Solving quadratic equations: factorising and the formula
Solve quadratics by factorising and with the quadratic formula, using worked examples. Covers GCSE quadratic equations and Algebra 1 and 2 methods.
GCSEA-LevelHigh SchoolUK · Ages 16–18
A-Level revision guides
Go deeper on topics that carry on into A-Level, including quadratics, the sine and cosine rules, logarithms, DNA, electrolysis and moles. Our A-Level collection is still growing, so check your specification for topics that are not listed here.
StudyMorrow guides are independent study aids, not official course materials, so check your own syllabus or exam specification.
➗ A-Level Maths
See all 10 →Find the equation of a line from two points
Work out the gradient (slope), find the y-intercept and write the equation of a line, plus parallel and perpendicular lines and midpoints.
GCSEA-LevelHigh SchoolQuadratic graphs: roots, turning points and symmetry
Sketch parabolas and find the roots, y-intercept, line of symmetry and turning point (vertex) of a quadratic, with step-by-step worked examples.
GCSEA-LevelHigh SchoolCompleting the square: method, examples and solutions
Rewrite quadratics in completed-square form to solve equations and find the turning point, with step-by-step examples for GCSE Higher and Algebra 2.
GCSEA-LevelHigh SchoolFunction notation: f(x), composite and inverse functions
Understand f(x) notation, work out composite functions such as fg(x) and find inverse functions, with worked examples for GCSE Higher and Algebra 2.
GCSEA-LevelHigh SchoolExponential growth and decay: formulas and worked examples
Model repeated percentage change with y = a × bˣ, including compound growth, depreciation and doubling, with step-by-step examples.
GCSEA-LevelHigh SchoolSine rule and cosine rule: formulas and worked examples
Solve non-right-angled triangles with the sine and cosine rules (law of sines and law of cosines) and find a triangle's area, with examples.
GCSEA-LevelHigh SchoolSurds (radicals): simplifying and rationalising
Simplify surds, calculate with them and rationalise denominators, with step-by-step examples. UK surds and US radicals, for GCSE Higher and Algebra 2.
GCSEA-LevelHigh SchoolCircle theorems explained: rules, examples and reasons
Learn the main circle theorems and use them to find angles with a reason for every step. GCSE Higher and high school Geometry, with worked examples.
GCSEA-LevelHigh SchoolLogarithms explained: laws, examples and solving equations
Understand logarithms as the inverse of powers, use the log laws and solve simple exponential equations. Algebra 2 and A-Level, with examples.
High SchoolA-LevelAP🧬 A-Level Biology
See all 1 →DNA, genes and inheritance: Punnett squares explained
Understand genes, alleles, dominant and recessive traits and how to complete a Punnett square, with worked examples for GCSE and high school.
GCSEA-LevelHigh SchoolAP⚗️ A-Level Chemistry
See all 4 →Ionic and covalent bonding: how atoms join, with examples
Compare ionic and covalent bonding, write ionic formulae and explain properties such as melting point and electrical conductivity.
GCSEA-LevelHigh SchoolAPMoles and molar mass: calculations explained step by step
Convert between mass and moles using Mr, use balanced equations to find reacting masses and calculate concentration, with worked examples.
GCSEA-LevelHigh SchoolAPElectrolysis explained: products at each electrode
See how electricity splits ionic compounds, and predict the products at the anode and cathode for molten and aqueous solutions.
GCSEA-LevelHigh SchoolAlkanes and alkenes: formulae, combustion and bromine test
Learn the hydrocarbon families, their general formulae, how they burn and how bromine water tells them apart, with worked examples.
GCSEA-LevelHigh School📖 A-Level English
See all 11 →How to write a thesis statement (with strong examples)
Turn a topic into a clear, arguable claim for your essay, with a simple formula, weak and strong examples and a quick test.
GCSEA-LevelHigh SchoolAPPEEL and CER paragraphs: how to structure analysis
Build clear paragraphs with PEEL (UK) or Claim-Evidence-Reasoning (US), with worked examples for English and science answers.
KS3GCSEA-LevelMiddle School+2Essay structure: how to plan and write a clear essay
Plan an essay step by step, from brainstorming to a strong introduction, well-organised paragraphs and a conclusion that answers the question.
GCSEA-LevelHigh SchoolAPHow to embed quotations in an essay (with examples)
Weave short quotations into your sentences and comment on key words, instead of dropping them in, with before-and-after examples.
GCSEA-LevelHigh SchoolAPLanguage analysis: how to analyse a quotation
Break a quotation down by word class, connotation and effect with the zoom-in method, to write detailed analysis.
GCSEA-LevelHigh SchoolAPAnalysing structure in texts: openings, shifts and endings
Look at how a writer organises a text, from openings and shifts in focus to pacing, sentence length and endings, with examples.
