Curriculum (United Kingdom)

Year 10 Maths

Year 10 maths (GCSE) according to the national curriculum in England: laws of indices and surds, quadratic equations and inequalities, simultaneous equations, circle theorems, sine and cosine rules, bearings and conditional probability. Every topic comes with ready-made task templates for printable worksheets.

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What does a child learn in Year 10 maths?

Year 10 starts the GCSE course of key stage 4: a child uses the laws of indices, simplifies surds and converts recurring decimals. Quadratic expressions are factorised and quadratic equations solved, also by completing the square; simultaneous equations, inequalities and graph transformations follow. In geometry come circle theorems, arcs and sectors, the sine and cosine rules and bearings; in statistics and probability — box plots, two-way tables and conditional probability.

About the national curriculum: the programmes of study for key stages 3 and 4 are set out for the whole key stage, not year by year. Placing a topic in this year is our decision, based on where it is usually taught; the statutory requirements of the key stage, quoted word for word, are in the section below.

Higher tier: content that the curriculum marks in braces { } is additional content for more highly attaining pupils — the GCSE Higher tier.

Curriculum scope

KS4.N (our numbering) · Teaching content · checked against the act

Number

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Number
KS4.N.1 (our numbering) · Teaching content · checked against the act

apply systematic listing strategies, {including use of the product rule for counting}

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Number, statutory requirement KS4.N.1
KS4.N.3 (our numbering) · Teaching content · checked against the act

calculate with roots, and with integer {and fractional} indices

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Number, statutory requirement KS4.N.3
KS4.N.4 (our numbering) · Teaching content

calculate exactly with fractions, {surds} and multiples of π; {simplify surd expressions involving squares [for example √12 = √(4 × 3) = √4 × √3 = 2√3] and rationalise denominators}

our summary of the point · National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Number, statutory requirement KS4.N.4
KS4.N.5 (our numbering) · Teaching content

calculate with numbers in standard form A × 10ⁿ, where 1 ≤ A < 10 and n is an integer

our summary of the point · National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Number, statutory requirement KS4.N.5
KS4.N.7 (our numbering) · Teaching content · checked against the act

identify and work with fractions in ratio problems

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Number, statutory requirement KS4.N.7
KS4.N.8 (our numbering) · Teaching content · checked against the act

apply and interpret limits of accuracy when rounding or truncating, {including upper and lower bounds}.

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Number, statutory requirement KS4.N.8
KS4.A (our numbering) · Teaching content · checked against the act

Algebra

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Algebra
KS4.A.1 (our numbering) · Teaching content · checked against the act

simplify and manipulate algebraic expressions (including those involving surds {and algebraic fractions}) by:

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Algebra, statutory requirement KS4.A.1
KS4.A.2 (our numbering) · Teaching content · checked against the act

know the difference between an equation and an identity; argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments {and proofs}

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Algebra, statutory requirement KS4.A.2
KS4.A.3 (our numbering) · Teaching content · checked against the act

where appropriate, interpret simple expressions as functions with inputs and outputs; {interpret the reverse process as the ‘inverse function’; interpret the succession of two functions as a ‘composite function’}

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Algebra, statutory requirement KS4.A.3
KS4.A.4 (our numbering) · Teaching content

use the form y = mx + c to identify parallel {and perpendicular} lines; find the equation of the line through two given points, or through one point with a given gradient

our summary of the point · National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Algebra, statutory requirement KS4.A.4
KS4.A.5 (our numbering) · Teaching content · checked against the act

identify and interpret roots, intercepts and turning points of quadratic functions graphically; deduce roots algebraically {and turning points by completing the square}

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Algebra, statutory requirement KS4.A.5
KS4.A.6 (our numbering) · Teaching content

recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions, the reciprocal function y = 1/x with x ≠ 0, {the exponential function y = kˣ for positive values of k, and the trigonometric functions (with arguments in degrees) y = sin x, y = cos x and y = tan x for angles of any size}

our summary of the point · National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Algebra, statutory requirement KS4.A.6
KS4.A.8 (our numbering) · Teaching content · checked against the act

plot and interpret graphs (including reciprocal graphs {and exponential graphs}) and graphs of non-standard functions in real contexts, to find approximate solutions to problems such as simple kinematic problems involving distance, speed and acceleration

