Roadmap
Number
Whole numbers
C1.1, C1.5, C1.6; E1.1, E1.5, E1.6 - Integers and the number line
C1.1, C1.6; E1.1, E1.6 - Place value and whole-number calculations
C1.1; E1.1 - Factors, multiples and primes
C1.1; E1.1 - Prime factorisation
C1.1; E1.1 - Highest common factors and lowest common multiples
C1.1, C1.3; E1.1, E1.3 - Squares, cubes and roots
C1.6; E1.6 - Signed products and order of operations
Fractions and decimals
C1.4, C1.5; E1.4, E1.5 - Fractions as numbers
C1.6; E1.6 - Adding and subtracting fractions
C1.1, C1.6; E1.1, E1.6 - Multiplying and dividing fractions
C1.4, C1.5, C1.6; E1.4, E1.5, E1.6 - Decimal place value and calculations
C1.4, C1.5; E1.4, E1.5 - Fractions, decimals and percentages
C1.1; E1.1 - Rational and irrational numbers
Powers and accuracy
C1.7; E1.7 - Integer index laws
E1.7 - Fractional indices
C1.8; E1.8 - Writing numbers in standard form
C1.8; E1.8 - Calculating in standard form
C1.9; E1.9 - Rounding and estimation
C1.10; E1.10 - Limits of rounded measurements
E1.18 - Simplifying and combining surds
Proportional reasoning
C1.11; E1.11 - Simplifying and sharing ratios
C1.11; E1.11 - Scaling quantities and comparing value
C1.13; E1.13 - Percentages of quantities
C1.13; E1.13 - Percentage change and interest
E1.13, E1.17 - Reverse percentages and repeated change
Measures and rates
C1.15; E1.15 - Time, clocks and timetables
C1.16, C1.12; E1.16, E1.12 - Money and exchange rates
C1.12; E1.12 - Rates and average speed
C1.14; E1.14 - Using a scientific calculator well
E1.10 - Calculating with bounds
Algebra
Expressions
C2.1, C2.5; E2.1, E2.5 - Letters, expressions and substitution
C2.2; E2.2 - Collecting like terms
C2.2; E2.2 - Expanding and taking out common factors
C2.2; E2.2 - Expanding two brackets
Locked
E2.2 - Several brackets and grouped factors
Locked
E2.2 - Factorising quadratic expressions
Locked
E2.2 - Completing the square
Locked
Indices and fractions
C2.4; E2.4 - Index laws with letters
Locked
E2.4 - Fractional powers with letters
Locked
E2.3 - Calculating with algebraic fractions
Locked
Equations and formulas
C2.5; E2.5 - Solving linear equations
Locked
C2.5; E2.5 - Simultaneous linear equations
Locked
C2.5; E2.5 - Changing the subject
Locked
E2.5 - Rearranging powers and repeated subjects
Locked
E2.5 - Solving quadratic equations
Locked
E2.5 - Equations with algebraic denominators
Locked
E2.5 - A line and a nonlinear equation
Locked
Inequalities and sequences
C2.6; E2.6 - Inequalities on a number line
Locked
E2.6 - Solving linear inequalities
Locked
C2.7; E2.7 - Patterns and linear sequences
Locked
C2.7; E2.7 - Square and cube sequences
Locked
E2.7 - Quadratic, cubic and exponential sequences
Locked
E2.8 - Direct and inverse proportion
Locked
Exact calculations with algebra
E1.4 - Recurring decimals as fractions
Locked
E1.18 - Rationalising denominators
Locked
Geometry
Shapes and construction
C4.1; E4.1 - Lines, angles and polygons
Locked
C4.1, C4.2; E4.1, E4.2 - Solids and their nets
Locked
C4.1; E4.1 - Parts of a circle
Locked
C4.2; E4.2 - Measuring and constructing triangles
Locked
C4.1, C4.3; E4.1, E4.3 - Scale drawings and bearings
Locked
C4.5; E4.5 - Line and rotational symmetry
Locked
E4.1, E4.5 - Planes and symmetry in solids
Locked
Angle reasoning
C4.6; E4.6 - Angles at points and in triangles
Locked
C4.6; E4.6 - Angles in parallel lines
Locked
C4.6; E4.6 - Angles in polygons
Locked
E4.6 - Reasoning with irregular polygons
Locked
Similarity and circles
C4.1, C4.4; E4.1, E4.4 - Similar shapes and length scale factors
Locked
E4.4 - Explaining triangle similarity
Locked
C4.7; E4.7 - Right angles in circles
Locked
E4.7 - Angles in the same circle
Locked
E4.8 - Chords and tangents
Locked
