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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
GRADES 1-2
Number
Integers: positive and negative numbers
Place value, ordering numbers and comparing values
Four operations: addition, subtraction, multiplication and division
BIDMAS / order of operations
Factors, multiples and prime numbers
Fractions: recognising, simplifying and equivalent fractions
Converting between simple fractions, decimals and percentages
Rounding to the nearest 10, 100 or whole number
Estimation and checking answers
Squares and square roots of simple numbers
Algebra
Understanding algebraic notation
Collecting like terms
Substitution into simple expressions
Expanding a single bracket
Solving simple linear equations
Finding the next term in a sequence
Recognising and using simple formulae
Ratio, proportion and percentages
Writing and simplifying ratios
Sharing an amount in a simple ratio
Finding fractions of amounts
Finding percentages of amounts
Percentage increase and decrease in simple cases
Using scales in simple contexts
Unit conversions: length, mass, time and money
Speed in simple problems
Geometry and measures
Types of angles and measuring angles
Angles on a straight line and around a point
Properties of triangles and quadrilaterals
Perimeter and area of rectangles, triangles and simple shapes
Circumference and area of a circle in straightforward questions
Basic properties of 3D shapes
Reflection, rotation and translation
Reading coordinates in four quadrants
Basic constructions
Probability
Probability scale from 0 to 1
Equally likely outcomes
Simple probability calculations
Using the fact that probabilities sum to 1
Statistics
Mean, median, mode and range
Reading tables, bar charts and pictograms
Interpreting simple graphs
Frequency tables
GRADE 3
Number
Operations with fractions, including simple mixed numbers
Calculations with negative numbers
HCF and LCM
Prime factorisation using factor trees
Powers, squares, cubes and roots
Standard form in straightforward cases
Fractions, decimals and percentages conversions
Rounding to decimal places and significant figures
Simple error intervals
Algebra
Expanding and simplifying expressions
Factorising expressions by taking out a common factor
Solving equations with the unknown on both sides in simple cases
Forming expressions from worded problems
Generating sequences and finding simple term-to-term rules
Plotting straight-line graphs
Coordinates and reading graphs
Ratio and proportion
Sharing quantities in a ratio
Ratio in practical problems
Best buys and unit pricing
Percentage change
Reverse percentages in simple cases
Direct proportion in numerical contexts
Converting compound units
Geometry
Angles in parallel lines
Angles in polygons
Area of compound shapes
Volume of cuboids and prisms
Pythagoras' theorem in straightforward problems
Scale drawings and bearings
Congruence and basic similarity
Transformations on a coordinate grid
Probability
Sample spaces and systematic listing
Frequency trees
Simple combined probability
Statistics
Averages from frequency tables
Pie charts and time-series graphs
Scatter graphs and correlation
Comparing data using averages and range
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