GCSEA-LevelHigh SchoolAPHow to compare two texts: structure, connectives and examples
Plan and write a comparison using similarities, differences and comparative connectives, with a clear method.
GCSEA-LevelHigh SchoolAPHow to read and analyse a Shakespeare play
Understand Shakespeare's language, verse and context so you can read and analyse his plays with confidence.
GCSEA-LevelHigh SchoolAPPoetry analysis: form, structure and language explained
Analyse a poem by looking at its form, rhyme, rhythm, structure and language, with a step-by-step approach.
GCSEA-LevelHigh SchoolAPLogical fallacies and how to evaluate an argument
Judge whether an argument is convincing and spot common logical fallacies such as ad hominem, straw man and false dilemma.
GCSEA-LevelHigh SchoolAPCiting sources: MLA, APA and Harvard basics for essays
Find reliable sources, avoid plagiarism by quoting and paraphrasing correctly and understand common citation styles.
GCSEA-LevelHigh SchoolAP🏛️ A-Level History
See all 3 →Causes of World War One: MAIN causes and the trigger
Learn the long-term causes of the First World War (militarism, alliances, imperialism, nationalism) and how the 1914 assassination set it off.
GCSEA-LevelHigh SchoolAPThe Cold War: causes, key events and how it ended
Understand the rivalry between the US and the Soviet Union from 1945 to 1991, with key events such as the Berlin Wall and the Cuban Missile Crisis.
GCSEA-LevelHigh SchoolAPThe Weimar Republic and how Hitler rose to power
See why the Weimar Republic struggled, how the Great Depression helped the Nazis and how Hitler gained power in 1933.
GCSEA-LevelHigh SchoolAP🌍 A-Level Geography
See all 1 →Climate change: the greenhouse effect and the 1.5°C target
Understand the greenhouse effect, what the Paris Agreement's 1.5°C goal means and the difference between mitigation and adaptation.
GCSEA-LevelHigh SchoolAP💻 A-Level Computing
See all 1 →Binary search and bubble sort: searching and sorting algorithms
Learn how linear search, binary search and bubble sort work, with step-by-step traces and when to use each.
GCSEA-LevelHigh School🧠 A-Level Study skills
See all 14 →Active recall: the best way to revise (with examples)
Learn why testing yourself beats rereading, and four simple ways to use active recall: flashcards, blank-page recall and practice questions.
KS3GCSEA-LevelMiddle School+3Spaced repetition: how to remember what you revise
Review material at increasing gaps to remember it long term, with an example schedule and the Leitner box system.
KS3GCSEA-LevelMiddle School+3How to make a revision timetable you can stick to
Plan backwards from your exam dates and use focused study blocks with breaks, with a simple way to share your time between subjects.
KS3GCSEA-LevelMiddle School+3Exam command words: describe, explain and evaluate
Learn what describe, explain, compare, analyse and evaluate really ask you to do in an exam, using an exam board's definitions.
GCSEA-LevelHigh SchoolAPCornell notes: how to take notes you can revise from
Set up Cornell notes with cue, notes and summary sections, and turn them into a self-test for revision.
KS3GCSEA-LevelMiddle School+2Mind maps for revision: how to make them work
Use mind maps to organise a topic, then turn them into a memory test so they actually help you remember.
KS3GCSEA-LevelMiddle School+2Interleaving: mix topics in your revision to remember more
Learn why mixing question types in one session can improve long-term learning, with an example maths and science session plan.
GCSEA-LevelHigh SchoolAPHow to use past papers to revise (and review your mistakes)
Turn past papers into focused practice with timing, mark schemes and an error review that shows exactly what to fix.
GCSEA-LevelHigh SchoolAP+1Exam stress: practical ways to cope and when to ask for help
Practical, non-medical ways to cope with exam pressure, from planning and breaks to talking to someone you trust.
GCSEA-LevelHigh SchoolAP+1Mnemonics and the memory palace: remember lists and facts
Use acronyms, acrostics and the method of loci to remember lists and ordered facts, and learn when mnemonics help most.
KS3GCSEA-LevelMiddle School+2The Feynman technique: study by explaining it simply
Check your understanding by explaining a topic in plain language, spotting the gaps and fixing them.
KS3GCSEA-LevelMiddle School+2How to stay focused when studying (and avoid your phone)
Set up your space, plan sessions and manage your phone so your study time is actually productive.
KS3GCSEA-LevelMiddle School+2SQ3R: how to read a textbook and remember it
Survey, Question, Read, Recite and Review: a five-step routine for learning from textbooks and long texts.
GCSEA-LevelHigh SchoolAP+1Exam day plan: what to do the week before and on the day
Plan the last week, the night before and the exam itself: equipment, timing and how to check your work.
GCSEA-LevelHigh SchoolAP+1