| A1 | Notation, vocabulary and manipulation | MA09-01 What Algebraic Notation Means Coming soon |
| A2 | Substitute numerical values into formulae and expressions, including scientific formulae | MA09-03 Substituting Values into Expressions and Formulae Coming soon |
| A3 | Understand and use the concepts and vocabulary of expressions, equations, formulae, inequalities, terms and factors | MA09-02 Algebra Vocabulary: Expressions, Equations, Formulae, Identities and Inequalities Coming soon |
| A4 | Notation, vocabulary and manipulation | 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 soonMA10-08 Simplifying and Manipulating Algebraic Fractions Coming soon |
| A5 | Understand and use standard mathematical formulae | MA11-03 Using and Rearranging a Formula (Subject Appears Once) Watch |
| A6 | Know the difference between an equation and an identity | MA10-09 Equations, Identities and Equivalent Expressions Coming soonMA10-10 Constructing Algebraic Proofs Coming soon |
| A7 | Where appropriate, interpret simple expressions as functions with inputs and outputs | MA14-01 Function Machines: Inputs, Outputs and Reversing WatchMA14-02 Inverse and Composite Functions Watch |
| A8 | Work with coordinates in all four quadrants | MA15-01 Coordinates in Four Quadrants Watch |
| A9 | Plot graphs of equations that correspond to straight-line graphs in the coordinate plane | 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 |
| A10 | Identify and interpret gradients and intercepts of linear functions graphically and algebraically | MA15-05 Gradient and Y-Intercept via y=mx+c Coming soon |
| A11 | Identify and interpret roots, intercepts and turning points of quadratic functions graphically | MA16-02 Roots, Y-Intercept and Turning Point of a Quadratic Graph Coming soonMA16-03 Turning Point by Completing the Square Coming soon |
| A12 | Recognise, sketch and interpret graphs of linear functions and quadratic functions | 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 |
| A13 | 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 |
| A14 | Plot and interpret 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 |
| 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 | MA17-03 Estimating the Gradient of a Curve Coming soonMA17-04 Estimating the Area Under a Graph Coming soon |
| A16 | Recognise and use the equation of a circle with centre at the origin | MA16-11 Recognising the Equation of a Circle Coming soonMA16-12 Finding the Equation of a Tangent to a Circle Coming soon |
| A17 | Solve linear equations in one unknown algebraically | MA11-01 Solving Linear Equations by Balancing WatchMA11-02 Solving Linear Equations with Brackets Watch |
| A18 | Solve quadratic equations algebraically by factorising | MA12-01 Solving x^2+bx+c=0 by Factorising WatchMA12-02 Rearranging and Factorising a General Quadratic Equation WatchMA12-03 Solving a Quadratic with the Quadratic Formula Watch |
| A19 | Solve two simultaneous equations in two variables (linear/linear) algebraically | MA12-04 Solving Simultaneous Linear Equations by Elimination WatchMA12-05 Simultaneous Equations: One Linear, One Quadratic Watch |
| A20 | Find approximate solutions to equations numerically using iteration | MA12-07 Solving Equations by Iteration Watch |
| A21 | Translate simple situations or procedures into algebraic expressions or formulae | MA11-05 Writing an Expression or Formula from a Context WatchMA11-06 Setting Up and Solving an Equation from a Context Watch |
| A22 | Solve linear inequalities in one variable | MA18-01 Inequality Symbols and Number-Line Conventions Coming soonMA18-02 Solving a Linear Inequality Coming soonMA18-03 Solving a Quadratic Inequality Coming soonMA18-04 Regions Satisfying Linear Inequalities in Two Variables Coming soon |
| A23 | 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 soonMA13-02 Recognising Special Sequences Watch |
| A24 | Recognise and use sequences of triangular, square and cube numbers and simple arithmetic progressions | MA13-02 Recognising Special Sequences WatchMA13-03 Sequences with a Surd Common Ratio Watch |
| A25 | Deduce expressions to calculate the nth term of linear sequences | MA13-04 Finding the nth Term of a Linear Sequence WatchMA13-05 Finding the nth Term of a Quadratic Sequence Watch |
| 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 | MA25-01 Geometry notation and types of angle Coming soon |
| 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) | 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 |
| G3 | Apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles | 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 |
