Eduqas GCSE C300 Maths: spec coverage
52of 187 spec points have a lesson out now
187have a lesson planned
Spec text is our short form of the board's statement. Always check the board's own specification.
| Spec | Statement | Lesson |
|---|---|---|
| FA1 | Use and interpret algebraic notation, 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/b in place of a ÷ b; coefficients written as fractions rather than as decimals; brackets | MA09-01 What Algebraic Notation Means Coming soon |
| FA2 | Substitute numerical values into formulae and expressions, including scientific formulae | MA09-03 Substituting Values into Expressions and Formulae Coming soon |
| FA3 | Understand and use the concepts and vocabulary of expressions, equations, formulae, identities, inequalities, terms and factors | MA09-02 Algebra Vocabulary: Expressions, Equations, Formulae, Identities and Inequalities Coming soon |
| FA4 | Simplify and manipulate algebraic expressions (including those involving surds) by: collecting like terms; multiplying a single term over a bracket; taking out common factors; expanding products of two binomials; factorising quadratic expressions of the form x² + bx + c, including the difference of two squares; simplifying expressions involving sums, products and powers, including the laws of indices | MA09-04 Collecting Like Terms Coming soonMA09-05 Laws of Indices for Algebraic Terms Coming soonMA10-01 Expanding a Single Bracket Coming soonMA10-02 Expanding Double Brackets Coming soonMA10-04 Factorising by Taking Out a Common Factor Coming soonMA10-05 Factorising a Quadratic x^2+bx+c, Including Difference of Two Squares Coming soon |
| FA5 | Understand and use standard mathematical formulae; rearrange formulae to change the subject | MA11-03 Using and Rearranging a Formula (Subject Appears Once) Watch |
| FA6 | 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 | MA10-09 Equations, Identities and Equivalent Expressions Coming soon |
| FA7 | Where appropriate, interpret simple expressions as functions with inputs and outputs | MA14-01 Function Machines: Inputs, Outputs and Reversing Watch |
| FA8 | Work with coordinates in all four quadrants | MA15-01 Coordinates in Four Quadrants Watch |
| FA9 | Plot graphs of equations that correspond to straight-line graphs in the coordinate plane; use the form y = mx + c to identify parallel lines; find the equation of the line through two given points, or through one point with a given gradient | MA15-03 Plotting Straight-Line Graphs Coming soonMA15-06 Finding the Equation of a Straight Line Coming soonMA15-07 Equations of Parallel Lines Coming soon |
| FA10 | Identify and interpret gradients and intercepts of linear functions graphically and algebraically | MA15-05 Gradient and Y-Intercept via y=mx+c Coming soon |
| FA11 | Identify and interpret roots, intercepts, turning points (stationary points) of quadratic functions graphically; deduce roots algebraically | MA16-02 Roots, Y-Intercept and Turning Point of a Quadratic Graph Coming soon |
| FA12 | Recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions, the reciprocal function y = 1/x, with x ≠ 0 | MA16-01 Recognising Linear and Quadratic Graphs Coming soonMA16-04 Cubic and Reciprocal Graphs Coming soon |
| FA13 | Plot and interpret graphs (including reciprocal 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 | MA17-01 Plotting and Interpreting Real-World Graphs Coming soon |
| FA14 | Solve linear equations in one unknown algebraically (including those with the unknown on both sides of the equation); find approximate solutions using a graph | MA11-01 Solving Linear Equations by Balancing WatchMA11-02 Solving Linear Equations with Brackets Watch |
| FA15 | Solve quadratic equations of the form x² + bx + c (NOT including those that require rearrangement) algebraically by factorising; find approximate solutions using a graph | MA12-01 Solving x^2+bx+c=0 by Factorising Watch |
| FA16 | Solve two simultaneous linear equations in two variables algebraically; find approximate solutions using a graph | MA12-04 Solving Simultaneous Linear Equations by Elimination Watch |
| FA17 | 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 | MA11-05 Writing an Expression or Formula from a Context WatchMA11-06 Setting Up and Solving an Equation from a Context Watch |
| FA18 | Solve linear inequalities in one variable; represent the solution set on a number line | MA18-01 Inequality Symbols and Number-Line Conventions Coming soonMA18-02 Solving a Linear Inequality Coming soon |
| FA19 | Generate terms of a sequence from either a term-to-term or a position-to-term rule | MA13-01 Generating Terms of a Sequence Coming soon |
| FA20 | 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 rational number > 0) | MA13-02 Recognising Special Sequences Watch |
| FA21 | Deduce expressions to calculate the nth term of linear sequences | MA13-04 Finding the nth Term of a Linear Sequence Watch |
| FG1 | 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 | MA25-01 Geometry notation and types of angle Coming soon |
| FG2 | 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 | MA24-01 Constructing the perpendicular bisector of a line segment WatchMA24-02 Constructing the bisector of an angle Coming soonMA24-03 Constructing a perpendicular to a line from or at a point Coming soonMA24-04 Solving loci problems with a single condition Coming soonMA24-05 Solving loci problems with combined conditions Coming soon |