Mensuration
Area and perimeter
C5.1; E5.1 - Metric units and conversions
Locked
C5.2; E5.2 - Perimeters and areas of polygons
Locked
C5.3; E5.3 - Circle area and circumference
Locked
C5.3; E5.3 - Arcs and sectors
Locked
E4.1, E5.3 - Major and minor sectors
Locked
C5.5; E5.5 - Compound areas and perimeters
Locked
Surface area and volume
C5.4; E5.4 - Prisms and cylinders
Locked
C5.4; E5.4 - Pyramids, cones and spheres
Locked
C5.5; E5.5 - Compound solids and exposed surfaces
Locked
E4.4 - Area and volume scale factors
Locked
E5.5 - Frustums and similar solids
Locked
Trigonometry
Right-angled triangles
C6.1; E6.1 - Pythagoras and missing lengths
Locked
C6.2; E6.2 - Using sine, cosine and tangent
Locked
C6.2; E6.2 - Finding angles in right triangles
Locked
C6.2; E6.2 - Bearings and linked right triangles
Locked
Extended trigonometry
E6.2 - Elevation, depression and shortest distance
Locked
E6.3 - Exact trigonometric values
Locked
E6.5 - Sine and cosine rules
Locked
E6.5 - Triangle area using sine
Locked
E6.6 - Lengths and angles in three dimensions
Locked
Coordinate geometry
Lines and coordinates
C3.1; E3.1 - Coordinates in four quadrants
Locked
C3.2, C3.3; E3.2, E3.3 - Drawing lines and finding gradients
Locked
C3.5; E3.5 - Equations of straight lines
Locked
C3.6; E3.6 - Parallel line equations
Locked
Extended line geometry
E3.3, E3.4 - Gradient, midpoint and distance
Locked
E2.11, E3.2, E3.5 - Linear equations in different forms
Locked
E3.7 - Perpendicular lines and bisectors
Locked
Graphs and functions
Real-life graphs
C2.9; E2.9 - Travel and conversion graphs
Locked
E2.9 - Speed, acceleration and distance
Locked
Curves and equations
C2.10; E2.10 - Plotting quadratic and reciprocal graphs
Locked
C2.11; E2.11 - Sketching lines and parabolas
Locked
E2.10, E2.11 - Cubic, reciprocal and exponential curves
Locked
E2.10, E2.11 - Turning points and growth models
Locked
E2.6 - Regions defined by inequalities
Locked
E6.4 - Trigonometric graphs and equations
Locked
Functions and calculus
E2.13 - Functions, domain and range
Locked
E2.13 - Inverse and composite functions
Locked
E2.12 - Gradients of curves and differentiation
Locked
E2.12 - Stationary points and their nature
Locked
Transformations and vectors
Transforming shapes
C7.1; E7.1 - Reflections and rotations
Locked
C7.1; E7.1 - Translations and enlargements
Locked
E7.1 - Negative enlargements and combined transformations
Locked
Vector reasoning
E7.2, E7.3 - Calculating with vectors
Locked
E7.4 - Position vectors and geometric paths
Locked
E7.4 - Parallel vectors and collinear points
Locked
Probability
Sets and chance
C1.2; E1.2 - Sets and two-set Venn diagrams
Locked
E1.2 - Three sets and set relationships
Locked
C8.1; E8.1 - Single-event probability
Locked
E8.1, E8.3 - Probability notation and Venn regions
Locked
Experiments and combined events
C8.2; E8.2 - Relative and expected frequency
Locked
C8.3; E8.3 - Sample spaces and combined events
Locked
C8.3; E8.3 - Tree diagrams with replacement
Locked
E8.3 - Events without replacement
Locked
E8.4 - Conditional probability
Locked
Statistics
Collecting and displaying data
C9.1; E9.1 - Classifying and organising data
Locked
C9.4; E9.4 - Bar charts, pie charts and pictograms
Locked
C9.4; E9.4 - Stem-and-leaf and frequency distributions
Locked
Summarising and comparing data
C9.3; E9.3 - Mean, median, mode and range
Locked
C9.2; E9.2 - Interpreting and comparing data
Locked
E9.2, E9.3 - Quartiles and interquartile range
Locked
E9.3 - Grouped-data averages
Locked
Relationships and distributions
C9.5; E9.5 - Scatter diagrams and correlation
Locked
E9.2, E9.6 - Cumulative frequency and percentiles
Locked
E9.7 - Histograms and frequency density
Locked