| G4 | Derive and apply the properties and definitions of: special types of quadrilaterals, including square, rectangle, parallelogram, trapezium, kite and rhombus | MA26-01 Naming triangles, quadrilaterals and polygons Coming soonMA26-02 Properties of special quadrilaterals and triangles Coming soon |
| G5 | Use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS) | MA26-03 Congruent triangles: SSS, SAS, ASA and RHS Coming soon |
| 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 | 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 |
| G7 | Identify, describe and construct congruent and similar shapes, including on coordinate axes, by considering rotation, reflection, translation and enlargement | 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 |
| G8 | Describe the changes and invariance achieved by combinations of rotations, reflections and translations | MA28-07 Describing combined transformations and invariance (Higher) Coming soon |
| G9 | Identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference | MA27-01 Circle vocabulary Coming soon |
| G10 | 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 |
| G11 | Solve geometrical problems on coordinate axes | MA28-09 Solving geometry problems on coordinate axes Coming soon |
| G12 | 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 |
| G13 | Interpret plans and elevations of 3D shapes | MA29-02 Interpreting plans and elevations Coming soonMA29-03 Constructing plans and elevations Coming soon |
| G14 | 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 |
| G15 | 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 |
| G16 | Know and apply formulae to calculate: area of triangles, parallelograms, trapezia; | MA23-02 Area of triangles, parallelograms and trapezia WatchMA29-05 Volume of prisms, cuboids and cylinders Coming soon |
| G17 | Know the formulae: circumference of a circle = 2πr = πd | 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 |
| G18 | Calculate arc lengths, angles and areas of sectors of circles | MA23-04 Arc length and sector area, including major sectors Watch |
| G19 | Apply the concepts of congruence and similarity, including the relationships between lengths in similar figures | 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 |
| G20 | Know the formulae for: Pythagoras’ theorem, a² + b² = c² and the trigonometric ratios, sinθ = opposite/hypotenuse, cosθ = adjacent/hypotenuse and tanθ = opposite/adjacent | 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 soonMA30-08 Pythagoras' theorem in three dimensions Coming soonMA30-11 Trigonometry in 3D and complex figures Coming soon |
| G21 | Know the exact values of sinθ and cosθ for θ = 0°, 30°, 45°, 60° and 90° | MA30-02 Trigonometric ratios: labelling sides and choosing sin, cos or tan Coming soon |
| G22 | Know and apply the sine rule, a/sinA = b/sinB = c/sinC and cosine rule, a² = b² + c² - 2bc cosA 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 |
| G23 | Know and apply Area = ½ ab sinC to calculate the area, sides or angles of any triangle | MA30-05 The sine rule and the area of a triangle Coming soon |
| G24 | Describe translations as 2D vectors | MA28-04 Translating a shape using a column vector Coming soon |
| G25 | 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 soonMA28-12 Using vectors to prove geometric results (Higher) Coming soon |
| N1 | Order positive and negative integers, decimals and fractions | MA01-01 Ordering positive and negative numbers using inequality symbols Watch |
| 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 | 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 |
| N3 | Recognise and use relationships between operations, including inverse operations (eg cancellation to simplify calculations and expressions) | MA01-05 Order of operations: brackets, powers, roots and BIDMAS WatchMA01-06 Inverse operations Watch |
| 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 | MA02-01 Types of number and prime factorisation WatchMA02-02 Highest common factor (HCF) WatchMA02-03 Lowest common multiple (LCM) Watch |
| N5 | Apply systematic listing strategies | MA02-04 Systematic listing strategies WatchMA02-05 The product rule for counting (Higher) Watch |
| N6 | 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 |
| N7 | 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 WatchMA03-05 Fractional indices (Higher) Watch |
| N8 | Calculate exactly with fractions | 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 |
| N9 | 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 |
| N10 | Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8) | MA04-08 Converting recurring decimals into fractions (Higher) WatchMA19-01 Convert between fractions and terminating decimals, and order them Coming soon |
| N11 | Identify and work with fractions in ratio problems | MA20-01 Ratio notation, simplifying and unitary form Coming soon |
