Study guides

Transverse and longitudinal waves

OCR·GCSE

Waves are the mechanism by which energy is transferred across space and matter, and this topic sits at the heart of OCR GCSE Physics. Candidates must master the precise distinction between transverse and longitudinal waves, command the wave equation v = fλ with confidence, and interpret both displacement-distance and displacement-time graphs accurately. Examiners consistently award marks for exact language — particularly the terms 'perpendicular', 'parallel', 'compression', and 'rarefaction' — making this a topic where precision of expression is as important as conceptual understanding.

Travel

Pearson Edexcel·GCSE

Pearson-GCSE-Chinese

This comprehensive GCSE Chinese Travel guide equips you with essential vocabulary for transport, accommodation, and directions. You will master three crucial grammar structures (要, 过, and measure words) to access higher marks across Listening, Speaking, Reading, and Writing.

Travel and tourist transactions

Pearson Edexcel·GCSE

Pearson-GCSE-French

Master the essentials of Travel and Tourist Transactions for GCSE French. This guide covers vital vocabulary, key grammar structures like the three time frames, and transactional role-plays to ensure you secure top marks across all four skills.

Treating Psychological Problems

OCR·GCSE

This study guide provides a comprehensive overview of how psychological problems are treated, focusing on the OCR GCSE Psychology specification. It contrasts biological treatments targeting brain chemistry with psychological therapies that address thoughts and behaviours, equipping students with the precise knowledge needed to excel in their exams.

Treating, curing and preventing disease

Eduqas·GCSE

WJEC-GCSE-Biology

This topic explores the vital mechanisms we use to fight communicable diseases, from the preventative power of vaccines to the curative role of antibiotics. Understanding how these work, alongside the rigorous process of drug development, is crucial for exam success as it frequently appears in high-mark extended response questions.

Trigonometry

AQA·A-Level

Master AQA A-Level Trigonometry, from reciprocal functions and compound angles to harmonic form and proofs. This guide provides everything you need to solve complex problems, secure top marks, and understand the maths of waves and oscillations."

Trigonometry

Pearson Edexcel·A-Level

Master Edexcel A-Level Trigonometry with this comprehensive guide. We break down complex identities, radians, and reciprocal functions into manageable chunks, providing examiner insights and worked examples to help you secure top marks.

Trigonometry

OCR·GCSE

This topic extends your trigonometry knowledge beyond right-angled triangles into the realm of any angle, trigonometric identities, and complex equation solving. You'll master the CAST diagram, apply the Sine and Cosine Rules to non-right-angled triangles in 2D and 3D contexts, and prove identities using fundamental relationships. This is a high-value topic in Further Maths exams, frequently appearing in multi-step problem-solving questions worth 4-6 marks.

Trigonometry

OCR·A-Level

Master OCR A-Level Trigonometry (4.9) with this comprehensive guide. We cover everything from reciprocal functions and compound angles to exam technique and common pitfalls, helping you secure top marks.

Tropical cyclones are extreme weather events that develop under specific conditions and in certain locations

Pearson Edexcel·GCSE

Pearson-GCSE-Geography

Master the dynamics of Tropical Cyclones for your GCSE Geography exam. This comprehensive guide covers their formation, global distribution, impacts, and responses, equipping you with the exact knowledge examiners look for when comparing developed and emerging countries.

Tropical rainforest ecosystems provide a range of goods and services, some of which are under threat

Pearson Edexcel·GCSE

Pearson-GCSE-Geography

Tropical rainforests are the most biodiverse ecosystems on Earth, providing essential goods like medicines and timber, alongside critical services like global climate regulation. This guide covers everything you need to know about the threats they face from climate change and deforestation, and how sustainable management strategies in the Amazon aim to protect them.

Tropical rainforests show a range of distinguishing features

Pearson Edexcel·GCSE

Pearson-GCSE-Geography

Tropical rainforests are the most biodiverse and productive ecosystems on Earth, yet they are incredibly fragile. Understanding their climate, structure, and nutrient cycling is essential for GCSE Geography, as examiners frequently test the concept of interdependence within this biome.

