Solving linear equations step by step (with examples)
Learn the balance method for solving linear equations, including brackets and x on both sides, with worked examples for GCSE and Algebra 1.
KS3GCSEMiddle SchoolHigh SchoolRevise GCSE maths, biology, chemistry, physics, English, history, geography and computer science topic by topic. Each guide gives a clear explanation, worked examples with every step shown, five practice questions with explained answers, and a printable PDF.
StudyMorrow guides are independent study aids, not official course materials, so check your own syllabus or exam specification.
Learn the balance method for solving linear equations, including brackets and x on both sides, with worked examples for GCSE and Algebra 1.
KS3GCSEMiddle SchoolHigh SchoolWork out a percentage of an amount, increase or decrease by a percentage and calculate percentage change, with worked examples for KS3 and GCSE.
KS3GCSEMiddle SchoolUse a² + b² = c² to find any side of a right-angled triangle. Worked examples for GCSE, and the Pythagorean theorem in US Geometry.
KS3GCSEMiddle SchoolHigh SchoolFind the mean, median, mode and range of a data set with clear worked examples, and learn which average to use when there is an outlier.
KS3GCSEMiddle SchoolHigh SchoolSolve quadratics by factorising and with the quadratic formula, using worked examples. Covers GCSE quadratic equations and Algebra 1 and 2 methods.
GCSEA-LevelHigh SchoolMultiply out single and double brackets, take out common factors and use the difference of two squares. GCSE factorising and US factoring.
GCSEHigh SchoolUse sine, cosine and tangent to find missing sides and angles in right-angled triangles, with step-by-step examples for GCSE and high school Geometry.
GCSEHigh SchoolLearn the area and circumference formulas for circles, how to use radius and diameter, and how to work with semicircles, with worked examples.
KS3GCSEMiddle SchoolHigh SchoolSolve two equations with two unknowns using elimination and substitution. Worked examples for GCSE simultaneous equations and Algebra 1 systems.
GCSEHigh SchoolLearn how to calculate probability, use 'not' events and find the probability of two events together, with worked examples for KS3 and GCSE.
KS3GCSEMiddle SchoolHigh SchoolLearn the correct order for working out a calculation, with worked examples and common traps. BIDMAS in the UK is the same as PEMDAS in the US.
KS3GCSEMiddle SchoolHigh SchoolLearn the rules for working with negative numbers, including subtracting a negative and multiplying signs, with number-line examples.
KS3GCSEMiddle SchoolHigh SchoolLearn what factors, multiples and prime numbers are, how to list them and how to test whether a number is prime, with worked examples.
KS3GCSEMiddle SchoolHigh SchoolWrite numbers as products of primes, then find the highest common factor (greatest common factor in the US) and the lowest common multiple.
GCSEMiddle SchoolHigh SchoolConvert between mixed numbers and improper fractions, then multiply and compare them, with step-by-step examples and practice questions.
KS3GCSEMiddle SchoolSwitch between fractions, decimals and percentages, including recurring decimals, with worked examples and practice questions to check your answers.
KS3GCSEMiddle SchoolHigh SchoolSimplify ratios, share an amount in a ratio and solve scaling problems with the unit method, with worked examples for GCSE and middle school.
KS3GCSEMiddle SchoolHigh SchoolLearn the index laws for multiplying, dividing and raising powers, plus zero and negative indices. UK indices and US exponent rules, with examples.
GCSEHigh SchoolWrite very large and very small numbers in standard form, convert them back and multiply them, with worked examples for GCSE and high school.
GCSEHigh SchoolCollect like terms, multiply and divide algebraic terms and simplify expressions with brackets, with step-by-step examples and practice questions.
KS3GCSEMiddle SchoolHigh SchoolMake any letter the subject of a formula using inverse operations, with worked examples including squares and square roots.
GCSEHigh SchoolSolve linear inequalities, including double inequalities, and remember to reverse the sign when dividing by a negative, with worked examples.
