# Maths Help

> Step-by-step percentage maths help, plus GCSE, A-Level, UK degree and UCAS points calculators.

## Calculators

- [Final Grade Needed Calculator](https://www.maths-help.co.uk/grades/final-grade-needed/) — What % do I need on the final exam to hit my target grade? UK A-Level and GCSE compatible.
- [GCSE Grade Calculator](https://www.maths-help.co.uk/grades/gcse/) — Convert your raw mark to a GCSE grade (9-1) using indicative boundaries.
- [A-Level Grade Calculator](https://www.maths-help.co.uk/grades/a-level/) — Convert raw A-Level marks to grades. Uses typical UMS-style boundaries.
- [UK Degree Classification](https://www.maths-help.co.uk/grades/uk-degree/) — Convert weighted university marks to UK degree classification.
- [UCAS Points Calculator](https://www.maths-help.co.uk/grades/ucas-points/) — UCAS tariff calculator for A-Level, AS, EPQ, BTEC, IB and Scottish Highers. Pick up to 5 qualifications and grades — total points calculated live.
- [Test Score Percentage](https://www.maths-help.co.uk/grades/test-score/) — Convert raw mark to percentage with approximate UK grade band.
- [Counting to 20](https://www.maths-help.co.uk/ks1/counting-to-20/) — How children learn to count to 20 — Reception and Year 1 progression with examples.
- [Counting to 100](https://www.maths-help.co.uk/ks1/counting-to-100/) — How children count to 100 in KS1 — counting in 1s, 2s, 5s, 10s with classroom examples.
- [Place value: tens and ones](https://www.maths-help.co.uk/ks1/place-value-tens-ones/) — KS1 place value with tens and ones — Year 1 and Year 2 worked examples.
- [Number bonds to 10 and 20](https://www.maths-help.co.uk/ks1/number-bonds/) — KS1 number bonds — pairs that sum to 10 and 20, Year 1 and Year 2.
- [Adding within 20](https://www.maths-help.co.uk/ks1/adding-within-20/) — KS1 addition within 20 — strategies and worked examples.
- [Subtracting within 20](https://www.maths-help.co.uk/ks1/subtracting-within-20/) — KS1 subtraction within 20 — three strategies with examples.
- [Doubling and halving](https://www.maths-help.co.uk/ks1/doubling-and-halving/) — KS1 doubling and halving — Year 1 and Year 2 mental maths.
- [2 times table](https://www.maths-help.co.uk/ks1/2-times-table/) — KS1 2 times table — the full list with patterns and tips.
- [5 times table](https://www.maths-help.co.uk/ks1/5-times-table/) — KS1 5 times table — counting in 5s with everyday examples.
- [10 times table](https://www.maths-help.co.uk/ks1/10-times-table/) — KS1 10 times table — the place-value shortcut.
- [Halves and quarters](https://www.maths-help.co.uk/ks1/halves-and-quarters/) — KS1 fractions: halves and quarters of shapes and amounts.
- [UK coins and notes](https://www.maths-help.co.uk/ks1/uk-money/) — KS1 UK money — coin recognition, totals, change for Year 1 and Year 2.
- [Telling the time](https://www.maths-help.co.uk/ks1/telling-the-time/) — KS1 telling the time — analogue clock, Year 1 and Year 2 progression.
- [2D shapes](https://www.maths-help.co.uk/ks1/2d-shapes/) — KS1 2D shapes — name, sides, corners (vertices) for Year 1 and Year 2.
- [3D shapes](https://www.maths-help.co.uk/ks1/3d-shapes/) — KS1 3D shapes — faces, edges, vertices for Year 1 and Year 2.
- [Place value to millions](https://www.maths-help.co.uk/ks2/place-value-millions/) — KS2 place value to 10 million — read, write, compare large numbers.
- [Long (column) addition](https://www.maths-help.co.uk/ks2/long-addition/) — KS2 column addition with carrying — Year 3, 4, 5 method.
