PEARSON EDEXCEL GCSE MATHS

The topics listed below are for Exedcel GCSE Maths, with exam codes:

• Foundation Tier – 1MA1/1F; 1MA1/2F; 1MA1/3F
• Higher Tier – 1MA1/1H; 1MA1/2H; 1MA1/3H

The list provides everything you need for your GCSE Exdecel exam, with topics broken in to the headings given by the exam board. More information is available here

[https://qualifications.pearson.com/content/dam/pdf/GCSE/mathematics/2015/specification-and-sample-assesment/gcse-maths-2015-specification.pdf]

For samples questions and papers, please click this link:

[https://qualifications.pearson.com/en/support/support-topics/exams/past-papers.html]

Everything you need to know about your GCSE (9-1) Maths specifications can be found here.

Foundation tier knowledge, skills and understanding

1. Number

Structure and Calculation

N1

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

N2

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)

N3

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

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

N5

apply systematic listing strategies

N6

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

N7

calculate with roots, and with integer indices

N8

calculate exactly with fractions and multiples of π

N9

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

Fractions, Decimals and Percentages

N10

work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/ 2 or 0.375 or 3/8 )

N11

identify and work with fractions in ratio problems

N12

interpret fractions and percentages as operators

Measures and Accuracy

N13

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

N14

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

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

N16

apply and interpret limits of accuracy

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2. Algebra

Notation, Vocabulary and Manipulation

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, a 3 in place of a × a × a, a 2 b in place of a × a × b
• a/b in place of a ÷ b
• coefficients written as fractions rather than as decimals
• brackets

A2

substitute numerical values into formulae and expressions, including scientific formulae

A3

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

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 ax² + 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

A5

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

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

A7

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’ (the use of formal function notation is expected)

Graphs

A8

work with coordinates in all four quadrants

A9

plot graphs of equations that correspond to straight-line graphs in the coordinate plane; 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

A10

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

A11

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

A12

recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions, the reciprocal function y = 1/x with x ≠ 0, exponential functions y = k× 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

A13

sketch translations and reflections of a given function

A14

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

A15

calculate or estimate gradients of graphs and areas under graphs (including quadratic and other non-linear graphs), and interpret results in cases such as distance-time graphs, velocity-time graphs and graphs in financial contexts (this does not include calculus)

A16

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

Solving equations and inequalities

A17

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

A18

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

A19

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

A20

find approximate solutions to equations numerically using iteration

A21

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

A22

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

Sequences

A23

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

A24

recognise and use sequences of triangular, square and cube numbers, simple
arithmetic progressions, Fibonacci type sequences, quadratic sequences, and
simple geometric progressions (r^n where n is an integer, and r is a rational number > 0 or a surd) and other sequences

A25

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

3. Ratio, Proportion and Rates of Change

R1

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

R2

use scale factors, scale diagrams and maps

R3

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

R4

use ratio notation, including reduction to simplest form

R5

divide a given quantity into two parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio; apply ratio to real contexts and problems (such as those involving conversion, comparison, scaling, mixing, concentrations)

R6

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

R7

understand and use proportion as equality of ratios

R8

relate ratios to fractions and to linear functions

R9

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

R10

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

R11

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

R12

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

R13

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

R14

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

R15

interpret the gradient at a point on a curve as the instantaneous rate of change; apply the concepts of average and instantaneous rate of change (gradients of chords and tangents) in numerical, algebraic and graphical contexts (this does not include calculus)

R16

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

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4. Geometry and Measures

Properties and Constructions

G1

use conventional terms and notations: points, lines, vertices, edges, planes, parallel lines, perpendicular lines, right angles, polygons, regular polygons and polygons with reflection and/or rotation symmetries; use the standard conventions for labelling and referring to the sides and angles of triangles; draw diagrams from written description

G2

use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle); use these to construct given figures and solve loci problems; know that the perpendicular distance from a point to a line is the shortest distance to the line

G3

apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles; understand and use alternate and corresponding angles on parallel lines; derive and use the sum of angles in a triangle (e.g. to deduce and use the angle sum in any polygon, and to derive properties of regular polygons)

G4

derive and apply the properties and definitions of: special types of quadrilaterals, including square, rectangle, parallelogram, trapezium, kite and rhombus; and triangles and other plane figures using appropriate language

G5

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

G6

apply angle facts, triangle congruence, similarity and properties of quadrilaterals to conjecture and derive results about angles and sides, including Pythagoras’ theorem and the fact that the base angles of an isosceles triangle are equal, and use known results to obtain simple proofs

G7

use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS)identify, describe and construct congruent and similar shapes, including on coordinate axes, by considering rotation, reflection, translation and enlargement (including fractional and negative scale factors)

G8

describe the changes and invariance achieved by combinations of rotations, reflections and translations

G9

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

G10

apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results

G11

solve geometrical problems on coordinate axes

G12

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

G13

construct and interpret plans and elevations of 3D shapes

Mensuration and Calculation

G14

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

G15

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

G16

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

G17

know the formulae: circumference of a circle = 2πr = πd , area of a circle = πr² ; calculate: perimeters of 2D shapes, including circles; areas of circles and composite shapes; surface area and volume of spheres, pyramids, cones and composite solids

G18

calculate arc lengths, angles and areas of sectors of circles

G19

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

G20

know the formulae for: Pythagoras’ theorem a² + b² = c², and the trigonometric ratios, sin θ = opposite/hypotenuse , cos θ = adjacent hypotenuse and tan θ = opposite adjacent ; apply them to find angles and lengths in right-angled triangles and, where possible, general triangles in two and three dimensional figures

G21

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°

G22

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

G23

know and apply Area = 1/2 ab sin C to calculate the area, sides or angles of any triangle

Vectors

G24

describe translations as 2D vectors

G25

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

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5. Probability

P1

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

P2

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

P3

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

P4

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

P5

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

P6

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

P7

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

P8

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

P9

calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and Venn diagrams

6. Statistics

S1

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

S2

interpret and construct tables, charts and diagrams, including frequency tables, bar charts, pie charts and pictograms for categorical data, vertical line charts for ungrouped discrete numerical data, tables and line graphs for time series data and know their appropriate use

S3

construct and interpret diagrams for grouped discrete data and continuous data, i.e. histograms with equal and unequal class intervals and cumulative frequency graphs, and know their appropriate use

S4

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

• appropriate graphical representation involving discrete, continuous and grouped data, including box plots
• appropriate measures of central tendency (median, mean, mode and modal class) and spread (range, including consideration of outliers, quartiles and inter-quartile range)

S5

apply statistics to describe a population

S6

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 while knowing the dangers of so doing