GCSEHigh SchoolPlot straight lines, work out the gradient and read the equation from a graph. Covers y = mx + c (slope-intercept form), with worked examples.
GCSEHigh SchoolWork out the gradient (slope), find the y-intercept and write the equation of a line, plus parallel and perpendicular lines and midpoints.
GCSEA-LevelHigh SchoolFind the nth term of arithmetic sequences, test whether a number is in a sequence and meet geometric and quadratic sequences, with worked examples.
GCSEHigh SchoolSketch 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 SchoolRewrite 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 SchoolUnderstand 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 SchoolModel repeated percentage change with y = a × bˣ, including compound growth, depreciation and doubling, with step-by-step examples.
GCSEA-LevelHigh SchoolUse y = kx and y = k/x to solve direct and inverse proportion problems, including y proportional to x squared, with worked examples.
GCSEHigh SchoolLearn the angle rules for straight lines, triangles, parallel lines and polygons, and how to give a reason for each step, with worked examples.
KS3GCSEMiddle SchoolHigh SchoolCalculate the perimeter and area of rectangles, triangles, parallelograms, trapeziums (trapezoids) and compound shapes, with worked examples.
KS3GCSEMiddle SchoolHigh SchoolFind the volume and surface area of cuboids, prisms, cylinders, cones and spheres, with worked examples and a quick formula list.
GCSEHigh SchoolUse scale factors to find missing lengths, and learn how area and volume scale with k squared and k cubed, with worked examples.
GCSEHigh SchoolDescribe and carry out the four transformations on a coordinate grid, including the details examiners expect, with worked examples.
GCSEHigh SchoolLearn the congruence conditions for triangles, why AAA does not prove congruence and how to use them in simple proofs, with worked examples.
GCSEHigh SchoolSolve 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 SchoolSimplify 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 SchoolPlot scatter graphs, describe correlation, draw a line of best fit and make estimates, and learn why correlation does not mean causation.
KS3GCSEMiddle SchoolHigh SchoolDraw tree diagrams for independent and dependent events, including picks without replacement, with worked examples and common mistakes.
GCSEHigh SchoolFind the median, quartiles and interquartile range, draw box plots (box and whisker plots) and compare data sets, with worked examples.
GCSEHigh SchoolWork backwards from a final price to the original amount, and calculate compound interest, with worked examples and practice questions.
GCSEHigh SchoolLearn 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 SchoolUse sets, Venn diagrams and the symbols for union, intersection and complement to solve problems and find probabilities, with examples.
KS3GCSEMiddle SchoolHigh SchoolLearn how plants make glucose and oxygen from light, water and carbon dioxide, with the equation, limiting factors and practice questions.
KS3GCSEMiddle SchoolHigh School+1Learn the parts of plant and animal cells, what each one does and how to calculate magnification, with worked examples and practice questions.
KS3GCSEMiddle SchoolHigh School+1Compare aerobic and anaerobic respiration in animals and yeast, with the equations, oxygen debt and practice questions to test yourself.
GCSEHigh SchoolAPUnderstand genes, alleles, dominant and recessive traits and how to complete a Punnett square, with worked examples for GCSE and high school.
GCSEA-LevelHigh SchoolAPLearn how enzymes work, why temperature and pH matter and which enzymes digest starch, protein and fat, with worked examples.
GCSEHigh SchoolAPLearn what happens at each stage of mitosis, why cells divide and how to count cells after division, with worked examples and practice questions.
GCSEHigh SchoolAPSee how meiosis makes four different gametes, how it differs from mitosis and why sexual reproduction creates variation, with practice questions.
GCSEHigh SchoolAPUnderstand variation, competition and inheritance, with examples such as peppered moths and antibiotic resistance, and practice questions.
GCSEHigh SchoolAPRead food chains and food webs, name trophic levels and calculate how much energy passes between them, with worked examples.
KS3GCSEMiddle SchoolHigh SchoolLearn the chambers of the heart, how blood flows around the body and how to calculate cardiac output, with worked examples.