| FG3 | 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) | MA25-02 Angles at a point, on a line and vertically opposite angles Coming soonMA25-03 Angles on parallel lines Coming soonMA25-05 Angle sum of a triangle and the exterior angle rule Coming soonMA25-06 Interior angles of polygons Coming soonMA25-07 Exterior angles and regular polygons Coming soon |
| FG4 | Derive and apply the properties and definitions of: special types of triangles, quadrilaterals (including square, rectangle, parallelogram, trapezium, kite and rhombus) and other plane figures using appropriate language | MA26-01 Naming triangles, quadrilaterals and polygons Coming soonMA26-02 Properties of special quadrilaterals and triangles Coming soon |
| FG5 | Use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS) | MA26-03 Congruent triangles: SSS, SAS, ASA and RHS Coming soon |
| FG6 | 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 | MA26-07 Proving results using congruent triangles and angle facts Coming soonMA26-08 Proving results using similarity and Pythagoras Coming soonMA30-01 Pythagoras' theorem in two dimensions Coming soon |
| FG7 | Identify, describe and construct congruent and similar shapes, including on coordinate axes, by considering rotation, reflection, translation and enlargement (including fractional scale factors) | MA28-01 Reflecting a shape in a mirror line Coming soonMA28-02 Finding the mirror line from a shape and its image Coming soonMA28-03 Rotating a shape and describing a rotation Coming soonMA28-04 Translating a shape using a column vector Coming soonMA28-05 Enlarging a shape by a positive or fractional scale factor Coming soon |
| FG8 | Identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference, tangent, arc, sector and segment | MA27-01 Circle vocabulary Coming soon |
| FG9 | Solve geometrical problems on coordinate axes | MA28-09 Solving geometry problems on coordinate axes Coming soon |
| FG10 | Identify properties of the faces, surfaces, edges and vertices of: cubes, cuboids, prisms, cylinders, pyramids, cones and spheres | MA29-01 Naming 3D solids and their properties Coming soon |
| FG11 | Construct and interpret plans and elevations of 3D shapes | MA29-02 Interpreting plans and elevations Coming soonMA29-03 Constructing plans and elevations Coming soon |
| FG12 | Use standard units of measure and related concepts (length, area, volume/capacity, mass, time, money, etc.) | MA22-01 Convert between standard and compound units Coming soon |
| FG13 | Measure line segments and angles in geometric figures, including interpreting maps and scale drawings and use of bearings | MA24-08 Three-figure bearings Coming soon |
| FG14 | Know and apply formulae to calculate: area of squares, rectangles, triangles, parallelograms, trapezia; volume of cuboids and other right prisms (including cylinders) | MA23-02 Area of triangles, parallelograms and trapezia WatchMA29-05 Volume of prisms, cuboids and cylinders Coming soon |
| FG15 | 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 | MA23-01 Perimeter of 2D and composite shapes WatchMA23-03 Circle circumference and area WatchMA29-06 Surface area and volume of a sphere and cone (Higher) Coming soonMA29-08 Composite solids: breaking a shape into parts Coming soon |
| FG16 | Calculate arc lengths, angles and areas of sectors of circles | MA23-04 Arc length and sector area, including major sectors Watch |
| FG17 | Apply the concepts of congruence and similarity, including the relationships between lengths in similar figures | MA26-12 Similar shapes: persisting the relationship across a question Coming soon |
| FG18 | Know the formulae for: Pythagoras' theorem, a² + b² = c², and the trigonometric ratios, sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent; apply them to find angles and lengths in right-angled triangles in two dimensional figures | MA30-01 Pythagoras' theorem in two dimensions Coming soonMA30-02 Trigonometric ratios: labelling sides and choosing sin, cos or tan Coming soonMA30-03 Using trigonometry to find missing sides and angles Coming soon |
| FG19 | 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° | MA30-02 Trigonometric ratios: labelling sides and choosing sin, cos or tan Coming soon |
| FG20 | Describe translations as 2D vectors | MA28-04 Translating a shape using a column vector Coming soon |
| FG21 | Apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors | MA28-10 Vector arithmetic: addition, subtraction and scalar multiplication Coming soon |
| FN1 | Order positive and negative integers, decimals and fractions; use the symbols =, ≠, <, >, ≤, ≥ | MA01-01 Ordering positive and negative numbers using inequality symbols Watch |
| FN2 | 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) | MA01-02 Place value and decimal notation WatchMA01-03 Adding, subtracting, multiplying and dividing positive and negative integers WatchMA01-04 Adding, subtracting, multiplying and dividing decimals WatchMA04-04 Adding and subtracting fractions and mixed numbers WatchMA04-05 Multiplying and dividing fractions and mixed numbers Watch |