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Algebra, statutory requirement KS4.A.8
KS4.A.11 (our numbering) · Teaching content · checked against the act

solve quadratic equations {including those that require rearrangement} algebraically by factorising, {by completing the square and by using the quadratic formula}; find approximate solutions using a graph

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Algebra, statutory requirement KS4.A.11
KS4.A.12 (our numbering) · Teaching content · checked against the act

solve two simultaneous equations in two variables (linear/linear {or linear/quadratic}) algebraically; find approximate solutions using a graph

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Algebra, statutory requirement KS4.A.12
KS4.A.14 (our numbering) · Teaching content · checked against the act

translate simple situations or procedures into algebraic expressions or formulae; derive an equation (or two simultaneous equations), solve the equation(s) and interpret the solution

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Algebra, statutory requirement KS4.A.14
KS4.A.15 (our numbering) · Teaching content · checked against the act

solve linear inequalities in one {or two} variable{s}, {and quadratic inequalities in one variable}; represent the solution set on a number line, {using set notation and on a graph}

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Algebra, statutory requirement KS4.A.15
KS4.A.16 (our numbering) · Teaching content

recognise and use sequences of triangular, square and cube numbers, simple arithmetic progressions, Fibonacci type sequences, quadratic sequences, and simple geometric progressions (rⁿ where n is an integer, and r is a positive rational number {or a surd}) {and other sequences}

our summary of the point · National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Algebra, statutory requirement KS4.A.16
KS4.A.17 (our numbering) · Teaching content · checked against the act

deduce expressions to calculate the nth term of linear {and quadratic} sequences.

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Algebra, statutory requirement KS4.A.17
KS4.A.1.a (our numbering) · Teaching content

factorising quadratic expressions of the form x² + bx + c, including the difference of two squares; {factorising quadratic expressions of the form ax² + bx + c}

our summary of the point · National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Algebra, statutory requirement KS4.A.1.a
KS4.A.1.b (our numbering) · Teaching content · checked against the act

simplifying expressions involving sums, products and powers, including the laws of indices

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Algebra, statutory requirement KS4.A.1.b
KS4.R (our numbering) · Teaching content · checked against the act

Ratio, proportion and rates of change

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Ratio, proportion and rates of change
KS4.R.1 (our numbering) · Teaching content · checked against the act

compare lengths, areas and volumes using ratio notation and/or scale factors; make links to similarity (including trigonometric ratios)

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Ratio, proportion and rates of change, statutory requirement KS4.R.1
KS4.R.2 (our numbering) · Teaching content · checked against the act

convert between related compound units (speed, rates of pay, prices, density, pressure) in numerical and algebraic contexts

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Ratio, proportion and rates of change, statutory requirement KS4.R.2
KS4.R.3 (our numbering) · Teaching content

understand that X is inversely proportional to Y is equivalent to X is proportional to 1/Y; {construct and} interpret equations that describe direct and inverse proportion

our summary of the point · National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Ratio, proportion and rates of change, statutory requirement KS4.R.3
KS4.R.4 (our numbering) · Teaching content · checked against the act

interpret the gradient of a straight line graph as a rate of change; recognise and interpret graphs that illustrate direct and inverse proportion

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Ratio, proportion and rates of change, statutory requirement KS4.R.4
KS4.R.6 (our numbering) · Teaching content · checked against the act

set up, solve and interpret the answers in growth and decay problems, including compound interest {and work with general iterative processes}.