GCSEHigh SchoolFollow the pathway from stimulus to response, and learn how reflexes differ from voluntary actions, with worked examples.
GCSEHigh SchoolLearn how the body keeps conditions steady, how insulin and glucagon control blood glucose and what happens in diabetes, with examples.
GCSEHigh SchoolAPCompare how substances move into and out of cells, what affects the rate and how to calculate percentage change in a potato practical.
GCSEHigh SchoolAPLearn atomic structure, atomic and mass number, isotopes and how the periodic table is organised, with worked examples.
KS3GCSEMiddle SchoolHigh SchoolCompare ionic and covalent bonding, write ionic formulae and explain properties such as melting point and electrical conductivity.
GCSEA-LevelHigh SchoolAPRead the pH scale, write neutralisation equations and name the salts acids make, with a titration calculation for Higher tier.
GCSEHigh SchoolLearn how to balance equations by counting atoms, with worked examples including combustion, plus practice questions with explained answers.
GCSEHigh SchoolConvert between mass and moles using Mr, use balanced equations to find reacting masses and calculate concentration, with worked examples.
GCSEA-LevelHigh SchoolAPUse the particle model to explain melting, boiling and condensing, and why temperature stays constant during a change of state.
KS3GCSEMiddle SchoolHigh SchoolWrite electron shell diagrams for the first 20 elements and work out the charges of ions, with worked examples and practice questions.
GCSEHigh SchoolOrder metals by reactivity, predict displacement reactions and link the reactivity series to how metals are extracted, with worked examples.
GCSEHigh SchoolLearn how temperature, concentration, surface area and catalysts change the rate of a reaction, and how to calculate a mean rate.
GCSEHigh SchoolSee how electricity splits ionic compounds, and predict the products at the anode and cathode for molten and aqueous solutions.
GCSEA-LevelHigh SchoolLearn the hydrocarbon families, their general formulae, how they burn and how bromine water tells them apart, with worked examples.
GCSEA-LevelHigh SchoolTell exothermic from endothermic reactions, read reaction profiles and calculate energy change from bond energies, with worked examples.
GCSEHigh SchoolChoose between filtration, crystallisation and distillation, and calculate Rf values in chromatography, with worked examples.
KS3GCSEMiddle SchoolHigh SchoolLearn Newton's three laws, use F = ma and understand inertia and action-reaction pairs, with worked examples and practice questions.
KS3GCSEMiddle SchoolHigh SchoolCalculate speed and acceleration, read distance-time and velocity-time graphs and use v² = u² + 2as, with worked examples.
KS3GCSEMiddle SchoolHigh SchoolUse the kinetic and gravitational potential energy formulas, apply conservation of energy and calculate efficiency, with worked examples.
GCSEHigh SchoolUse V = IR, compare series and parallel circuits and calculate power, with worked examples and practice questions.
GCSEHigh SchoolUse v = fλ, tell transverse from longitudinal waves and put the types of electromagnetic radiation in order, with worked examples.
GCSEHigh SchoolAdd forces to find the resultant (net) force, draw free body diagrams and calculate weight, with worked examples and practice questions.
KS3GCSEMiddle SchoolHigh SchoolCalculate momentum, solve collision problems with conservation of momentum and link force to change in momentum, with worked examples.
GCSEHigh SchoolUse density = mass ÷ volume, convert units and measure the density of regular and irregular objects, with worked examples.
KS3GCSEMiddle SchoolHigh SchoolCalculate pressure from force and area, find pressure in liquids and see how atmospheric pressure changes, with worked examples.
GCSEHigh SchoolCompare alpha, beta and gamma radiation and use half-life in calculations, with worked examples and practice questions.
GCSEHigh SchoolLearn magnetic fields, how electromagnets work and the motor effect, with a worked force calculation and practice questions.
GCSEHigh SchoolLearn the law of reflection and how light bends when it changes medium, with ray diagram examples and practice questions.
KS3GCSEMiddle SchoolHigh SchoolUse the specific heat capacity equation to calculate the energy needed to heat a material, with worked examples and practice questions.
