Study guides

Algebra

Eduqas·GCSE

WJEC-GCSE-Mathematics

Algebra is the language of mathematics, using letters to represent unknown values and general rules. Mastering algebra unlocks the ability to solve complex problems across the entire specification, making it a critical foundation for exam success.

Algebra

AQA·GCSE

8300

Algebra is the mathematical language of variables and unknowns, forming the foundation of GCSE Mathematics. Mastering these concepts is essential for accessing higher marks across the entire specification, as algebra connects deeply to geometry, statistics, and number problems.

Algebra

OCR·GCSE

J560

Master the essential connections between fractions, decimals, and percentages to unlock high marks across the GCSE Maths paper. This guide covers everything from basic conversions to complex percentage multipliers and recurring decimals.

Algebra

Pearson Edexcel·GCSE

1MA1

Master the language of mathematics with this comprehensive guide to GCSE Algebra. From expanding brackets to solving quadratic equations, we'll build the fluency you need to secure top marks in your exams.

Algebra

Pearson Edexcel·GCSE

601/4700/3

Sequences are the heartbeat of algebraic patterns, testing your ability to spot relationships and express them mathematically. Mastering term-to-term and position-to-term rules is essential for unlocking high marks in your GCSE Mathematics exam.

Algebra and Functions

WJEC·A-Level

603/1977/X

Algebra and Functions is where WJEC A-Level Mathematics becomes a connected system: exact manipulation produces equations, equations produce graphs, and graphs explain the answers. Mastering these routines protects method marks across the AS Unit 1 paper and prepares you for coordinate geometry, calculus and modelling.

Angles

OCR·GCSE

Master the fundamental principles of angles for your OCR GCSE Maths exam. This guide breaks down everything from basic angle types to complex geometric proofs, providing examiner insights and memory hooks to help you secure every possible mark.

Approximation and Estimation

OCR·GCSE

J560

Master the art of Approximation and Estimation, a foundational topic that underpins almost every paper in GCSE Mathematics. From avoiding the common traps of significant figures to calculating error bounds for complex measurements, this guide provides everything you need to secure method marks and tackle multi-step problems with confidence.

Area and Perimeter

OCR·GCSE

Master OCR GCSE Area and Perimeter (3.6) with this comprehensive guide. We will break down complex shapes, demystify formulas, and provide you with the examiner insights needed to secure top marks. This topic is a cornerstone of geometry and a guaranteed feature in your exam, making it essential for a high grade.

Basic Geometry

OCR·GCSE

J560

Master the fundamental connections between fractions, decimals, and percentages. These core skills are essential for both Foundation and Higher tier exams, unlocking marks across multiple topics from probability to compound interest.

Calculations

OCR·GCSE

Master the core of your GCSE Maths exam with this guide to Calculations. Learn the secrets to using your calculator effectively, conquer the order of operations (BIDMAS), and perfect your rounding skills to secure every possible mark.

Congruence and Similarity

OCR·GCSE

J560

Master the principles of congruence and similarity, a high-yield topic that bridges geometry and proportional reasoning. Learn how to prove triangles are identical, apply scale factors to lengths, areas, and volumes, and secure top marks in multi-step exam questions.

Constructions

OCR·GCSE

Master OCR GCSE Constructions by learning to use a ruler and compasses with precision. This guide breaks down perpendicular bisectors, angle bisectors, and complex loci to help you secure every mark. Forget the protractor and learn the techniques that examiners reward.

Data Handling

OCR·GCSE

Master OCR GCSE Data Handling with this guide, covering everything from basic charts to advanced histograms and cumulative frequency. Learn to interpret data, nail exam questions, and secure top marks.

Differentiation

WJEC·A-Level

603/1977/X

Differentiation is the WJEC A-Level tool for converting a curve into precise information about gradient, change and optimum values. Master the route from derivative to interpretation and you can pick up marks across tangents, normals, stationary points, graphs and modelling.

Equations

OCR·GCSE

Equations (Topic 2.2) is a cornerstone of OCR GCSE Mathematics, testing your ability to solve linear, quadratic, and simultaneous equations across both Foundation and Higher tiers. Mastering this topic unlocks marks throughout the exam, from pure algebra questions to problem-solving in geometry and statistics. This guide provides you with the core methods, exam techniques, and memory hooks to confidently tackle any equation question.