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Ratio, proportion and rates of change, statutory requirement KS4.R.6
KS4.GM (our numbering) · Teaching content · checked against the act

Geometry and measures

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Geometry and measures
KS4.GM.1 (our numbering) · Teaching content · checked against the act

interpret and use fractional {and negative} scale factors for enlargements

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Geometry and measures, statutory requirement KS4.GM.1
KS4.GM.3 (our numbering) · Teaching content · checked against the act

identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference, tangent, arc, sector and segment

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Geometry and measures, statutory requirement KS4.GM.3
KS4.GM.5 (our numbering) · Teaching content · checked against the act

construct and interpret plans and elevations of 3D shapes

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Geometry and measures, statutory requirement KS4.GM.5
KS4.GM.6 (our numbering) · Teaching content · checked against the act

interpret and use bearings

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Geometry and measures, statutory requirement KS4.GM.6
KS4.GM.7 (our numbering) · Teaching content · checked against the act

calculate arc lengths, angles and areas of sectors of circles

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Geometry and measures, statutory requirement KS4.GM.7
KS4.GM.8 (our numbering) · Teaching content · checked against the act

calculate surface areas and volumes of spheres, pyramids, cones and composite solids

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Geometry and measures, statutory requirement KS4.GM.8
KS4.GM.9 (our numbering) · Teaching content · checked against the act

apply the concepts of congruence and similarity, including the relationships between lengths, {areas and volumes} in similar figures

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Geometry and measures, statutory requirement KS4.GM.9
KS4.GM.10 (our numbering) · Teaching content · checked against the act

apply Pythagoras’ Theorem and trigonometric ratios to find angles and lengths in right-angled triangles {and, where possible, general triangles} in two {and three} dimensional figures

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Geometry and measures, statutory requirement KS4.GM.10
KS4.GM.11 (our numbering) · Teaching content

know the exact values of sin θ and cos θ for θ = 0°, 30°, 45°, 60° and 90°; know the exact value of tan θ for θ = 0°, 30°, 45° and 60°

our summary of the point · National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Geometry and measures, statutory requirement KS4.GM.11
KS4.GM.14 (our numbering) · Teaching content · checked against the act

describe translations as 2D vectors

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Geometry and measures, statutory requirement KS4.GM.14
KS4.GM.15 (our numbering) · Teaching content · checked against the act

apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors; {use vectors to construct geometric arguments and proofs}.

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Geometry and measures, statutory requirement KS4.GM.15
KS4.P (our numbering) · Teaching content · checked against the act

Probability

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Probability
KS4.P.1 (our numbering) · Teaching content · checked against the act

apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to one

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Probability, statutory requirement KS4.P.1
KS4.P.2 (our numbering) · Teaching content · checked against the act

use a probability model to predict the outcomes of future experiments; understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Probability, statutory requirement KS4.P.2
KS4.P.3 (our numbering) · Teaching content · checked against the act

calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Probability, statutory requirement KS4.P.3
KS4.S (our numbering) · Teaching content · checked against the act

Statistics

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Statistics
KS4.S.1 (our numbering) · Teaching content · checked against the act

infer properties of populations or distributions from a sample, whilst knowing the limitations of sampling

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Statistics, statutory requirement KS4.S.1
KS4.S.2 (our numbering) · Teaching content · checked against the act

interpret and construct tables and line graphs for time series data

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Statistics, statutory requirement KS4.S.2
KS4.S.4 (our numbering) · Teaching content · checked against the act

interpret, analyse and compare the distributions of data sets from univariate empirical distributions through:

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Statistics, statutory requirement KS4.S.4
KS4.S.5 (our numbering) · Teaching content · checked against the act

apply statistics to describe a population

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Statistics, statutory requirement KS4.S.5
KS4.S.6 (our numbering) · Teaching content · checked against the act

use and interpret scatter graphs of bivariate data; recognise correlation and know that it does not indicate causation; draw estimated lines of best fit; make predictions; interpolate and extrapolate apparent trends whilst knowing the dangers of so doing.

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Statistics, statutory requirement KS4.S.6
KS4.S.4.a (our numbering) · Teaching content · checked against the act

appropriate graphical representation involving discrete, continuous and grouped data, {including box plots}

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Statistics, statutory requirement KS4.S.4.a
KS4.S.4.b (our numbering) · Teaching content · checked against the act

appropriate measures of central tendency (including modal class) and spread {including quartiles and inter-quartile range}

National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Statistics, statutory requirement KS4.S.4.b

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