GCSEHigh SchoolCalculate the work done by a force and the power of a machine or appliance, with step-by-step examples and practice questions.
KS3GCSEMiddle SchoolHigh SchoolTurn a topic into a clear, arguable claim for your essay, with a simple formula, weak and strong examples and a quick test.
GCSEA-LevelHigh SchoolAPFix the most common punctuation mistakes: its and it's, possession with apostrophes and comma splices, with examples and practice.
KS3GCSEMiddle SchoolHigh SchoolBuild clear paragraphs with PEEL (UK) or Claim-Evidence-Reasoning (US), with worked examples for English and science answers.
KS3GCSEA-LevelMiddle School+2Use ethos, pathos, logos and devices such as the rule of three and rhetorical questions in speeches and articles, with examples.
KS3GCSEMiddle SchoolHigh School+1Spot and explain similes, metaphors, personification, alliteration and onomatopoeia, and learn how to describe their effect.
KS3GCSEMiddle SchoolHigh SchoolIdentify clauses and build simple, compound and complex sentences for clearer, more varied writing, with examples.
KS3GCSEMiddle SchoolHigh SchoolLink ideas with semicolons, introduce lists with colons and add emphasis with dashes, with clear rules and examples.
GCSEHigh SchoolAPMake verbs agree with their subjects, including collective nouns, either/or and phrases that sit between the subject and the verb.
KS3GCSEMiddle SchoolHigh SchoolRecognise and convert active and passive sentences, and learn when each voice is the better choice, with examples.
GCSEHigh SchoolChoose between their, there and they're, affect and effect, your and you're, and other mixed-up words, with a quick test for each pair.
KS3GCSEMiddle SchoolHigh SchoolLearn the most useful spelling rules for endings, plurals and prefixes, with common exceptions and UK and US spelling differences.
KS3GCSEMiddle SchoolHigh SchoolPlan an essay step by step, from brainstorming to a strong introduction, well-organised paragraphs and a conclusion that answers the question.
GCSEA-LevelHigh SchoolAPUse linking words to connect ideas within and between paragraphs so your writing flows, with examples for each type.
KS3GCSEMiddle SchoolHigh SchoolWeave short quotations into your sentences and comment on key words, instead of dropping them in, with before-and-after examples.
GCSEA-LevelHigh SchoolAPBreak a quotation down by word class, connotation and effect with the zoom-in method, to write detailed analysis.
GCSEA-LevelHigh SchoolAPLook at how a writer organises a text, from openings and shifts in focus to pacing, sentence length and endings, with examples.
GCSEA-LevelHigh SchoolAPFind information stated directly in a text and read between the lines to infer what is not said, with examples.
KS3GCSEMiddle SchoolHigh SchoolPlan and write a comparison using similarities, differences and comparative connectives, with a clear method.
GCSEA-LevelHigh SchoolAPUse the senses, 'show, don't tell', figurative language and varied sentences to paint a picture with words.
KS3GCSEMiddle SchoolHigh SchoolPlan a story with a five-part plot structure, write a strong opening and punctuate dialogue correctly.
KS3GCSEMiddle SchoolHigh SchoolLay out a formal letter or email, choose the right sign-off and match your tone to your audience, with examples.
KS3GCSEMiddle SchoolHigh SchoolUnderstand Shakespeare's language, verse and context so you can read and analyse his plays with confidence.
GCSEA-LevelHigh SchoolAPAnalyse a poem by looking at its form, rhyme, rhythm, structure and language, with a step-by-step approach.
GCSEA-LevelHigh SchoolAPJudge whether an argument is convincing and spot common logical fallacies such as ad hominem, straw man and false dilemma.
GCSEA-LevelHigh SchoolAPFind reliable sources, avoid plagiarism by quoting and paraphrasing correctly and understand common citation styles.
GCSEA-LevelHigh SchoolAPLearn the long-term causes of the First World War (militarism, alliances, imperialism, nationalism) and how the 1914 assassination set it off.