| FN3 | 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) | MA01-05 Order of operations: brackets, powers, roots and BIDMAS WatchMA01-06 Inverse operations Watch |
| FN4 | 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 | MA02-01 Types of number and prime factorisation WatchMA02-02 Highest common factor (HCF) WatchMA02-03 Lowest common multiple (LCM) Watch |
| FN5 | Apply systematic listing strategies | MA02-04 Systematic listing strategies Watch |
| FN6 | Use positive integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5 | MA03-01 Square numbers, cube numbers and calculating them WatchMA03-02 Square roots, cube roots and higher roots Watch |
| FN7 | Calculate with roots, and with integer indices | MA03-03 Index laws: multiplying and dividing powers WatchMA03-04 Power of a power, and zero and negative indices Watch |
| FN8 | Calculate exactly with fractions and multiples of π | MA05-01 Calculating exactly with fractions WatchMA05-02 Calculating exactly with multiples of pi Watch |
| FN9 | Calculate with and interpret standard form A × 10ⁿ, where 1 ≤ A < 10 and n is an integer | MA03-06 Converting to and from standard form WatchMA03-07 Calculating with numbers in standard form Watch |
| FN10 | Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8) | MA19-01 Convert between fractions and terminating decimals, and order them Coming soon |
| FN11 | Identify and work with fractions in ratio problems | MA20-01 Ratio notation, simplifying and unitary form Coming soon |
| FN12 | Interpret fractions and percentages as operators | MA19-02 Find a percentage of a quantity Coming soon |
| FN13 | Use standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate | MA22-01 Convert between standard and compound units Coming soonMA22-03 Density: mass, volume and the direction of division Coming soonMA22-04 Pressure: force, area and recognising when to use it Coming soon |
| FN14 | Estimate answers; check calculations using approximation and estimation, including answers obtained using technology | MA07-02 Estimating a calculation by rounding Coming soon |
| FN15 | 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 | MA07-01 Rounding to significant figures and decimal places Coming soonMA07-05 Error intervals from rounding and truncation Coming soon |
| FN16 | Apply and interpret limits of accuracy | MA07-06 Limits of accuracy: upper and lower bounds Coming soon |
| FP1 | Record describe and analyse the frequency of outcomes of probability experiments using tables and frequency trees | MA34-02 Frequency tables and frequency trees Coming soon |
| FP2 | Apply ideas of randomness, fairness and equally likely events to calculate expected outcomes of multiple future experiments | MA34-05 Expected frequency: probability times number of trials Coming soon |
| FP3 | Relate relative expected frequencies to theoretical probability, using appropriate language and the 0 - 1 probability scale | MA34-01 Probability scale, vocabulary and simple probability Coming soonMA34-04 Sample size, reliability and theoretical probability language Coming soon |
| FP4 | 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 | MA35-01 The complement rule: P(not A) = 1 - P(A) Coming soonMA35-02 Mutually exclusive events: the addition rule Coming soon |
| FP5 | Understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size | MA34-04 Sample size, reliability and theoretical probability language Coming soon |
| FP6 | Enumerate sets and combinations of sets systematically, using tables, grids, Venn diagrams and tree diagrams | MA06-02 Venn diagrams: universal set, empty set and complement WatchMA35-04 Reading Venn diagrams and n(...) notation Coming soonMA36-01 Constructing tree diagrams Coming soonMA36-02 Combining probabilities on a tree diagram Coming soon |
| FP7 | Construct theoretical possibility spaces for single and combined experiments with equally likely outcomes and use these to calculate theoretical probabilities | MA35-03 Constructing sample space diagrams Coming soon |
| FP8 | Calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions | MA36-03 Combined events: independent and dependent probabilities Coming soon |
| FR1 | 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 | MA22-01 Convert between standard and compound units Coming soon |
| FR2 | Understand the concept of density and be able to use the relationship between density, mass and volume; understand the concept of pressure and be able to use the relationship between pressure, force and area | MA22-03 Density: mass, volume and the direction of division Coming soonMA22-04 Pressure: force, area and recognising when to use it Coming soon |
| FR3 | Use scale factors, scale diagrams and maps | MA24-09 Scale drawings and maps Coming soon |
| FR4 | Express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1 | MA04-06 Fraction of a quantity; expressing a number as a fraction of another Watch |
| FR5 | Use ratio notation, including reduction to simplest form | MA20-01 Ratio notation, simplifying and unitary form Coming soon |
| FR6 | Divide a given quantity into two parts in a given part:part or part:whole ratio; divide a given quantity into more than two parts; 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) | MA20-02 Share an amount in a given ratio Coming soonMA20-03 Share in a ratio when only a difference or one part is known Coming soon |