- [Long (column) subtraction](https://www.maths-help.co.uk/ks2/long-subtraction/) — KS2 column subtraction with borrowing — exchange method.
- [Times tables 2 to 12](https://www.maths-help.co.uk/ks2/times-tables-2-12/) — KS2 times tables 2-12 — Year 4 MTC, fluency strategies.
- [Long multiplication](https://www.maths-help.co.uk/ks2/long-multiplication/) — KS2 long multiplication — column method and grid method.
- [Long division](https://www.maths-help.co.uk/ks2/long-division/) — KS2 long division — bus stop method, chunking, with remainders.
- [BIDMAS — order of operations](https://www.maths-help.co.uk/ks2/bidmas/) — KS2 BIDMAS — brackets first, then indices, then ×÷, then +−.
- [Equivalent fractions](https://www.maths-help.co.uk/ks2/equivalent-fractions/) — KS2 equivalent fractions — multiplying or dividing top and bottom by the same number.
- [Adding and subtracting fractions](https://www.maths-help.co.uk/ks2/adding-fractions/) — KS2 adding and subtracting fractions — common denominator method.
- [Multiplying fractions](https://www.maths-help.co.uk/ks2/multiplying-fractions/) — KS2 multiplying fractions — top × top, bottom × bottom.
- [Decimals](https://www.maths-help.co.uk/ks2/decimals/) — KS2 decimals — tenths, hundredths, thousandths, comparing and operations.
- [Fractions, decimals, percentages](https://www.maths-help.co.uk/ks2/fraction-decimal-percentage/) — KS2 fractions, decimals, percentages — converting between the three.
- [Percentages of amounts](https://www.maths-help.co.uk/ks2/percentages-of-amounts/) — KS2 percentages of amounts — 10%, 25%, 50%, 75% mental strategies.
- [Ratio (introduction)](https://www.maths-help.co.uk/ks2/ratio-introduction/) — KS2 ratio — Year 6 introduction with worked examples.
- [Area of rectangles](https://www.maths-help.co.uk/ks2/area-rectangles/) — KS2 area of rectangles — length × width with worked examples.
- [Perimeter](https://www.maths-help.co.uk/ks2/perimeter/) — KS2 perimeter — sum of side lengths, missing sides in compound shapes.
- [Volume of cuboids](https://www.maths-help.co.uk/ks2/volume-of-cuboids/) — KS2 volume of cuboids — length × width × height in cm³.
- [Types of angle](https://www.maths-help.co.uk/ks2/angles-types/) — KS2 types of angle — acute, right, obtuse, reflex; measuring with a protractor.
- [Coordinates](https://www.maths-help.co.uk/ks2/coordinates/) — KS2 coordinates — first quadrant (Year 4) and four quadrants (Year 6).
- [Translation and reflection](https://www.maths-help.co.uk/ks2/translation-reflection/) — KS2 translation and reflection — geometry transformations.
- [Mean, median, mode and range](https://www.maths-help.co.uk/ks2/mean-median-mode-range/) — KS2 mean, median, mode, range — Year 6 SATs essentials.
- [Pictograms and bar charts](https://www.maths-help.co.uk/ks2/pictograms-bar-charts/) — KS2 pictograms and bar charts — reading and drawing for SATs.
- [Pie charts](https://www.maths-help.co.uk/ks2/pie-charts/) — KS2 pie charts — reading sectors as fractions of 360° or as percentages.
- [Probability (introduction)](https://www.maths-help.co.uk/ks2/probability-introduction/) — KS2 probability introduction — likelihood vocabulary.
- [Roman numerals](https://www.maths-help.co.uk/ks2/roman-numerals/) — KS2 Roman numerals — Year 4 and Year 5 progression.
- [Negative numbers](https://www.maths-help.co.uk/ks2/negative-numbers/) — KS2 negative numbers — temperature, number line, calculations.