| N12 | Interpret fractions and percentages as operators | MA19-02 Find a percentage of a quantity Coming soon |
| N13 | 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 |
| N14 | Estimate answers | MA07-02 Estimating a calculation by rounding Coming soon |
| N15 | Round numbers and measures to an appropriate degree of accuracy (eg to a specified number of decimal places or significant figures) | MA07-01 Rounding to significant figures and decimal places Coming soonMA07-05 Error intervals from rounding and truncation Coming soon |
| N16 | Apply and interpret limits of accuracy | MA07-04 Bounds of a calculated result (Higher) Coming soonMA07-06 Limits of accuracy: upper and lower bounds Coming soon |
| P1 | 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 |
| P2 | 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 |
| P3 | Relate relative expected frequencies to theoretical probability, using appropriate language and the 0 to 1 probability scale | MA34-01 Probability scale, vocabulary and simple probability Coming soonMA34-04 Sample size, reliability and theoretical probability language Coming soon |
| P4 | Apply the property that the probabilities of an exhaustive set of outcomes sum to 1 | MA35-01 The complement rule: P(not A) = 1 - P(A) Coming soonMA35-02 Mutually exclusive events: the addition rule Coming soon |
| P5 | 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 |
| P6 | Enumerate sets and combinations of sets systematically, using tables, grids, Venn 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 |
| P7 | 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 |
| P8 | 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 |
| P9 | 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 |
| R1 | Change freely between related standard units (eg time, length, area, volume/capacity, mass) and compound units (eg speed, rates of pay, prices) in numerical contexts | MA22-01 Convert between standard and compound units Coming soon |
| R2 | Use scale factors, scale diagrams and maps | MA24-09 Scale drawings and maps Coming soon |
| R3 | 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 |
| R4 | Use ratio notation, including reduction to simplest form | MA20-01 Ratio notation, simplifying and unitary form Coming soon |
| R5 | Divide a given quantity into two parts in a given part : part or part : whole ratio | 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 |
| R6 | Express a multiplicative relationship between two quantities as a ratio or a fraction | MA20-04 Express a multiplicative relationship as a ratio Coming soon |
| R7 | Understand and use proportion as equality of ratios | MA21-01 Solve direct proportion problems Coming soon |
| R8 | Relate ratios to fractions and to linear functions | MA21-01 Solve direct proportion problems Coming soon |
| R9 | Define percentage as ‘number of parts per hundred’ | 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 |
| R10 | 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 |
| R11 | Use compound units such as speed, rates of pay, unit pricing | 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 |
| R12 | Compare lengths, areas and volumes using ratio notation | 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 |
| R13 | Understand that X is inversely proportional to Y is equivalent to X is proportional to 1/Y | MA21-02 Recognise and interpret inverse proportion Coming soonMA21-04 Construct direct and inverse proportion equations, including powers and roots Coming soon |
| R14 | Interpret the gradient of a straight-line graph as a rate of change | MA16-10 Graphs of Direct and Inverse Proportion Coming soonMA21-06 Gradient of a straight line as a rate of change Coming soon |
| R15 | Interpret the gradient at a point on a curve as the instantaneous rate of change | MA21-07 Instantaneous rate of change: the gradient of a tangent Coming soonMA21-08 Estimate the area under a curve using trapezia Coming soon |
| R16 | 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 |
| S1 | 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 |
| 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, 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 |
| S3 | Construct and interpret diagrams for grouped discrete data and continuous data, ie 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 |
| S4 | • including box plots | 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 |
| S5 | Apply statistics to describe a population | MA32-06 Comparing distributions with box plots Coming soon |
| S6 | Use and interpret scatter graphs of bivariate data | MA32-09 Scatter graphs and types of correlation Coming soonMA32-10 Line of best fit, correlation vs causation, and prediction Coming soon |