| FR7 | Express a multiplicative relationship between two quantities as a ratio or a fraction | MA20-04 Express a multiplicative relationship as a ratio Coming soon |
| FR8 | Understand and use proportion as equality of ratios | MA21-01 Solve direct proportion problems Coming soon |
| FR9 | Relate ratios to fractions and to linear functions | MA21-01 Solve direct proportion problems Coming soon |
| FR10 | 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 | MA19-02 Find a percentage of a quantity Coming soonMA19-03 Calculate a percentage increase or decrease Coming soonMA19-04 Calculate a percentage change between two values Coming soonMA19-05 Reverse percentages: find the original value Coming soonMA19-06 Simple interest Coming soon |
| FR11 | Solve problems involving direct and inverse proportion, including graphical and algebraic representations | MA21-01 Solve direct proportion problems Coming soonMA21-03 Solve inverse proportion problems Coming soon |
| FR12 | Use compound units such as speed, rates of pay, unit pricing, density and pressure | MA22-02 Compare rates: speed, pay and unit pricing Coming soonMA22-03 Density: mass, volume and the direction of division Coming soonMA22-04 Pressure: force, area and recognising when to use it Coming soon |
| FR13 | Compare lengths, areas and volumes using ratio notation; make links to similarity (including trigonometric ratios) and scale factors | MA26-05 Area ratio of similar shapes Coming soonMA26-06 Volume ratio of similar shapes (Higher) Coming soonMA26-12 Similar shapes: persisting the relationship across a question Coming soon |
| FR14 | Understand that X is inversely proportional to Y is equivalent to X is proportional to 1/Y; interpret equations that describe direct and inverse proportion | MA21-02 Recognise and interpret inverse proportion Coming soon |
| FR15 | Interpret the gradient of a straight line graph as a rate of change; recognise and interpret graphs that illustrate direct and inverse proportion | MA16-10 Graphs of Direct and Inverse Proportion Coming soonMA21-06 Gradient of a straight line as a rate of change Coming soon |
| FR16 | Set up, solve and interpret the answers in growth and decay problems, including compound interest | MA19-07 Growth and decay using repeated percentage multipliers Coming soon |
| FS1 | Infer properties of populations or distributions from a sample, whilst knowing the limitations of sampling | MA31-01 Sampling methods, bias and questionnaire design Coming soon |
| FS2 | Designing and criticising questions for a questionnaire, including notion of fairness | MA31-01 Sampling methods, bias and questionnaire design Coming soon |
| FS3 | 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 | MA31-04 Bar charts, pictograms and vertical line charts Coming soonMA31-05 Pie charts: calculating angles and constructing Coming soonMA31-06 Time series graphs and trends Coming soon |
| FS4 | Interpret, analyse and compare the distributions of data sets from univariate empirical distributions through: appropriate graphical representation involving discrete, continuous and grouped data; appropriate measures of central tendency (median, mean, mode and modal class) and spread (range, including consideration of outlier) | MA32-01 Mean, median, mode and range WatchMA32-02 Finding the modal class Coming soonMA32-07 Outliers Coming soon |
| FS5 | Apply statistics to describe a population | MA32-06 Comparing distributions with box plots Coming soon |
| FS6 | 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 | MA32-09 Scatter graphs and types of correlation Coming soonMA32-10 Line of best fit, correlation vs causation, and prediction Coming soon |
| HA1 | Use and interpret algebraic notation, 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/b in place of a ÷ b; coefficients written as fractions rather than as decimals; brackets | MA09-01 What Algebraic Notation Means Coming soon |
| HA2 | Substitute numerical values into formulae and expressions, including scientific formulae | MA09-03 Substituting Values into Expressions and Formulae Coming soon |
| HA3 | Understand and use the concepts and vocabulary of expressions, equations, formulae, identities, inequalities, terms and factors | MA09-02 Algebra Vocabulary: Expressions, Equations, Formulae, Identities and Inequalities Coming soon |
| HA4 | 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; completing the square; simplifying expressions involving sums, products and powers, including the laws of indices | MA09-04 Collecting Like Terms Coming soonMA09-05 Laws of Indices for Algebraic Terms Coming soonMA10-01 Expanding a Single Bracket Coming soonMA10-02 Expanding Double Brackets Coming soonMA10-03 Expanding Three or More Brackets Coming soonMA10-04 Factorising by Taking Out a Common Factor Coming soonMA10-05 Factorising a Quadratic x^2+bx+c, Including Difference of Two Squares Coming soonMA10-06 Factorising a General Quadratic ax^2+bx+c Coming soonMA10-07 Completing the Square Coming soonMA10-08 Simplifying and Manipulating Algebraic Fractions Coming soon |
| HA5 | Understand and use standard mathematical formulae; rearrange formulae to change the subject | MA11-03 Using and Rearranging a Formula (Subject Appears Once) Watch |
