Roadmap
Number
Number sense
FN1–FN2, HN1–HN2 - Place value and number order
FN2–FN3, HN2–HN3 - Calculating with integers
FN3, FN6, HN3, HN6 - Powers and roots
Factors and fractions
FN4, HN4 - Factors and prime numbers
FN4, HN4 - Highest common factors and lowest common multiples
FN1–FN3, FN10, HN1–HN3, HN10 - Equivalent fractions and number order
FN2, FN8, HN2, HN8 - Adding and subtracting fractions
FN2–FN3, FN8, FN12, HN2–HN3, HN8, HN12 - Multiplying and dividing fractions
Decimals and accuracy
FN2–FN3, HN2–HN3 - Calculating with decimals
FN10, HN10 - Fractions and terminating decimals
FN14–FN15, HN14–HN15 - Rounding and estimation
FN15–FN16, HN15–HN16 - Accuracy and error intervals
FN13, FR1, FG12, HN13, HR1, HG14 - Units and conversions
Powers and exact values
FN3, FN7, HN3, HN7 - Laws of indices
FN9, HN9 - Standard form
FN5, HN5 - Listing possibilities
Higher number
HN6–HN7 - Fractional indices
HN8 - Working with surds
HN10 - Recurring decimals as fractions
HN16 - Calculating with bounds
HN5 - Counting with the product rule
Algebra
Expressions and formulae
FA1, FA3, FA17, HA1, HA3, HA21 - Writing algebraic expressions
FA2, FA5, HA2, HA5 - Substituting into formulae
FA4, HA4 - Collecting terms and expanding brackets
FA4, HA4 - Taking out common factors
FA4, HA4 - Exact expressions with roots
FA4, HA4 - Simplifying powers in algebra
Equations and inequalities
FA14, HA17 - Solving linear equations
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FA17, HA21 - Forming equations from problems
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FA5, HA5 - Changing the subject
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FA18, HA22 - Linear inequalities
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Sequences and functions
FA19–FA21, HA23–HA25 - Linear sequences
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FA19–FA20, HA23–HA24 - Recognising number patterns
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FA7, HA7 - Inputs and outputs
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Straight-line graphs
FA8–FA9, HA8–HA9 - Coordinates and plotting
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FA9–FA10, HA9–HA10 - Gradient and intercept
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FA9–FA10, HA9–HA10 - Finding a line equation
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FA16–FA17, HA19, HA21 - Simultaneous linear equations
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Quadratics and curves
FA4, HA4 - Expanding two brackets
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FA4, HA4 - Factorising quadratic expressions
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FA15, HA18 - Solving quadratics by factorising
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FA11–FA12, FA15, HA11–HA12, HA18 - Quadratic graphs and roots
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FA12, HA12 - Cubic and reciprocal graphs
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FA13, HA14 - Graphs in real situations
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Algebraic forms
HA4 - More demanding factorisation
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HA4, HA11, HA18 - Completing the square
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HA18 - Solving general quadratic equations
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HA4 - Algebraic fractions
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FA6, HA6 - Identities and algebraic arguments
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Higher functions and equations
HA6 - Proof with algebra
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HA7 - Composite and inverse functions
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HA19 - Linear and quadratic simultaneous equations
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HA20 - Numerical solutions and iteration
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HA22 - Quadratic and graphical inequalities
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HA23–HA25 - Quadratic and geometric sequence rules
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Ratio and proportion
Ratios and sharing
FN11, FR4–FR5, FR7, HN11, HR4–HR5, HR7 - Writing and simplifying ratios
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FR6, FR8–FR9, HR6, HR8–HR9 - Sharing and solving ratio problems
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Percentages and growth
FN12, FR10, HN12, HR10 - Percentages as operators
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FR10, HR10 - Percentage change and original values
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FR10, FR16, HR10, HR17 - Interest, growth and decay
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Rates and proportionality
FR1, FR12, HR1, HR12 - Unit rates and compound measures
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FR2, FR12, HR2, HR12 - Density and pressure
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FR8, FR11, FR14–FR15, HR8, HR11, HR14–HR15 - Direct and inverse proportion
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Higher proportionality
HR11, HR14 - Constructing proportional models
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HR17 - Repeated change models
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Geometry and measures
Angles and shapes
FG1, FG4, HG1, HG4 - Describing shapes and symmetry
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FG3, HG3 - Angle facts and parallel lines
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FG3–FG4, HG3–HG4 - Angles in triangles and polygons
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FG5–FG6, HG5–HG6 - Congruence and geometric proof
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Constructions and scale
FG2, HG2 - Ruler and compass constructions
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FG2, HG2 - Loci and regions
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FR3, FG13, HR3, HG15 - Scale drawings and bearings
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Transformations and vectors
FG7, FG9, FG20, HG7, HG11, HG24 - Reflections, rotations and translations
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FG7, FG17, FR13, HG7, HG19, HR13 - Enlargement and similarity
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FG21, HG25 - Calculating with vectors
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Area and circles
FG14–FG15, HG16–HG17 - Perimeter and polygon areas
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FN8, FG8, FG15, HN8, HG9, HG17 - Circles, circumference and area
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FG16, HG18 - Arc lengths and sector areas
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Solids and volume
FG10–FG11, HG12–HG13 - Three-dimensional shapes and views
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FG14, HG16 - Volumes of prisms and cylinders
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FG15, HG17 - Surface area and curved solids
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Right-angled triangles
FG6, FG18, HG6, HG20 - Pythagoras' theorem
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FG18, HG20 - Right-angled trigonometry
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FG19, HG21 - Exact trigonometric values
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Higher geometry
HG7–HG8 - Negative enlargements and combined transformations
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HG19, HR13 - Area and volume scale factors
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HG10 - Angles in circles
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HG10 - Tangents and chords
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Higher trigonometry
HG22 - Sine and cosine rules
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HG23 - Area of any triangle
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HG20 - Three-dimensional trigonometry
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HG25 - Geometric arguments with vectors
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Higher graphs
Lines and curves
HA9, HA16 - Perpendicular lines and circle tangents
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Functions and rates
HA12 - Exponential and trigonometric graphs
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HA13 - Transforming function graphs
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HA14–HA15, HR16 - Rates and areas under graphs
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Probability
Chance and experiments
FP2–FP4, HP2–HP4 - Probability and expected outcomes
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FP1–FP3, FP5, HP1–HP3, HP5 - Experiments and relative frequency
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Representing outcomes
FP6–FP7, HP6–HP7 - Sample spaces and Venn diagrams
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FP6, FP8, HP6, HP8 - Combined events and tree diagrams
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Higher probability
HP9 - Conditional probability
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Statistics
Collecting data
FS1–FS2, FS5, HS1–HS2, HS6 - Populations, samples and questionnaires
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Displaying data
FS3, HS3 - Tables and categorical charts
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FS3–FS4, HS3, HS5 - Discrete and time-series graphs
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Comparing distributions
FS4, HS5 - Averages and range
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FS4–FS5, HS5–HS6 - Averages from frequency tables
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FS6, HS7 - Scatter graphs and prediction
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Higher statistics
HS4 - Histograms and frequency density
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HS4–HS5 - Cumulative frequency and quartiles
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HS5–HS6 - Box plots and comparing distributions
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