Truth tables

Pearson Edexcel·GCSE

Pearson-GCSE-Computer-Science

Master the logic behind digital systems with this comprehensive guide to Truth Tables. Learn how to map out every possible outcome for AND, OR, and NOT gates, ensuring you never drop a mark on these satisfying, puzzle-like exam questions.

Turning Points in Physics

AQA·A-Level

This guide explores the pivotal experiments and theories that revolutionised physics, from the null result of the Michelson-Morley experiment to Einstein's theories of special relativity and the quantum nature of light. It's a crucial A-Level topic that bridges classical and modern physics, and mastering it is key to top marks.

Twelfth Night

Pearson Edexcel·GCSE

Pearson-GCSE-English-Literature

Dive into Shakespeare's brilliantly chaotic comedy of mistaken identity, unrequited love, and festive misrule. 'Twelfth Night' offers rich opportunities for high-level analysis of gender, social ambition, and the illusion of romance.

Types of Crime

OCR·GCSE

Types of Crime is a cornerstone topic in OCR GCSE Sociology (J204), requiring candidates to move beyond common-sense understandings and apply precise sociological classifications to criminal behaviour. From the white-collar boardroom to the digital world of cyber-crime, this topic reveals how power, inequality, and social construction shape what society labels as 'criminal'. Mastering this topic is essential for high-mark responses, as examiners consistently reward candidates who can distinguish between crime types, link them to theoretical perspectives, and critically evaluate official statistics.

Typography

OCR·GCSE

This guide explores Typography within OCR GCSE Art and Design, focusing on how to use letterforms as an expressive visual language. Candidates will learn to manipulate type anatomy, hierarchy, and layout to create compelling graphic communication and earn high marks across all four Assessment Objectives."

Ultrasound

OCR·GCSE

Ultrasound (Topic 4.9) explores how sound waves above 20,000 Hz are used in medical imaging and sonar through the principle of partial reflection at boundaries between media of different densities. Mastery of this topic requires candidates to perform precise echo-sounding calculations using d = v × t/2, apply correct scientific language in extended answers, and evaluate ultrasound against X-rays — skills that appear in both Foundation and Higher tier papers and carry marks across all three assessment objectives.

Understand and use composite functions; inverse functions and their graphs

Pearson Edexcel·A-Level

9MA0

Composite and inverse functions turn algebra into a chain of controlled processes: apply rules in the right order, then reverse them only when the mapping is one-to-one. In Pearson Edexcel A-level Mathematics, this compact topic can test notation, domains, graph reflection and algebraic rearrangement in a single multi-mark question.

Understand and use moments in simple static contexts

Pearson Edexcel·A-Level

9MA0

Moments turn a static diagram into a solvable mechanics problem: calculate a turning effect, then combine it with force equilibrium. This guide gives candidates an examiner-friendly routine for beams, rods and ladder problems, where accurate diagrams and perpendicular distances secure the method marks.

Understand and use Newton's third law; equilibrium of forces on a particle and motion in a straight line (restricted to forces in two perpendicular directions or simple cases of forces given as 2-D vectors); application to problems involving smooth pulleys and connected particles; resolving forces in 2 dimensions; equilibrium of a particle under coplanar forces

Pearson Edexcel·A-Level

9MA0

Mechanics becomes much more reliable when you treat every question as a force-modelling task: select one particle, draw the forces, choose axes and then write the appropriate Newton’s-law equation. This Pearson Edexcel A-Level guide covers the full 8.4 extension, including resolved forces, coplanar equilibrium and smooth-pulley systems, so candidates can turn a difficult diagram into creditable method marks.

Understand and use position vectors; calculate the distance between two points represented by position vectors

Pearson Edexcel·A-Level

9MA0

Position vectors give a precise language for locating points from an origin, while displacement and magnitude convert that location data into journeys and distances. In Pearson Edexcel 10.4, candidates must work securely in both 2D and 3D, where a correct direction, clear working and an exact final distance can unlock dependable marks in Pure and synoptic mechanics questions.