| HA6 | 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 | MA10-09 Equations, Identities and Equivalent Expressions Coming soonMA10-10 Constructing Algebraic Proofs Coming soon |
| HA7 | 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' | MA14-01 Function Machines: Inputs, Outputs and Reversing WatchMA14-02 Inverse and Composite Functions Watch |
| HA8 | Work with coordinates in all four quadrants | MA15-01 Coordinates in Four Quadrants Watch |
| HA9 | 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 | MA15-03 Plotting Straight-Line Graphs Coming soonMA15-06 Finding the Equation of a Straight Line Coming soonMA15-07 Equations of Parallel Lines Coming soonMA15-08 Equations of Perpendicular Lines Coming soon |
| HA10 | Identify and interpret gradients and intercepts of linear functions graphically and algebraically | MA15-05 Gradient and Y-Intercept via y=mx+c Coming soon |
| HA11 | Identify and interpret roots, intercepts, turning points (stationary points) of quadratic functions graphically; deduce roots algebraically, turning points (stationary points) by completing the square | MA16-02 Roots, Y-Intercept and Turning Point of a Quadratic Graph Coming soonMA16-03 Turning Point by Completing the Square Coming soon |
| HA12 | 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 = 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 | MA16-01 Recognising Linear and Quadratic Graphs Coming soonMA16-04 Cubic and Reciprocal Graphs Coming soonMA16-05 Exponential Graphs Coming soonMA16-06 Trigonometric Graphs: sin, cos and tan Coming soon |
| HA13 | Sketch translations and reflections of a given function | MA16-08 Translating a Graph: Vocabulary and y=f(x)+a, y=f(x+a) Coming soonMA16-09 Stretching and Reflecting a Graph: y=af(x), y=f(ax) Coming soon |
| HA14 | 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 | MA17-01 Plotting and Interpreting Real-World Graphs Coming soonMA17-02 Interpreting Non-Standard and Exponential Real-World Graphs Coming soon |
| HA15 | 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 | MA17-03 Estimating the Gradient of a Curve Coming soonMA17-04 Estimating the Area Under a Graph Coming soon |
| HA16 | 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 | MA16-11 Recognising the Equation of a Circle Coming soonMA16-12 Finding the Equation of a Tangent to a Circle Coming soon |
| HA17 | Solve linear equations in one unknown algebraically (including those with the unknown on both sides of the equation); find approximate solutions using a graph | MA11-01 Solving Linear Equations by Balancing WatchMA11-02 Solving Linear Equations with Brackets Watch |
| HA18 | Solve quadratic equations of the form x² + bx + c and ax² + bx + c (including those that require rearrangement) algebraically by factorising, by completing the square and by using the quadratic formula; find approximate solutions using a graph | MA12-02 Rearranging and Factorising a General Quadratic Equation WatchMA12-03 Solving a Quadratic with the Quadratic Formula Watch |
| HA19 | Solve two simultaneous equations in two variables (linear/linear or linear/quadratic) algebraically; find approximate solutions using a graph | MA12-05 Simultaneous Equations: One Linear, One Quadratic Watch |
| HA20 | Find approximate solutions to equations numerically using iteration, e.g. trial and improvement, decimal search or interval bisection | MA12-07 Solving Equations by Iteration Watch |
| HA21 | 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 | MA11-05 Writing an Expression or Formula from a Context WatchMA11-06 Setting Up and Solving an Equation from a Context Watch |
| HA22 | 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 | MA18-03 Solving a Quadratic Inequality Coming soonMA18-04 Regions Satisfying Linear Inequalities in Two Variables Coming soon |
| HA23 | Generate terms of a sequence from either a term-to-term or a position-to-term rule | MA13-01 Generating Terms of a Sequence Coming soon |
| HA24 | 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 rational number > 0 or a surd) and other sequences | MA13-02 Recognising Special Sequences WatchMA13-03 Sequences with a Surd Common Ratio Watch |
| HA25 | Deduce expressions to calculate the nth term of linear and quadratic sequences | MA13-04 Finding the nth Term of a Linear Sequence WatchMA13-05 Finding the nth Term of a Quadratic Sequence Watch |
| HG1 | 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 | MA25-01 Geometry notation and types of angle Coming soon |
| HG2 | 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 | MA24-01 Constructing the perpendicular bisector of a line segment WatchMA24-02 Constructing the bisector of an angle Coming soonMA24-03 Constructing a perpendicular to a line from or at a point Coming soonMA24-04 Solving loci problems with a single condition Coming soonMA24-05 Solving loci problems with combined conditions Coming soon |
| HG3 | 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) | MA25-02 Angles at a point, on a line and vertically opposite angles Coming soonMA25-03 Angles on parallel lines Coming soonMA25-05 Angle sum of a triangle and the exterior angle rule Coming soonMA25-06 Interior angles of polygons Coming soonMA25-07 Exterior angles and regular polygons Coming soon |
