top of page

The grade groupings (Grades 1–3, 4–6 and 7–9) are intended as a general guide only. They are approximate and are not fixed boundaries, as the difficulty of a topic can vary depending on the question and the skills required. Some topics may overlap between grade groups, and students may need to revisit earlier skills before progressing to more challenging material. The actual GCSE grade achieved will depend on overall performance across the full exam, not on individual topics alone

GRADE 4

Number

’        Calculations with fractions and mixed numbers

’        Product of prime factors

’        HCF and LCM using prime factorisation

’        Standard form calculations

’        Significant figures and estimation

’        Upper and lower bounds in simple problems

’        Recurring decimals in accessible cases

Algebra

’        Expanding double brackets in straightforward cases

’        Factorising quadratic expressions of the form \(x^2+bx+c\)

’        Solving linear equations with brackets and fractions

’        Simultaneous equations: linear pairs

’        Sequences and nth term of linear sequences

’        Straight-line graphs in the form \(y=mx+c\)

’        Rearranging simple formulae

’        Inequalities and number-line representations

’        Algebraic proof in simple cases

Ratio and proportion

’        Compound ratios and three-part ratios

’        Reverse percentages

’        Direct proportion

’        Speed, density and pressure calculations

’        Similar shapes and scale factors

’        Percentage multipliers

Geometry

’        Pythagoras' theorem in multi-step questions

’        Trigonometry in right-angled triangles (SOHCAHTOA)

’        Area of trapezia and compound shapes

’        Surface area and volume of prisms

’        Similar triangles

’        Congruence and geometric reasoning

’        Constructions and loci

’        Plans and elevations

Probability

’        Probability tree diagrams with independent events

’        Combined events

’        Venn diagrams and set notation in accessible problems

Statistics

’        Frequency polygons

’        Comparing distributions

’        Box plots in straightforward contexts

’        Interpreting scatter graphs and lines of best fit

GRADE 5

Number

’        Calculations with powers and roots

’        Fractional and negative indices in accessible cases

’        Surds: simplifying simple expressions

’        Rational and recurring decimals

’        Bounds and error intervals

’        Calculations with standard form

’        Repeated percentage change

Algebra

’        Expanding double brackets and factorising quadratics

’        Difference of two squares

’        Solving quadratic equations by factorisation

’        Simultaneous linear equations using elimination and substitution

’        Changing the subject of a formula

’        Algebraic fractions in simple cases

’        Linear and quadratic sequences

’        Equation of a straight line through a point or two points

’        Parallel lines and gradients

’        Algebraic proof and identities

’        Linear inequalities

Ratio and proportion

’        Direct and inverse proportion in numerical problems

’        Compound measures in multi-step contexts

’        Reverse percentages

’        Similarity: lengths, areas and volumes

’        Growth and decay using multipliers

’        Compound interest

Geometry

’        Trigonometry in multi-step problems

’        Exact values of basic trigonometric ratios

’        Sine rule and cosine rule in introductory cases

’        Area of a triangle using \(\frac12 ab\sin C\)

’        Circle circumference, area, arcs and sectors

’        Circle theorems in standard problems

’        Enlargement with fractional and negative scale factors

’        Geometric proofs using angle facts

’        Vectors: notation and simple operations

Probability

’        Dependent and independent events

’        Tree diagrams with changing probabilities

’        Venn diagrams and two-way tables

’        Experimental and theoretical probability

Statistics

’       Cumulative frequency graphs

’       Quartiles and interquartile range

’       Histograms with equal class widths

’       Sampling and limitations of data

GRADE 6

Number
    Surds: simplifying, adding and multiplying
    Rationalising denominators in accessible cases
    Fractional indices
    Complex bounds problems
    Standard form in multi-step calculations
    Upper and lower bounds in calculations involving formulae
Algebra
    Factorising \(ax^2+bx+c\)
    Quadratic equations requiring rearrangement
    Completing the square in straightforward cases
    Quadratic formula
    Simultaneous equations involving linear and quadratic equations
    Algebraic fractions: simplifying and manipulating
    Composite and inverse functions
    Algebraic proof involving identities
    Quadratic inequalities in straightforward cases
    Finding the nth term of quadratic sequences
    Graphs of quadratic and cubic functions
    Translating and reflecting graphs
Ratio and proportion
    Algebraic direct and inverse proportion
    Compound growth and decay
    Repeated percentage change and compound interest
    Similarity involving area and volume scale factors
    Gradients as rates of change
Geometry
    Sine rule and cosine rule in multi-step problems
    3D Pythagoras and trigonometry
    Circle theorems with reasoning
    Tangents to circles
    Sector arc lengths and areas in compound problems
    Surface area and volume of cones, spheres and composite solids
    Vector calculations and geometric arguments
    Proof using congruence and similarity
Probability
    Conditional probability using tables, trees and Venn diagrams
    Dependent events
    Combined events requiring more than one method
Statistics
    Histograms with unequal class widths
    Cumulative frequency and box plots together
    Estimating medians, quartiles and interquartile range
    Comparing distributions and interpreting data critically