GCSEA-LevelHigh SchoolAPFind out why the Industrial Revolution began in Britain, how factories and steam power changed life and what reforms followed.
KS3GCSEMiddle SchoolHigh School+1Get a clear overview of why World War Two began, who fought, the key events and how the war ended in Europe and Asia.
KS3GCSEMiddle SchoolHigh School+1Learn why three men claimed the English throne in 1066, what happened at Hastings and how the Normans took control.
KS3GCSEUnderstand 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 SchoolAPSee why the Weimar Republic struggled, how the Great Depression helped the Nazis and how Hitler gained power in 1933.
GCSEA-LevelHigh SchoolAPLearn how Earth's plates move, the three types of plate boundary and why earthquakes and volcanoes happen, with real examples.
KS3GCSEMiddle SchoolHigh SchoolUnderstand the greenhouse effect, what the Paris Agreement's 1.5°C goal means and the difference between mitigation and adaptation.
GCSEA-LevelHigh SchoolAPLearn how rivers shape the land from source to mouth, and how V-shaped valleys, meanders and oxbow lakes form.
KS3GCSEMiddle SchoolHigh SchoolUnderstand machine learning, training data and large language models, plus the limits of AI and how to use it responsibly.
KS3GCSEMiddle SchoolHigh SchoolBuild strong passwords, turn on two-factor authentication and spot phishing messages, and know what to do if you click a bad link.
KS3GCSEMiddle SchoolHigh SchoolLearn what happens when you open a website, from DNS lookups to packets and HTTPS, in plain English.
KS3GCSEMiddle SchoolHigh SchoolLearn how computers store data as bits and bytes, convert between binary and decimal and add binary numbers, with worked examples.
KS3GCSEMiddle SchoolHigh SchoolLearn how linear search, binary search and bubble sort work, with step-by-step traces and when to use each.
GCSEA-LevelHigh SchoolUnderstand variables, data types, selection and loops, with pseudocode examples you can trace by hand.
KS3GCSEMiddle SchoolHigh SchoolLearn why testing yourself beats rereading, and four simple ways to use active recall: flashcards, blank-page recall and practice questions.
KS3GCSEA-LevelMiddle School+3Review material at increasing gaps to remember it long term, with an example schedule and the Leitner box system.
KS3GCSEA-LevelMiddle School+3Plan 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+3Learn what describe, explain, compare, analyse and evaluate really ask you to do in an exam, using an exam board's definitions.
GCSEA-LevelHigh SchoolAPSet up Cornell notes with cue, notes and summary sections, and turn them into a self-test for revision.
KS3GCSEA-LevelMiddle School+2Use mind maps to organise a topic, then turn them into a memory test so they actually help you remember.
KS3GCSEA-LevelMiddle School+2Learn why mixing question types in one session can improve long-term learning, with an example maths and science session plan.
GCSEA-LevelHigh SchoolAPTurn past papers into focused practice with timing, mark schemes and an error review that shows exactly what to fix.
GCSEA-LevelHigh SchoolAP+1Practical, non-medical ways to cope with exam pressure, from planning and breaks to talking to someone you trust.
GCSEA-LevelHigh SchoolAP+1Use acronyms, acrostics and the method of loci to remember lists and ordered facts, and learn when mnemonics help most.
KS3GCSEA-LevelMiddle School+2Check your understanding by explaining a topic in plain language, spotting the gaps and fixing them.
KS3GCSEA-LevelMiddle School+2Set up your space, plan sessions and manage your phone so your study time is actually productive.
KS3GCSEA-LevelMiddle School+2Survey, Question, Read, Recite and Review: a five-step routine for learning from textbooks and long texts.
GCSEA-LevelHigh SchoolAP+1Plan the last week, the night before and the exam itself: equipment, timing and how to check your work.
GCSEA-LevelHigh SchoolAP+1How GCSE grading works in England: the 9 to 1 scale, what a standard and strong pass means and how grade boundaries work.
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