| HG4 | Derive and apply the properties and definitions of: special types of triangles, quadrilaterals (including square, rectangle, parallelogram, trapezium, kite and rhombus) and other plane figures using appropriate language | MA26-01 Naming triangles, quadrilaterals and polygons Coming soonMA26-02 Properties of special quadrilaterals and triangles Coming soon |
| HG5 | Use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS) | MA26-03 Congruent triangles: SSS, SAS, ASA and RHS Coming soon |
| HG6 | 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 | MA26-07 Proving results using congruent triangles and angle facts Coming soonMA26-08 Proving results using similarity and Pythagoras Coming soonMA30-01 Pythagoras' theorem in two dimensions Coming soon |
| HG7 | 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) | MA28-01 Reflecting a shape in a mirror line Coming soonMA28-02 Finding the mirror line from a shape and its image Coming soonMA28-03 Rotating a shape and describing a rotation Coming soonMA28-04 Translating a shape using a column vector Coming soonMA28-05 Enlarging a shape by a positive or fractional scale factor Coming soonMA28-06 Enlarging a shape by a negative scale factor (Higher) Coming soon |
| HG8 | Describe the changes and invariance achieved by combinations of rotations, reflections and translations | MA28-07 Describing combined transformations and invariance (Higher) Coming soon |
| HG9 | Identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference, tangent, arc, sector and segment | MA27-01 Circle vocabulary Coming soon |
| HG10 | Apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results | MA27-02 Circle theorem: angle at the centre Coming soonMA27-03 Circle theorem: angle in a semicircle Coming soonMA27-04 Circle theorem: angles in the same segment Coming soonMA27-05 Circle theorem: cyclic quadrilaterals Coming soonMA27-06 Circle theorem: tangent and radius Coming soonMA27-07 Circle theorem: alternate segment theorem Coming soonMA27-08 Circle theorem: tangents from an external point Coming soonMA27-09 Circle theorems: chords and the centre Coming soon |
| HG11 | Solve geometrical problems on coordinate axes | MA28-09 Solving geometry problems on coordinate axes Coming soon |
| HG12 | Identify properties of the faces, surfaces, edges and vertices of: cubes, cuboids, prisms, cylinders, pyramids, cones and spheres | MA29-01 Naming 3D solids and their properties Coming soon |
| HG13 | Construct and interpret plans and elevations of 3D shapes | MA29-02 Interpreting plans and elevations Coming soonMA29-03 Constructing plans and elevations Coming soon |
| HG14 | Use standard units of measure and related concepts (length, area, volume/capacity, mass, time, money, etc.) | MA22-01 Convert between standard and compound units Coming soon |
| HG15 | Measure line segments and angles in geometric figures, including interpreting maps and scale drawings and use of bearings | MA24-08 Three-figure bearings Coming soon |
| HG16 | Know and apply formulae to calculate: area of squares, rectangles, triangles, parallelograms, trapezia; volume of cuboids and other right prisms (including cylinders) | MA23-02 Area of triangles, parallelograms and trapezia WatchMA29-05 Volume of prisms, cuboids and cylinders Coming soon |
| HG17 | 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 | MA23-01 Perimeter of 2D and composite shapes WatchMA23-03 Circle circumference and area WatchMA29-06 Surface area and volume of a sphere and cone (Higher) Coming soonMA29-08 Composite solids: breaking a shape into parts Coming soon |
| HG18 | Calculate arc lengths, angles and areas of sectors of circles | MA23-04 Arc length and sector area, including major sectors Watch |
| HG19 | Apply the concepts of congruence and similarity, including the relationships between lengths, areas and volumes in similar figures | MA26-05 Area ratio of similar shapes Coming soonMA26-06 Volume ratio of similar shapes (Higher) Coming soon |
| HG20 | Know the formulae for: Pythagoras' theorem, a² + b² = c², and the trigonometric ratios, sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent, apply them to find angles and lengths in right-angled triangles in two dimensional figures and, where possible, general triangles in two and three dimensional figures | MA30-08 Pythagoras' theorem in three dimensions Coming soonMA30-11 Trigonometry in 3D and complex figures Coming soon |
| HG21 | 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° | MA30-02 Trigonometric ratios: labelling sides and choosing sin, cos or tan Coming soon |
| HG22 | 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 | MA30-05 The sine rule and the area of a triangle Coming soonMA30-07 The cosine rule Coming soon |
| HG23 | Know and apply Area = ½ ab sin C to calculate the area, sides or angles of any triangle | MA30-05 The sine rule and the area of a triangle Coming soon |
| HG24 | Describe translations as 2D vectors | MA28-04 Translating a shape using a column vector Coming soon |
| HG25 | 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 | MA28-10 Vector arithmetic: addition, subtraction and scalar multiplication Coming soonMA28-12 Using vectors to prove geometric results (Higher) Coming soon |
