GCSE MATHS

Notation, Vocabulary and Manipulation

• Use and interpret algebraic notation
• Coefficients written as fractions rather than as decimals
• Use of brackets
• Substitute numerical values into formulae and expressions, including scientific formulae
• Understand and use the concepts and vocabulary of expressions, equations, formulae, inequalities, terms and factors
• Simplify and manipulate algebraic expressions by: collecting like terms; multiplying a single term over a bracket; taking out common factors; simplifying expressions involving sums, products and powers, including the laws of indices
• Understand and use standard mathematical formulae
• Rearrange formulae to change the subject
• Interpret simple expressions as functions with inputs and outputs

Graphs

• Work with coordinates in all four quadrants
• Plot graphs of equations that correspond to straight-line graphs in the coordinate plane
• Identify and interpret gradients and intercepts of linear functions graphically and algebraically
• Recognise, sketch and interpret graphs of linear functions and quadratic functions
• Plot and interpret graphs, and graphs of non-standard functions in real contexts

Solving Equations and Inequalities 

• Solve linear equations in one unknown algebraically
• Find approximate solutions using a graph
• Students should know the conventions of an open circle on a number line for a strict inequality and a closed circle for an included boundary

Sequences

• Generate terms of a sequence from either a term-to-term or a position-to-term rule
• Recognise and use sequences of triangular, square and cube numbers and simple arithmetic progressions
• Deduce expressions to calculate the nth term of linear sequences

• Change freely between related standard units (e.g. time, length, area, volume/capacity, mass) and compound units (e.g. speed, rates of pay, prices) in numerical contexts
• Use scale factors, scale diagrams and maps
• Express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1
• Use ratio notation, including reduction to simplest form
• 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
• Express a multiplicative relationship between two quantities as a ratio or a fraction
• Understand and use proportion as equality of ratios
• Relate ratios to fractions and to linear functions
• 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
• Solve problems involving direct and inverse proportion, including graphical and algebraic representations
• Use compound units such as speed, rates of pay, unit pricing
• Compare lengths, areas and volumes using ratio notation scale factors

Properties and Constructions

• 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
• 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
• Derive and apply the properties and definitions of: special types of quadrilaterals, including square, rectangle, parallelogram, trapezium, kite and rhombus
• Identify, describe and construct congruent and similar shapes
• Identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference

Mensuration and Calculation

• Use standard units of measure and related concepts
• Measure line segments and angles in geometric figures
• Know and apply formulae to calculate: area of triangles, parallelograms, trapezia; volume of cuboids and other right prisms

Vectors 

• Describe translations as 2D vectors
• Use vectors to construct geometric arguments and proofs (Higher Tier only)

• Record, describe and analyse the frequency of outcomes of probability experiments using tables and frequency trees
• Apply ideas of randomness, fairness and equally likely events to calculate expected outcomes of multiple future experiments
• Relate relative expected frequencies to theoretical probability, using appropriate language and the 0 to 1 probability scale
• Apply the property that the probabilities of an exhaustive set of outcomes sum to 1 apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to 1
• Enumerate sets and combinations of sets systematically, using tables, grids, Venn diagrams
• Construct theoretical possibility spaces for single and combined experiments with equally likely outcomes and use these to calculate theoretical probabilities

• 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
• Interpret, analyse and compare the distributions of data sets from empirical distributions
• Apply statistics to describe a population
• Use and interpret scatter graphs of bivariate data
• Recognise correlation