Three-figure bearings
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Similarity, symmetry and circles
C5.1, C5.3; E5.1, E5.3 - Similar shapes and scale factors
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E5.3 - Explaining similar triangles (Extended)
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E5.3 - Similar areas and volumes (Extended)
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C5.4; E5.4 - Line and rotational symmetry
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E5.4 - Symmetry of solids (Extended)
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C5.6, C5.7; E5.6, E5.7 - Right angles and tangents in circles
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E5.6 - Circle angle theorems (Extended)
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E5.6, E5.7 - Chords and the alternate segment (Extended)
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Mensuration
Measures and areas
C6.1; E6.1 - Metric units and conversions
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C6.2; E6.2 - Perimeter and area
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C6.3; E6.3 - Circle circumference and area
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C6.3; E6.3 - Arcs and sectors
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E6.3 - Major and general sectors (Extended)
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C6.5; E6.5 - Compound areas and perimeters
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Surface areas and volumes
C6.4; E6.4 - Prisms and cylinders
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C6.4; E6.4 - Pyramids and cones
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C6.4; E6.4 - Surface area of solids
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C6.4, C6.5; E6.4, E6.5 - Spheres and parts of solids
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E6.5 - Frustums and similar solids (Extended)
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Trigonometry
Right-angled triangles
C7.1; E7.1 - Pythagoras theorem
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C7.1; E7.1 - Pythagoras in circles and coordinates
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C7.2; E7.2 - Finding sides with trigonometry
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C7.2; E7.2 - Finding angles with trigonometry
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C7.2; E7.2 - Trigonometry with bearings
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E7.2 - Elevation, depression and shortest distance (Extended)
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Further trigonometry
E7.3 - Exact trigonometric values (Extended)
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E7.5 - The sine rule (Extended)
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E7.5 - The cosine rule (Extended)
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E7.5 - Area using two sides and an angle (Extended)
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E7.6 - Pythagoras and trigonometry in 3D (Extended)
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Coordinate geometry
Points and straight lines
C4.1; E4.1 - Cartesian coordinates
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C4.2; E4.2 - Gradient from a graph
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E4.2 - Gradient from two points (Extended)
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C4.4; E4.4 - Equations of straight lines
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E4.4 - Different forms of a line (Extended)
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C4.3; E4.3 - Midpoints and lengths
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C4.5; E4.5 - Parallel straight lines
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E4.6 - Perpendicular lines and bisectors (Extended)
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E2.6 - Inequalities in two variables (Extended)
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Functions
Function notation and graphs
C3.3; E3.3 - Function notation
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C3.1; E3.1 - Linear and quadratic graph shapes
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C3.2; E3.2 - Graphs, tables and windows on a calculator
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C3.2; E3.2 - Zeros, vertices and intersections
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C2.5, C3.2; E2.5, E3.2 - Solving equations graphically
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E2.6 - Solving inequalities with graphs (Extended)
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E3.3 - Domain and range (Extended)
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E3.1, E3.5 - Cubic and reciprocal graphs (Extended)
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E3.1 - Exponential graphs (Extended)
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Trigonometric and transformed functions
E3.1, E3.5, E7.4 - Trigonometric graphs (Extended)
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E7.4 - Trigonometric equations (Extended)
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E3.3 - Inverse functions (Extended)
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E3.3 - Composite functions (Extended)
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E3.4 - Finding a quadratic function (Extended)
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E3.6 - Translating function graphs (Extended)
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E3.7 - Logarithms and exponential equations (Extended)
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Transformations and vectors
Transforming shapes
C8.1; E8.1 - Reflections
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E8.1 - Reflections in oblique lines (Extended)
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C8.1; E8.1 - Rotations
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C8.1; E8.1 - Enlargements
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E8.1 - Negative enlargements (Extended)
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C8.1; E8.1, E8.2 - Translations and column vectors
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E8.1 - Combining and reversing transformations (Extended)
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Vector calculations
E8.2 - Adding and scaling vectors (Extended)
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E8.3 - Magnitude of a vector (Extended)
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Probability
Events and experiments
C9.1; E9.1 - Probability and complements
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C9.2; E9.2 - Relative and expected frequencies
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Combined events
C9.3; E9.3 - Combined events and sample spaces
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C9.3; E9.3 - Probability tree diagrams
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E9.3 - Events without replacement (Extended)
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E9.1, E9.3 - Probability from Venn diagrams (Extended)
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Statistics
Data and displays
C10.1, C10.3; E10.1, E10.3 - Classifying and tabulating data
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C10.2, C10.6; E10.2, E10.6 - Bar charts and pictograms
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C10.6; E10.6 - Pie charts and stem-and-leaf diagrams
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C10.6; E10.6 - Frequency distributions
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Averages and spread
C10.4; E10.4 - Mean, median and mode
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C10.4; E10.4 - Quartiles and measures of spread
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E10.4 - Grouped averages (Extended)
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C10.5; E10.5 - Statistics on a calculator
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Relationships and conclusions
C10.7; E10.7 - Scatter diagrams and lines of best fit
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E10.7 - Linear regression on a calculator (Extended)
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E10.8 - Cumulative frequency, quartiles and percentiles (Extended)
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C10.2; E10.2 - Comparing data and judging conclusions
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Investigation and modelling
Investigating patterns
AO1, AO2 - Systematic investigations
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C2.7; E2.7; AO2 - From patterns to general rules
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AO2 - Explaining an investigation
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Mathematical models
AO2 - Building a mathematical model (Extended)
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AO2 - Using and revising a model (Extended)
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