- [Prime factor decomposition](https://www.maths-help.co.uk/ks3/prime-factor-decomposition/) — KS3 prime factor decomposition — factor tree method.
- [Lowest common multiple and highest common factor](https://www.maths-help.co.uk/ks3/lcm-and-hcf/) — KS3 LCM and HCF — listing method and prime-factor method.
- [Square numbers and cube numbers](https://www.maths-help.co.uk/ks3/squares-and-cubes/) — KS3 square and cube numbers — recognition and calculation.
- [Indices (powers and bases)](https://www.maths-help.co.uk/ks3/indices-introduction/) — KS3 indices introduction — base, exponent, multiplication and division rules.
- [Standard form (scientific notation)](https://www.maths-help.co.uk/ks3/standard-form/) — KS3 standard form — scientific notation a×10^n.
- [Operations with negative numbers](https://www.maths-help.co.uk/ks3/operations-with-negatives/) — KS3 negative number arithmetic — addition, subtraction, multiplication, division.
- [Fractions, decimals and percentages (KS3)](https://www.maths-help.co.uk/ks3/fractions-decimals-percentages/) — KS3 fractions decimals percentages — conversion and arithmetic.
- [Percentage change (increase, decrease, profit, loss)](https://www.maths-help.co.uk/ks3/percentage-change/) — KS3 percentage change — increase, decrease, profit, loss formula.
- [Ratio and proportion](https://www.maths-help.co.uk/ks3/ratio-and-proportion/) — KS3 ratio and proportion — sharing, simplifying, equivalent ratios.
- [Direct and inverse proportion](https://www.maths-help.co.uk/ks3/direct-inverse-proportion/) — KS3 direct and inverse proportion — y = kx and y = k/x.
- [Speed, distance, time](https://www.maths-help.co.uk/ks3/speed-distance-time/) — KS3 speed distance time — formula, triangle, mph and m/s conversions.
- [Density, mass, volume](https://www.maths-help.co.uk/ks3/density-mass-volume/) — KS3 density mass volume — formula and unit conversions.
- [Algebraic expressions](https://www.maths-help.co.uk/ks3/algebraic-expressions/) — KS3 algebraic expressions — variables, terms, simplification.
- [Expanding brackets](https://www.maths-help.co.uk/ks3/expanding-brackets/) — KS3 expanding brackets — single and double bracket method.
- [Factorising into a single bracket](https://www.maths-help.co.uk/ks3/factorising-single-bracket/) — KS3 factorising single bracket — common factor method.
- [Solving linear equations](https://www.maths-help.co.uk/ks3/solving-linear-equations/) — KS3 solving linear equations — balance method, inverse operations.
- [Inequalities (introduction)](https://www.maths-help.co.uk/ks3/inequalities/) — KS3 inequalities — symbols, solving, number-line representation.
- [Sequences and the nth term](https://www.maths-help.co.uk/ks3/sequences-nth-term/) — KS3 sequences nth term — linear and arithmetic with worked examples.
- [Coordinates and graphs](https://www.maths-help.co.uk/ks3/coordinates-and-graphs/) — KS3 coordinates and graphs — plotting, reading values, intersections.
- [y = mx + c (straight-line graphs)](https://www.maths-help.co.uk/ks3/y-equals-mx-plus-c/) — KS3 y = mx + c — gradient and y-intercept.
- [Pythagoras' theorem](https://www.maths-help.co.uk/ks3/pythagoras/) — KS3 Pythagoras' theorem — finding the hypotenuse or a shorter side.
- [SOHCAHTOA (right-angled trigonometry)](https://www.maths-help.co.uk/ks3/sohcahtoa/) — KS3 SOHCAHTOA — sin, cos, tan ratios in right-angled triangles.