Understand and use simple, discrete probability distributions (calculation of mean and variance of discrete random variables is excluded), including the binomial distribution, as a model; calculate probabilities using the binomial distribution

Pearson Edexcel·A-Level

9MA0

This guide turns Edexcel Topic 4.1 into a dependable exam routine: define the count, test the binomial assumptions, translate the probability wording, then calculate. It matters because Paper 3 rewards both accurate calculator work and the mathematical judgement needed to model or criticise a real situation.

Understand and use the definitions of secant, cosecant and cotangent and of arcsin, arccos and arctan; their relationships to sine, cosine and tangent; understanding of their graphs; their ranges and domains

Pearson Edexcel·A-Level

9MA0

Reciprocal and inverse trigonometric functions reward accuracy because a single denominator, asymptote or principal range controls the whole answer. Master the difference between a ratio and an angle-returning function, and Edexcel graph, domain/range and equation questions become a predictable source of marks.

Understand and use the equation of a straight line, including the forms y – y₁ = m(x – x₁) and ax + by + c = 0; gradient conditions for two straight lines to be parallel or perpendicular; be able to use straight line models in a variety of contexts

Pearson Edexcel·A-Level

9MA0

Straight lines are the algebraic language of constant rate of change: one gradient and one point fix a unique line. Pearson Edexcel candidates must move confidently between equation forms, use negative reciprocals for perpendicular lines and interpret models, because these short questions can test algebra, graph skills and contextual reasoning at once.

Understand and use the laws of indices for all rational exponents

Pearson Edexcel·A-Level

9MA0

Mastering the Laws of Indices is essential for unlocking algebra and higher-level mathematics. This guide breaks down the five core rules—from multiplication to fractional indices—giving you the tools to simplify complex expressions and secure vital marks in your GCSE exams.

Understand and use the Normal distribution as a model; find probabilities using the Normal distribution; link to histograms, mean, standard deviation, points of inflection and the binomial distribution

Pearson Edexcel·A-Level

9MA0

The Normal distribution is the bell-curve model that turns continuous data into exam-ready probabilities, percentiles and modelling decisions. Pearson Edexcel expects more than a calculator answer: candidates must interpret μ and σ², show the correct event, and use continuity correction when linking to the binomial distribution. Master the routine and this becomes one of the most reliable sources of Paper 3 marks.

Understand and use the sine, cosine and tangent functions; their graphs, symmetries and periodicity; know and use exact values of sin and cos for 0, π/6, π/4, π/3, π/2, π and multiples thereof, and exact values of tan for 0, π/6, π/4, π/3, π and multiples thereof

Pearson Edexcel·A-Level

9MA0

Trigonometry becomes far easier once you see it as coordinates moving around a unit circle. This guide turns Edexcel Topic 5.3 into exact-value patterns, graph routines and solution strategies that convert directly into marks on Pure Mathematics papers.

Understand and use the standard small angle approximations of sine, cosine and tangent: sin θ ≈ θ, cos θ ≈ 1 – θ²/2, tan θ ≈ θ where θ is in radians

Pearson Edexcel·A-Level

9MA0

Small-angle approximations let you replace trigonometric functions with simple algebra when the angle is close to zero in radians. In Edexcel Topic 5.2, the formulae are provided, so the marks come from accurate substitution of the whole argument, clear algebra and a disciplined check of the angle unit.

Understand and use the structure of mathematical proof, proceeding from given assumptions through a series of logical steps to a conclusion; use methods of proof, including: Proof by deduction, Proof by exhaustion, Disproof by counter example, Proof by contradiction (including proof of the irrationality of √2 and the infinity of primes, and application to unfamiliar proofs)

Pearson Edexcel·A-Level

9MA0

Mathematical Proof is the art of demonstrating that a statement is true beyond any doubt, using logical steps rather than just examples. Mastering proof methods—like deduction, exhaustion, counter-example, and contradiction—will not only secure you top marks in the exam but also sharpen your logical thinking skills.