| HN1 | Order positive and negative integers, decimals and fractions; use the symbols =, ≠, <, >, ≤, ≥ | MA01-01 Ordering positive and negative numbers using inequality symbols Watch |
| HN2 | 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) | MA01-02 Place value and decimal notation WatchMA01-03 Adding, subtracting, multiplying and dividing positive and negative integers WatchMA01-04 Adding, subtracting, multiplying and dividing decimals WatchMA04-04 Adding and subtracting fractions and mixed numbers WatchMA04-05 Multiplying and dividing fractions and mixed numbers Watch |
| HN3 | 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) | MA01-05 Order of operations: brackets, powers, roots and BIDMAS WatchMA01-06 Inverse operations Watch |
| HN4 | 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 | MA02-01 Types of number and prime factorisation WatchMA02-02 Highest common factor (HCF) WatchMA02-03 Lowest common multiple (LCM) Watch |
| HN5 | Apply systematic listing strategies including use of the product rule for counting | MA02-05 The product rule for counting (Higher) Watch |
| HN6 | 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 | MA03-01 Square numbers, cube numbers and calculating them WatchMA03-02 Square roots, cube roots and higher roots Watch |
| HN7 | Calculate with roots, and with integer and fractional indices | MA03-03 Index laws: multiplying and dividing powers WatchMA03-04 Power of a power, and zero and negative indices WatchMA03-05 Fractional indices (Higher) Watch |
| HN8 | 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 | MA05-01 Calculating exactly with fractions WatchMA05-02 Calculating exactly with multiples of pi WatchMA05-03 Simplifying surds (Higher) WatchMA05-04 Rationalising the denominator (Higher) Watch |
| HN9 | Calculate with and interpret standard form A × 10ⁿ, where 1 ≤ A < 10 and n is an integer | MA03-06 Converting to and from standard form WatchMA03-07 Calculating with numbers in standard form Watch |
| HN10 | Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8); change recurring decimals into their corresponding fractions and vice versa | MA04-08 Converting recurring decimals into fractions (Higher) WatchMA19-01 Convert between fractions and terminating decimals, and order them Coming soon |
| HN11 | Identify and work with fractions in ratio problems | MA20-01 Ratio notation, simplifying and unitary form Coming soon |
| HN12 | Interpret fractions and percentages as operators | MA19-02 Find a percentage of a quantity Coming soon |
| HN13 | Use standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate | MA22-01 Convert between standard and compound units Coming soonMA22-03 Density: mass, volume and the direction of division Coming soonMA22-04 Pressure: force, area and recognising when to use it Coming soon |
| HN14 | Estimate answers; check calculations using approximation and estimation, including answers obtained using technology | MA07-02 Estimating a calculation by rounding Coming soon |
| HN15 | 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 | MA07-01 Rounding to significant figures and decimal places Coming soonMA07-05 Error intervals from rounding and truncation Coming soon |
| HN16 | Apply and interpret limits of accuracy, including upper and lower bounds | MA07-04 Bounds of a calculated result (Higher) Coming soonMA07-06 Limits of accuracy: upper and lower bounds Coming soon |
| HP1 | Record describe and analyse the frequency of outcomes of probability experiments using tables and frequency trees | MA34-02 Frequency tables and frequency trees Coming soon |
| HP2 | Apply ideas of randomness, fairness and equally likely events to calculate expected outcomes of multiple future experiments | MA34-05 Expected frequency: probability times number of trials Coming soon |
| HP3 | Relate relative expected frequencies to theoretical probability, using appropriate language and the 0 - 1 probability scale | MA34-01 Probability scale, vocabulary and simple probability Coming soonMA34-04 Sample size, reliability and theoretical probability language Coming soon |
| HP4 | 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 | MA35-01 The complement rule: P(not A) = 1 - P(A) Coming soonMA35-02 Mutually exclusive events: the addition rule Coming soon |
| HP5 | Understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size | MA34-04 Sample size, reliability and theoretical probability language Coming soon |
| HP6 | Enumerate sets and combinations of sets systematically, using tables, grids, Venn diagrams and tree diagrams | MA06-02 Venn diagrams: universal set, empty set and complement WatchMA35-04 Reading Venn diagrams and n(...) notation Coming soonMA36-01 Constructing tree diagrams Coming soonMA36-02 Combining probabilities on a tree diagram Coming soon |
| HP7 | Construct theoretical possibility spaces for single and combined experiments with equally likely outcomes and use these to calculate theoretical probabilities | MA35-03 Constructing sample space diagrams Coming soon |
| HP8 | Calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions | MA36-03 Combined events: independent and dependent probabilities Coming soon |
| HP9 | Calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and Venn diagrams | MA36-04 Conditional probability using diagrams Coming soon |
