Year 10 Maths

Number Properties I

Optional enrichment: Factors, prime powers and common multiples

Number Properties II

Optional enrichment: Divisor counts and HCF/LCM relationships

Number Structure

Optional enrichment: Perfect powers, divisibility and constrained prime factors

Fraction Reasoning

Optional enrichment: Remaining fractions, rates, recurring decimals and rational relationships

Percentage Modelling

Optional enrichment: Repeated changes, weighted percentages and reverse compound growth

Proportional Modelling

Optional enrichment: Changing ratios, inverse variation and joint proportion

Integer Constraints

Optional enrichment: Integer bounds, absolute values and signed relationships

Indices and Surds

Optional enrichment: Fractional indices, conjugates and exact surd relationships

Whole-number Decisions

Compare feasible pack purchases and reconstruct whole-number quantities

Fraction Decisions

Exact versus rounded totals and reversing a mixture transfer

Percentage Decisions

Compare net percentage returns and reconstruct compound balances

Ratio Decisions

Link ratios across changing shares and interrupted work rates

Signed-number Decisions

Whole-day financial thresholds and reconstructing signed scores

Powers and Scientific Notation

Track accumulated rounding error and model storage with powers of ten

Fraction equations

Quadratic Equations

Optional extension. Rearrange equations and factorise ax² + bx + c, including fractional roots.

Exponential Equations

Matching bases and powers

Algebraic Structure

Identities, factor structure and coefficients

Equation Systems

Simultaneous equations and parameter constraints

Sequence Modelling

Quadratic patterns, sums and geometric sequences

Function Modelling

Lines, intersections and quadratic functions

Expression Reasoning

Substitution, equivalent expressions and quadratic identities.

Linear Reasoning

Equations, inequalities and simultaneous models.

Quadratic Modelling

Build and solve factorisable quadratic models, then interpret their solutions.

Quadratic Patterns

Infer a quadratic pattern and use it to find or compare stages.

Graph Relationships

Infer linear rules and connect them to intersections and models.

Exponential Models

Infer and compare growth or decay rules using exact common-base values.

Linear graphing

Infer rules from tables and graphs, work with fractional gradients and find parallel lines and intersections.

Volume

Composite solids and inverse dimensions

Pythagoras

Diagonals and real situations

Trigonometry: Side Lengths

Sine, cosine and tangent

Circle and Polygon Reasoning

Optional extension: Circle theorems, tangent angles and regular polygon exterior angles

Composite Area

Annuli, sectors and area constraints

Composite Solids

Optional extension: Cones, hollow solids and changing dimensions

Spatial Pythagoras

Optional extension: Space diagonals, tangents and combined lengths

Similarity Modelling

Area and volume ratios, removed cones and nested shapes

Connected Angle Problems

Combine parallel lines, isosceles triangles, ratios and bisectors

Area Constraints

Infer dimensions before comparing and combining areas

Composite Surface Area

Infer hidden dimensions and account for holes or joined faces

Spatial Reasoning

Use right triangles in three dimensions and unfolded surfaces

Linked Trigonometry

Solve practical linked triangles using supplied exact ratios

Similarity Constraints

Connect corresponding lengths, areas and volumes

Statistics Revision

Bring together comparisons, box plots, two-way tables and sampling.

Data Displays

Histograms, scatter plots and misleading displays

Box Plots

Read the five-number summary

Sampling and Data

Sample variation and evidence

Data Modelling · Extension

Optional extension: Frequency density, interpolation and fitted lines

Distribution Reasoning · Extension

Optional extension: Combined means, variance and missing observations

Frequency Modelling · Extension

Optional extension: Unknown frequencies, grouped estimates and weighted spread

Sampling Models · Extension

Optional extension: Stratification, capture–recapture and sample precision

Data Display Reasoning

Data Display Reasoning

Distribution Reasoning

Distribution Reasoning

Frequency Reasoning

Frequency Reasoning

Evaluating Surveys

Evaluating Surveys

Frequency Tables

Two-way tables and relative frequency

Probability

Conditional probability, overlapping events and reverse reasoning

Conditional Chance

Conditional Chance