Topic guides
Maths topic guides
Clear explanations, worked examples, common mistakes and interactive practice for every topic we support.
Linear equations
Solve equations in one variable by keeping both sides balanced, including brackets, fractions and special cases.
Systems of linear equations
Solve two linear equations together by substitution or elimination, and recognise when a system has no solution or infinitely many.
Linear functions and straight-line graphs
Interpret gradient (slope) and intercept, find equations of lines, and use parallel and perpendicular lines.
Quadratic equations
Solve quadratics by factorising, the quadratic formula and completing the square; use the discriminant and vertex form.
Exponential growth and decay
Model repeated percentage change with multipliers, compound interest and exponential functions.
Laws of indices (exponents)
Multiply, divide and raise powers; work with zero, negative and fractional indices.
Percentages
Find percentages of amounts, percentage change, reverse percentages and successive changes.
Ratio and proportion
Share quantities in a ratio, use unit rates and scales, and solve direct and inverse proportion problems.
Averages and spread
Calculate and compare mean, median, mode and range, and reason about how data changes affect them.
Probability
Find probabilities of single and combined events, use complements and work with and without replacement.
Pythagoras and right-triangle trigonometry
Use Pythagoras' theorem and sine, cosine and tangent to find sides and angles in right-angled triangles.
Circles: area, arcs, sectors and equations
Find circumference, area, arc length and sector area, and read the equation of a circle.
Sequences
Find and use the nth term of arithmetic, geometric and simple quadratic sequences.
Linear inequalities
Solve and interpret linear inequalities, including flipping the sign, integer solutions and real-world constraints.
Expanding, factorising and equivalent expressions
Expand and factorise expressions, recognise equivalent forms and simplify algebraic fractions.
Area, surface area and volume
Find areas of 2D shapes and volumes and surface areas of prisms, cylinders, cones and spheres, including scaling.
Angles, parallel lines and similar triangles
Use angle facts, parallel-line rules, polygon angle sums and similar triangles to find missing angles and lengths.
Scatter plots and lines of best fit
Interpret scatter plots, correlation and lines of best fit, and use models to make predictions.
Sampling, margin of error and statistical claims
Judge what conclusions data supports: random samples, margins of error, bias, and experiments versus observational studies.
SAT Words in Context
Choose the most precise word for a blank, or the meaning of a word as it's used in a short text.
SAT Text Structure and Purpose
Identify why a text was written, how it is organized, and what job a particular sentence does.
SAT Cross-Text Connections
Compare two short texts on the same topic and predict how one author would respond to the other.
SAT Central Ideas and Details
Identify a text's main idea and locate details it states directly.
SAT Command of Evidence (Textual)
Choose the quotation or finding that most directly supports, illustrates or weakens a claim.
SAT Command of Evidence (Quantitative)
Use data from a table or graph to complete or support a claim in a short text.
SAT Inferences
Complete a text with the conclusion that most logically follows from the information given.
SAT Boundaries (Punctuation)
Punctuate sentence boundaries, supplementary elements and lists correctly: periods, semicolons, colons, commas and dashes.
SAT Form, Structure, and Sense (Grammar)
Choose grammatically correct forms: subject–verb and pronoun agreement, verb tense, plurals and possessives, and modifier placement.
SAT Transitions
Choose the transition word or phrase that shows the logical relationship between ideas.
SAT Rhetorical Synthesis
Use information from a student's notes to write a sentence that accomplishes a specific goal.
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