Evaluate the analytical solution of simple first order differential equations with separable variables, including finding particular solutions (separation of variables may require factorisation involving a common factor)

Pearson Edexcel·A-Level

9MA0

Mastering first-order differential equations unlocks your ability to model real-world change, from population growth to radioactive decay. This guide breaks down the separation of variables technique into a foolproof 4-step method to secure maximum marks in your exam.

Exponentials and Logarithms

WJEC·A-Level

603/1977/X

Exponentials and logarithms turn repeated multiplication into a precise language for growth, decay, inverse functions and data modelling. WJEC 2.1.6 rewards candidates who can show why the rules work, not just press calculator buttons. Master the graph axes, logarithm laws and equation methods, and this topic becomes a reliable source of method marks.

Expressions and Formulae

OCR·GCSE

Expressions and Formulae is a cornerstone topic in OCR GCSE Mathematics, testing your ability to manipulate algebraic expressions, substitute values accurately, factorise efficiently, and rearrange formulae with confidence. This topic accounts for approximately 60% of AO1 marks in this section and underpins almost every other algebra topic you'll encounter, from quadratics to simultaneous equations. Mastering these skills will unlock consistent marks across both Foundation and Higher tier papers.

Forces and Newton's Laws

WJEC·A-Level

603/1977/X

Forces and Newton’s laws turn everyday motion into a short mathematical model: identify the particle, show every external force and apply the resultant-force equation with disciplined signs. In WJEC 2.2.8, the marks are highly recoverable because a correct free-body diagram, clear direction and visible method earn credit before the final calculation. Master the system-then-single approach for pulleys and you will make connected-particle questions predictable rather than intimidating.

Fractions, Decimals and Percentages

OCR·GCSE

Master the essential GCSE Maths topic of Fractions, Decimals, and Percentages (FDP). This guide will equip you to confidently switch between forms, tackle complex percentage problems, and secure maximum marks in your OCR exam. It's a cornerstone of the curriculum, vital for both calculator and non-calculator papers.

Geometry and measures

Pearson Edexcel·GCSE

1MA1

Geometry and Measures is a fundamental GCSE Mathematics topic covering everything from basic shape properties to advanced trigonometry, circle theorems, and vector calculus. Mastering this topic is essential for unlocking top grades, as examiners frequently use it to test multi-step problem-solving and logical reasoning skills.

Geometry and measures

Eduqas·GCSE

WJEC-GCSE-Mathematics

Geometry and Measures is a fundamental pillar of GCSE Mathematics, testing your ability to understand spatial relationships, apply formulas, and construct logical geometric proofs. Mastering this topic is crucial, as it often features in high-tariff questions that separate the top grades.

Geometry and measures

AQA·GCSE

8300

Geometry and Measures is a foundational pillar of GCSE Mathematics, testing both your spatial reasoning and algebraic application. Mastering these concepts is essential for accessing the highest grades, as they appear consistently across multiple papers.

Geometry and measures

Pearson Edexcel·GCSE

601/4700/3

Geometry and Measures forms the foundation of spatial reasoning in GCSE Mathematics. Mastering angle rules, polygons, and parallel lines guarantees you can secure highly predictable marks in both Foundation and Higher tier papers.

Graphs

OCR·GCSE

Master OCR GCSE Maths Graphs by learning to translate functions into visuals. This guide focuses on earning maximum marks by mastering plotting, interpreting gradients, and avoiding common examiner traps for linear and quadratic graphs.

Graphs of Equations and Functions

OCR·GCSE

J560

Master the visual language of Mathematics. This comprehensive guide covers linear, quadratic, cubic, reciprocal, exponential, and circle graphs, showing you exactly how to secure top marks in every graph question.

Indices and Surds

OCR·GCSE

J560

Master the foundational rules of Indices and Surds to unlock higher-level algebra. This topic covers the manipulation of powers, roots, and exact values, essential for maximizing marks in both calculator and non-calculator papers.

Mensuration

OCR·GCSE

J560

Mensuration is the mathematics of measuring shapes — from calculating the perimeter of a 2D field to finding the volume of a 3D sphere. It is a cornerstone of the GCSE Mathematics specification, appearing in almost every paper, and mastering these formulas guarantees reliable, accessible marks.

Number

Pearson Edexcel·GCSE

601/4700/3

Mastering fractions, decimals, and percentages is the foundation of GCSE Mathematics. This topic unlocks marks across the entire specification, teaching you how to fluently convert between forms and apply the powerful multiplier method to solve percentage change problems quickly and accurately.