Study guides

Algebra - Notation, vocabulary and manipulation: 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) (Higher tier)

Pearson Edexcel·GCSE

1MA1

Function notation is a compact language for turning inputs into outputs, combining rules and undoing them. Master the order of composite functions and the algebra of inverses to tackle Pearson Edexcel GCSE Higher questions with clear working and fewer avoidable errors.

Algebra - Notation, vocabulary and manipulation: where appropriate, interpret simple expressions as functions with inputs and outputs. (Foundation tier)

Pearson Edexcel·GCSE

1MA1

Algebra - Sequences: deduce expressions to calculate the nth term of linear and quadratic sequences (Higher tier)

Pearson Edexcel·GCSE

1MA1

Turn a list of numbers into a rule that jumps straight to any term. Master constant first and second differences, recover every part of a quadratic expression, and show the working that gives an examiner evidence to award credit.

Algebra - Sequences: deduce expressions to calculate the nth term of linear sequences (Foundation tier)

Pearson Edexcel·GCSE

1MA1

Turn a number pattern into a rule that finds any term without listing all the earlier ones. Learn how to secure marks on Edexcel Foundation sequence questions, handle decreasing patterns and prove whether a number belongs.

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

Pearson Edexcel·GCSE

1MA1

Algebra - Sequences: 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 (Higher tier)

Pearson Edexcel·GCSE

1MA1

Algebra - Sequences: 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) (Foundation tier)

Pearson Edexcel·GCSE

1MA1

Number patterns stop being guesses when you know what to test. Learn to recognise seven sequence families, extend them accurately and justify whether a value belongs, using clear working that can earn credit in Pearson Edexcel Foundation questions.

Algebra - Solving equations and inequalities: find approximate solutions to equations numerically using iteration (Higher tier only)

Pearson Edexcel·GCSE

1MA1

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

Pearson Edexcel·GCSE

1MA1

Algebra - Solving equations and inequalities: 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 (Higher tier)

Pearson Edexcel·GCSE

1MA1

Algebra - Solving equations and inequalities: solve linear inequalities in one variable; represent the solution set on a number line (Foundation tier)

Pearson Edexcel·GCSE

1MA1

Algebra - Solving equations and inequalities: 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 (Higher tier)

Pearson Edexcel·GCSE

1MA1

Algebra - Solving equations and inequalities: solve quadratic equations algebraically by factorising; find approximate solutions using a graph (Foundation tier)

Pearson Edexcel·GCSE

1MA1

Turn a quadratic into brackets, then turn the brackets into marks. This Foundation-tier guide explains why factorising works, how to keep every valid solution and how to read approximate roots from a graph, with examiner-style examples, visual explanations and a ten-minute tutor podcast.

Algebra - Solving equations and inequalities: solve two simultaneous equations in two variables (linear/linear or linear/quadratic) algebraically; find approximate solutions using a graph (Higher tier)

Pearson Edexcel·GCSE

1MA1

Two equations, one shared set of answers: learn to eliminate or substitute, then keep every x matched with its y. This Higher-tier guide turns linear/quadratic algebra and graph intersections into a repeatable, mark-focused process, with worked solutions, visual explanations and a ten-minute revision podcast.

Algebra - Solving equations and inequalities: solve two simultaneous equations in two variables (linear/linear) algebraically; find approximate solutions using a graph (Foundation tier)

Pearson Edexcel·GCSE

1MA1

Two equations, one shared answer: learn to find the pair that makes both conditions true, then see why it is the crossing point of two lines. Master elimination, substitution and accurate graph reading to secure method and accuracy marks in Pearson Edexcel GCSE Mathematics, including Foundation-tier A19.

Algebra - Solving equations and inequalities: 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

Pearson Edexcel·GCSE

1MA1

Algebraic Fractions

OCR·GCSE

Master OCR GCSE Further Maths Algebraic Fractions (2.1) with this comprehensive study guide. Learn to simplify complex expressions, solve equations, and avoid common exam pitfalls through expert-written content, worked examples, and engaging multi-modal resources designed to secure top marks.

Algorithms

OCR·A-Level

Master OCR A-Level Computer Science Algorithms (2.1) with this comprehensive guide. We'll break down algorithm analysis using Big O notation, explore standard sorting and searching algorithms, and demystify pathfinding with Dijkstra's and A*. This guide is packed with exam-focused advice, worked examples, and memory hooks to help you secure top marks.

Algorithms

Pearson Edexcel·GCSE

Pearson-GCSE-Computer-Science

Master the logic behind every computer program. This topic covers how to design, trace, and evaluate algorithms using sequence, selection, and iteration, plus the essential searching and sorting techniques you'll need for your exam.

Alkanes

AQA·A-Level

Master AQA A-Level Chemistry's core topic, Alkanes (3.2). This guide breaks down everything from boiling point trends governed by van der Waals forces to the critical mechanisms of combustion and free-radical substitution, providing examiner insights to help you secure top marks.

Alkenes

AQA·A-Level

Unlock the secrets of carbon-based life with this essential guide to Organic Chemistry. From mastering IUPAC nomenclature to predicting complex reaction pathways, this module builds the foundation for understanding everything from fuels to pharmaceuticals."

All Cells Arise from Other Cells

AQA·A-Level

Master the foundation of all biology: Cells. This comprehensive guide covers cell structure, specialisation, microscopy, and cell division, providing the essential knowledge needed to secure top marks in your GCSE exams.

All design and technological practice takes place within contexts which inform outcomes

Pearson Edexcel·GCSE

Pearson-GCSE-Design-and-Technology

This topic covers how the intended environment and user shape every design decision. You will learn how to select and justify materials, components, and manufacturing processes based on their performance characteristics to solve specific problems within given contexts.

Alteration of the Sequence of Bases

AQA·A-Level

Unlock top marks by mastering how a single change in a DNA base can have catastrophic effects on a protein's structure and function. This guide breaks down the complete causal chain, from mutation to non-functional enzyme, giving you the precise language and exam technique AQA rewards.

Alternative methods of extracting metals (HT only): Bioleaching uses bacteria to produce leachate solutions that contain metal compounds.

AQA·GCSE

8464

Alternative methods of extracting metals (HT only): Copper ores are becoming scarce and new ways of extracting copper from low-grade ores include phytomining, and bioleaching. These methods avoid traditional mining methods of digging, moving and disposing of large amounts of rock.

AQA·GCSE

8464

Alternative methods of extracting metals (HT only): Phytomining uses plants to absorb metal compounds. The plants are harvested and then burned to produce ash that contains metal compounds.

AQA·GCSE

8464

Alternative methods of extracting metals (HT only): Students should be able to evaluate alternative biological methods of metal extraction, given appropriate information.

AQA·GCSE

8464

Alternative methods of extracting metals (HT only): The Earth’s resources of metal ores are limited.

AQA·GCSE

8464

Alternative methods of extracting metals (HT only): The metal compounds can be processed to obtain the metal. For example, copper can be obtained from solutions of copper compounds by displacement using scrap iron or by electrolysis.

AQA·GCSE

8464