Edexcel GCSE Maths (1MA1) Higher — revision checklist

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

N1

Apply the four operations, including formal written methods, to integers, decimals and simple fractions (proper and improper), and mixed numbers, positive and negative; understand and use place value

N2

Recognise and use relationships between operations, including inverse operations; use conventional notation for priority of operations, including brackets, powers, roots and reciprocals

N3

Prime numbers, factors (divisors), multiples, common factors and multiples, highest common factor, lowest common multiple, prime factorisation with product notation and unique factorisation theorem

N4

Apply systematic listing strategies, including use of the product rule for counting (m ways of doing one task and n ways of doing another gives m × n ways in total)

N5

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

N6

Calculate with roots, and with integer and fractional indices

N7

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

N8

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

N9

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

N10

Identify and work with fractions in ratio problems

N11

Interpret fractions and percentages as operators

N12

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

N13

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

N14

Round numbers and measures to an appropriate degree of accuracy (decimal places or significant figures); use inequality notation to specify simple error intervals due to truncation or rounding

N15

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

N16

Use and interpret algebraic manipulation: ab for a × b, 3y for y + y + y and 3 × y, a² for a × a, a³ for a × a × a, a²b for a × a × b, a/b for a ÷ b, coefficients as fractions, brackets

A1

Substitute numerical values into formulae and expressions, including scientific formulae

A2

Understand and use the concepts and vocabulary of expressions, equations, formulae, identities, inequalities, terms and factors

A3

Simplify and manipulate algebraic expressions (incl. surds and algebraic fractions): like terms, common factors, expanding two or more binomials, factorising quadratics incl. ax² + bx + c, indices

A4

Understand and use standard mathematical formulae; rearrange formulae to change the subject

A5

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

A6

Interpret simple expressions as functions with inputs and outputs; interpret the reverse as the 'inverse function' and two successive functions as a 'composite function' (formal notation expected)

A7

Work with coordinates in all four quadrants

A8

Plot graphs of straight-line equations; use y = mx + c to identify parallel and perpendicular lines; find the equation of a line through two given points, or one point with a given gradient

A9

Identify and interpret gradients and intercepts of linear functions graphically and algebraically

A10

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

A11

Recognise, sketch and interpret graphs of linear, quadratic and simple cubic functions, the reciprocal y = 1/x (x ≠ 0), exponential y = k^x (k > 0), and y = sin x, cos x, tan x for angles of any size

A12

Sketch translations and reflections of a given function [Higher only]

A13

Plot and interpret graphs (including reciprocal and exponential graphs) and graphs of non-standard functions in real contexts, to find approximate solutions e.g. simple kinematic problems

A14

Calculate or estimate gradients of graphs and areas under graphs (incl. quadratic and other non-linear); interpret e.g. distance-time, velocity-time and financial graphs (not calculus) [Higher only]

A15

Recognise and use the equation of a circle with centre at the origin; find the equation of a tangent to a circle at a given point [Higher only]

A16

Solve linear equations in one unknown algebraically (including those with the unknown on both sides of the equation); find approximate solutions using a graph

A17

Solve quadratic equations (including those requiring rearrangement) algebraically by factorising, by completing the square and by using the quadratic formula; find approximate solutions using a graph

A18

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

A19

Find approximate solutions to equations numerically using iteration [Higher only]

A20

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

A21

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

A22

Generate terms of a sequence from either a term-to-term or a position-to-term rule

A23

Recognise and use triangular, square and cube numbers, arithmetic progressions, Fibonacci type sequences, quadratic sequences, simple geometric progressions (r^n, r rational > 0 or a surd) and others

A24

Deduce expressions to calculate the nth term of linear and quadratic sequences

A25

Change freely between related standard units (time, length, area, volume/capacity, mass) and compound units (speed, rates of pay, prices, density, pressure) in numerical and algebraic contexts

R1

Use scale factors, scale diagrams and maps

R2

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

R3

Use ratio notation, including reduction to simplest form

R4

Divide a quantity in a given part:part or part:whole ratio; express division into two parts as a ratio; apply ratio to real problems (conversion, comparison, scaling, mixing, concentrations)

R5

Express a multiplicative relationship between two quantities as a ratio or a fraction

R6

Understand and use proportion as equality of ratios

R7

Relate ratios to fractions and to linear functions

R8

Define percentage as 'number of parts per hundred'; interpret percentages and percentage changes as fractions/decimals, multiplicatively; percentages > 100%; percentage change and simple interest

