GCSE maths · strand

Number

26 topics, each with printable practice questions and a full answer key. Every sheet is generated, so you can make a fresh one whenever you need it.

Foundation and Higher tier 14 topics

Part Foundation, part Higher only 9 topics

Higher tier only 3 topics

All strands by tier: Foundation tier · Higher tier

GCSE subject content 19 DfE statements

simplify and manipulate algebraic expressions (including those involving surds and algebraic fractions) by: collecting like terms; multiplying a single term over a bracket; taking out common factors; expanding products of two or more binomials; factorising quadratic expressions of the form x² + bx + c, including the difference of two squares; factorising quadratic expressions of the form ax² + bx + c; simplifying expressions involving sums, products and powers, including the laws of indices

Fractional and Negative Indices · Indices

G14

use standard units of measure and related concepts (length, area, volume/capacity, mass, time, money, etc.)

Time

order positive and negative integers, decimals and fractions; use the symbols =, ≠, <, >, ≤, ≥

Negative Numbers · Writing, Simplifying and Ordering Fractions

apply the four operations, including formal written methods, to integers, decimals and simple fractions (proper and improper), and mixed numbers – all both positive and negative; understand and use place value (e.g. when working with very large or very small numbers, and when calculating with decimals)

Addition and Subtraction · Calculation Problems · Fractions · Multiplication and Division · Negative Numbers · Place Value · Using a Calculator · Writing, Simplifying and Ordering Fractions

recognise and use relationships between operations, including inverse operations (e.g. cancellation to simplify calculations and expressions; use conventional notation for priority of operations, including brackets, powers, roots and reciprocals

BIDMAS · Multiplication and Division · Using a Calculator · Writing, Simplifying and Ordering Fractions

use the concepts and vocabulary of prime numbers, factors (divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation theorem

Factors and Multiples · Prime Factors, HCF and LCM

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

Systematic Listing · The Product Rule for Counting

use positive integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5; estimate powers and roots of any given positive number

Estimating · Powers and Roots · Prime Factors, HCF and LCM · Using a Calculator

calculate with roots, and with integer and fractional indices

Fractional and Negative Indices · Indices

calculate exactly with fractions, surds and multiples of π; simplify surd expressions involving squares (e.g. √12 = √(4×3) = √4 × √3 = 2√3) and rationalise denominators

Surds

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

Standard Form

N10

work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 or 3/8); change recurring decimals into their corresponding fractions and vice versa

Fractions, Decimals and Percentages · Recurring Decimals to Fractions

N12

interpret fractions and percentages as operators

Fractions of an Amount

N13

use standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate

Time

N14

estimate answers; check calculations using approximation and estimation, including answers obtained using technology

Estimating

N15

round numbers and measures to an appropriate degree of accuracy (e.g. to a specified number of decimal places or significant figures); use inequality notation to specify simple error intervals due to truncation or rounding

Bounds · Error Intervals · Estimating · Rounding · Using a Calculator

N16

apply and interpret limits of accuracy, including upper and lower bounds

Bounds · Error Intervals

express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1

Fractions of an Amount

define percentage as ‘number of parts per hundred’; interpret percentages and percentage changes as a fraction or a decimal, and interpret these multiplicatively; express one quantity as a percentage of another; compare two quantities using percentages; work with percentages greater than 100%; solve problems involving percentage change, including percentage increase/decrease and original value problems, and simple interest including in financial mathematics

Fractions, Decimals and Percentages

Statements from the Department for Education's GCSE mathematics subject content. Contains public sector information licensed under the Open Government Licence v3.0.

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