GRADE 7

Number
    Surds and rationalising denominators in multi-step problems
    Exact calculations involving surds and \(\pi\)
    Fractional and negative indices
    Bounds in compound calculations
    Error intervals and maximum/minimum possible values
Algebra
    Completing the square and interpreting quadratic graphs
    Quadratic formula in complex contexts
    Simultaneous linear/quadratic equations
    Algebraic fractions with multiple operations
    Composite and inverse functions
    Algebraic proof and identities involving several steps
    Iteration to solve equations approximately
    Solving inequalities and representing regions graphically
    Intersections of graphs and approximate solutions
    Gradients and areas under non-linear graphs
Ratio and proportion
    Complex direct and inverse proportion
    Algebraic ratio problems
    Growth and decay with compound interest
    Multi-step similarity problems involving lengths, areas and volumes
    Average and instantaneous rates of change
Geometry
    Circle theorem proofs
    Complex bearings and scale diagrams
    3D trigonometry
    Sine rule and cosine rule in unfamiliar contexts
    Vectors: proving parallel lines and geometric relationships
    Transformations and combinations of transformations
    Complex area, surface area and volume problems
Probability
    Conditional probability in unfamiliar contexts
    Multi-stage probability tree diagrams
    Venn diagrams with algebraic probabilities
Statistics
    Histograms and cumulative frequency in multi-step problems
    Comparing data sets using several statistical measures
    Critical interpretation of sampling, correlation and extrapolation

GRADE 8

Number
    Complex surd manipulation and rationalisation
    Exact values in multi-step calculations
    Bounds problems involving several operations and formulae
Algebra
    Complex algebraic fractions
    Completing the square to find turning points and roots
    Quadratic inequalities and graphical interpretation
    Composite functions and inverse functions in multi-step problems
    Iteration and numerical solutions
    Graph transformations
    Circle equations and tangents
    Algebraic identities used to prove equivalence
    Non-linear graphs and their intersections
    Gradients and areas under curves
Ratio and proportion
    Complex algebraic proportionality
    Combined direct and inverse proportion
    Growth and decay in unfamiliar contexts
    Problems linking proportion, graphs and geometry
Geometry
    Complex circle theorem proofs
    Vectors used in formal geometric proofs
    Multi-step 3D trigonometry
    Composite shapes involving similarity and trigonometry
    Advanced use of sine rule, cosine rule and triangle area formula
Probability
    Conditional probability and combined events
    Multi-stage problems combining trees, Venn diagrams and tables
Statistics
    Multi-step histogram and cumulative frequency questions
    Statistical comparisons requiring justification
    Interpreting limitations and reliability of data

GRADE 9

Number
    Complex exact calculations involving surds, indices and standard form
    Multi-step upper and lower bounds problems
    Proof and reasoning involving numerical relationships
Algebra
    Challenging algebraic identities and proof
    Complex factorisation and quadratic equations
    Completing the square in unfamiliar contexts
    Composite functions and inverse functions
    Iteration and accuracy of numerical solutions
    Complex quadratic inequalities
    Circle equations and tangent problems
    Graph transformations and intersections of functions
    Interpreting gradients and areas under non-linear graphs
    Multi-step problems combining algebra, graphs and geometry
Ratio and proportion
    Unfamiliar direct and inverse proportion problems
    Multi-stage growth and decay
    Compound percentage and proportionality problems
    Problems connecting algebra, similarity and rates of change

Geometry
    Multi-step circle theorem proofs
    Advanced vector proofs
    Complex 3D trigonometry
    Problems combining sine rule, cosine rule, area and similarity
    Unfamiliar geometric reasoning and proof
    Composite mensuration involving several shapes and formulae
Probability
    Complex conditional probability
    Multi-stage problems requiring selection of an efficient method
    Algebraic probability and interpretation of assumptions
Statistics
    Complex interpretation and comparison of distributions
    Combining statistical measures with reasoning
    Evaluating conclusions, sampling limitations and extrapolation
 

bottom of page