R9

Solve problems involving direct and inverse proportion, including graphical and algebraic representations

R10

Use compound units such as speed, rates of pay, unit pricing, density and pressure

R11

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

R12

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

R13

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

R14

Interpret the gradient at a point on a curve as the instantaneous rate of change; apply average and instantaneous rates of change (gradients of chords and tangents) (not calculus) [Higher only]

R15

Set up, solve and interpret the answers in growth and decay problems, including compound interest and work with general iterative processes

R16

Use conventional terms/notations: points, lines, vertices, edges, planes, parallel and perpendicular lines, right angles, polygons; standard triangle labelling; draw diagrams from written description

G1

Use standard ruler and compass constructions (perpendicular bisector, perpendicular from/at a point, angle bisector); construct figures, solve loci problems; perpendicular distance is shortest

G2

Apply angles at a point, on a straight line, vertically opposite angles; use alternate and corresponding angles on parallel lines; derive and use the angle sum of a triangle and of any polygon

G3

Derive and apply properties and definitions of special quadrilaterals (square, rectangle, parallelogram, trapezium, kite, rhombus), triangles and other plane figures using appropriate language

G4

Use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS)

G5

Apply angle facts, congruence, similarity and quadrilateral properties to derive results about angles and sides, incl. Pythagoras' theorem and isosceles base angles, and obtain simple proofs

G6

Identify, describe and construct congruent and similar shapes, incl. on coordinate axes, by rotation, reflection, translation and enlargement (including fractional and negative scale factors)

G7

Describe the changes and invariance achieved by combinations of rotations, reflections and translations [Higher only]

G8

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

G9

Apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results [Higher only]

G10

Solve geometrical problems on coordinate axes

G11

Identify properties of the faces, surfaces, edges and vertices of: cubes, cuboids, prisms, cylinders, pyramids, cones and spheres

G12

Construct and interpret plans and elevations of 3D shapes

G13

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

G14

Measure line segments and angles in geometric figures, including interpreting maps and scale drawings and use of bearings

G15

Know and apply formulae to calculate: area of triangles, parallelograms, trapezia; volume of cuboids and other right prisms (including cylinders)

G16

Know circumference of a circle = 2πr = πd and area = πr²; calculate perimeters of 2D shapes incl. circles, areas of circles and composite shapes, surface area and volume of spheres, pyramids, cones

G17

Calculate arc lengths, angles and areas of sectors of circles

G18

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

G19

Know Pythagoras' theorem a² + b² = c² and the trigonometric ratios sin, cos and tan; apply them to find angles and lengths in right-angled and, where possible, general triangles in 2D and 3D figures

G20

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°

G21

Know and apply the sine rule a/sin A = b/sin B = c/sin C, and cosine rule a² = b² + c² - 2bc cos A, to find unknown lengths and angles [Higher only]

G22

Know and apply Area = ½ ab sin C to calculate the area, sides or angles of any triangle [Higher only]

G23

Describe translations as 2D vectors

G24

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

G25

Record, describe and analyse the frequency of outcomes of probability experiments using tables and frequency trees

P1

Apply ideas of randomness, fairness and equally likely events to calculate expected outcomes of multiple future experiments

P2

Relate relative expected frequencies to theoretical probability, using appropriate language and the 0-1 probability scale

P3

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

P4

Understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size

P5

Enumerate sets and combinations of sets systematically, using tables, grids, Venn diagrams and tree diagrams

P6

Construct theoretical possibility spaces for single and combined experiments with equally likely outcomes and use these to calculate theoretical probabilities

P7

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

P8

Calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and Venn diagrams [Higher only]

P9

Infer properties of populations or distributions from a sample, while knowing the limitations of sampling

S1

Interpret and construct frequency tables, bar charts, pie charts and pictograms (categorical data), vertical line charts (ungrouped discrete numerical data), tables and line graphs (time series)

S2

Construct and interpret diagrams for grouped discrete and continuous data, i.e. histograms with equal and unequal class intervals and cumulative frequency graphs [Higher only]

S3

Interpret, analyse and compare data-set distributions via graphs (incl. box plots), central tendency (median, mean, mode, modal class) and spread (range, outliers, quartiles, inter-quartile range)

S4

Apply statistics to describe a population

S5

Use and interpret scatter graphs of bivariate data; recognise correlation, know it does not indicate causation; draw estimated lines of best fit; make predictions; interpolate/extrapolate with caution

S6