| HR1 | 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 | MA22-01 Convert between standard and compound units Coming soon |
| HR2 | Understand the concept of density and be able to use the relationship between density, mass and volume; understand the concept of pressure and be able to use the relationship between pressure, force and area | MA22-03 Density: mass, volume and the direction of division Coming soonMA22-04 Pressure: force, area and recognising when to use it Coming soon |
| HR3 | Use scale factors, scale diagrams and maps | MA24-09 Scale drawings and maps Coming soon |
| HR4 | Express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1 | MA04-06 Fraction of a quantity; expressing a number as a fraction of another Watch |
| HR5 | Use ratio notation, including reduction to simplest form | MA20-01 Ratio notation, simplifying and unitary form Coming soon |
| HR6 | Divide a given quantity into two parts in a given part:part or part:whole ratio; divide a given quantity into more than two parts; 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) | MA20-02 Share an amount in a given ratio Coming soonMA20-03 Share in a ratio when only a difference or one part is known Coming soon |
| HR7 | Express a multiplicative relationship between two quantities as a ratio or a fraction | MA20-04 Express a multiplicative relationship as a ratio Coming soon |
| HR8 | Understand and use proportion as equality of ratios | MA21-01 Solve direct proportion problems Coming soon |
| HR9 | Relate ratios to fractions and to linear functions | MA21-01 Solve direct proportion problems Coming soon |
| HR10 | 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 | MA19-02 Find a percentage of a quantity Coming soonMA19-03 Calculate a percentage increase or decrease Coming soonMA19-04 Calculate a percentage change between two values Coming soonMA19-05 Reverse percentages: find the original value Coming soonMA19-06 Simple interest Coming soon |
| HR11 | Solve problems involving direct and inverse proportion, including graphical and algebraic representations | MA21-01 Solve direct proportion problems Coming soonMA21-03 Solve inverse proportion problems Coming soon |
| HR12 | Use compound units such as speed, rates of pay, unit pricing, density and pressure | MA22-02 Compare rates: speed, pay and unit pricing Coming soonMA22-03 Density: mass, volume and the direction of division Coming soonMA22-04 Pressure: force, area and recognising when to use it Coming soon |
| HR13 | Compare lengths, areas and volumes using ratio notation; make links to similarity (including trigonometric ratios) and scale factors | MA26-05 Area ratio of similar shapes Coming soonMA26-06 Volume ratio of similar shapes (Higher) Coming soonMA26-12 Similar shapes: persisting the relationship across a question Coming soon |
| HR14 | 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 | MA21-02 Recognise and interpret inverse proportion Coming soonMA21-04 Construct direct and inverse proportion equations, including powers and roots Coming soon |
| HR15 | Interpret the gradient of a straight line graph as a rate of change; recognise and interpret graphs that illustrate direct and inverse proportion | MA16-10 Graphs of Direct and Inverse Proportion Coming soonMA21-06 Gradient of a straight line as a rate of change Coming soon |
| HR16 | 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 | MA21-07 Instantaneous rate of change: the gradient of a tangent Coming soonMA21-08 Estimate the area under a curve using trapezia Coming soon |
| HR17 | Set up, solve and interpret the answers in growth and decay problems, including compound interest and work with general iterative processes | MA19-07 Growth and decay using repeated percentage multipliers Coming soon |
| HS1 | Infer properties of populations or distributions from a sample, whilst knowing the limitations of sampling | MA31-01 Sampling methods, bias and questionnaire design Coming soon |
| HS2 | Designing and criticising questions for a questionnaire, including notion of fairness. | MA31-01 Sampling methods, bias and questionnaire design Coming soon |
| HS3 | 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 | MA31-04 Bar charts, pictograms and vertical line charts Coming soonMA31-05 Pie charts: calculating angles and constructing Coming soonMA31-06 Time series graphs and trends Coming soon |
| HS4 | 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 | MA33-01 Constructing histograms with frequency density Coming soonMA33-02 Reading and calculating from histograms Coming soonMA33-03 Constructing a cumulative frequency diagram Coming soonMA33-04 Reading estimates from a cumulative frequency diagram Coming soon |
| HS5 | 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) | MA32-01 Mean, median, mode and range WatchMA32-02 Finding the modal class Coming soonMA32-04 Quartiles and interquartile range Coming soonMA32-05 Constructing and reading box plots Coming soonMA32-06 Comparing distributions with box plots Coming soonMA32-07 Outliers Coming soon |
| HS6 | Apply statistics to describe a population | MA32-06 Comparing distributions with box plots Coming soon |
| HS7 | 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 | MA32-09 Scatter graphs and types of correlation Coming soonMA32-10 Line of best fit, correlation vs causation, and prediction Coming soon |