GCSE Mathematics

Maths equations

A6: 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

A5: understand and use standard mathematical formulae; rearrange formulae to change the subject

A4: 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 x^2 + bx + c, including the difference of two squares; factorising quadratic expressions of the form ax^2 + bx + c ● simplifying expressions involving sums, products and powers, including the laws of indices

A3: understand and use the concepts and vocabulary of expressions, equations, formulae, identities, inequalities, terms and factors

A2: substitute numerical values into formulae and expressions, including scientific formulae

A1: use and interpret algebraic manipulation, including: • ab in place of a × b • 3y in place of y + y + y and 3 × y • a2 in place of a × a, a3 in place of a × a × a, a2b in place of a × a × b a • in place of a ÷ b b ● coefficients written as fractions rather than as decimals ● brackets

N16: apply and interpret limits of accuracy, including upper and lower bounds

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

N14: estimate answers; check calculations using approximation and estimation, including answers obtained using technology

N13: use standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate

N12: interpret fractions and percentages as operators

N11: identify and work with fractions in ratio problems

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

N9: calculate with and interpret standard form A × 10^n , where 1 ≤ A < 10 and n is an integer

N8: 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

N7: calculate with roots, and with integer and fractional indices

N6: 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

N5: apply systematic listing strategies, including use of the product rule for counting (i.e. if there are m ways of doing one task and for each of these, there are n ways of doing another task, then the total number of ways the two tasks can be done is m × n ways)

N4: 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