- [Transformations (translation, reflection, rotation, enlargement)](https://www.maths-help.co.uk/ks3/transformations/) — KS3 transformations — translation, reflection, rotation, enlargement.
- [Probability (KS3 introduction)](https://www.maths-help.co.uk/ks3/probability-introduction/) — KS3 probability introduction — equally likely outcomes, sample space.
- [Scatter graphs and correlation](https://www.maths-help.co.uk/ks3/scatter-graphs/) — KS3 scatter graphs — correlation positive negative none, line of best fit.
- [Place value and rounding](https://www.maths-help.co.uk/gcse/place-value-and-rounding/) — GCSE place value and rounding — significant figures, decimal places, estimation.
- [Upper and lower bounds (error intervals)](https://www.maths-help.co.uk/gcse/upper-and-lower-bounds/) — GCSE upper and lower bounds — error intervals, addition/subtraction/multiplication of bounds.
- [Standard form (GCSE)](https://www.maths-help.co.uk/gcse/standard-form/) — GCSE standard form — calculation, calculator practice.
- [Surds](https://www.maths-help.co.uk/gcse/surds/) — GCSE surds — simplifying, rationalising the denominator.
- [Indices: negative and fractional](https://www.maths-help.co.uk/gcse/indices/) — GCSE indices — negative and fractional powers, all index laws.
- [Recurring decimals as fractions](https://www.maths-help.co.uk/gcse/recurring-decimals/) — GCSE recurring decimals — algebraic conversion to fractions.
- [Percentages (GCSE)](https://www.maths-help.co.uk/gcse/percentages/) — GCSE percentages — multiplier method for fast calculations.
- [Compound interest](https://www.maths-help.co.uk/gcse/compound-interest/) — GCSE compound interest — formula and worked examples.
- [Reverse percentages](https://www.maths-help.co.uk/gcse/reverse-percentages/) — GCSE reverse percentages — find original from changed value.
- [Ratio (GCSE)](https://www.maths-help.co.uk/gcse/ratio/) — GCSE ratio — simplifying, sharing, three-part, ratio to fraction.
- [Expanding brackets (GCSE)](https://www.maths-help.co.uk/gcse/expanding-brackets-gcse/) — GCSE expanding brackets — single, double and triple bracket method.
- [Factorising](https://www.maths-help.co.uk/gcse/factorising/) — GCSE factorising — single bracket, quadratic, difference of two squares.
- [The quadratic formula](https://www.maths-help.co.uk/gcse/quadratic-formula/) — GCSE quadratic formula — solving any quadratic equation.
- [Completing the square](https://www.maths-help.co.uk/gcse/completing-the-square/) — GCSE completing the square — Higher tier algebra method.
- [Solving quadratic equations](https://www.maths-help.co.uk/gcse/solving-quadratics/) — GCSE solving quadratic equations — three methods compared.
- [Simultaneous equations](https://www.maths-help.co.uk/gcse/simultaneous-equations/) — GCSE simultaneous equations — elimination and substitution methods.
- [Algebraic fractions](https://www.maths-help.co.uk/gcse/algebraic-fractions/) — GCSE algebraic fractions — simplification and operations.
- [Inequalities (GCSE)](https://www.maths-help.co.uk/gcse/inequalities-gcse/) — GCSE inequalities — linear and quadratic, set notation.
- [Sequences (GCSE)](https://www.maths-help.co.uk/gcse/sequences-gcse/) — GCSE sequences — linear, quadratic, geometric.
- [Functions](https://www.maths-help.co.uk/gcse/functions/) — GCSE functions — composite and inverse functions.
- [Iteration](https://www.maths-help.co.uk/gcse/iteration/) — GCSE iteration — recurrence relation method.
- [Graphs (GCSE)](https://www.maths-help.co.uk/gcse/graphs/) — GCSE graphs — recognising and sketching standard graphs.
- [Pythagoras (GCSE)](https://www.maths-help.co.uk/gcse/pythagoras/) — GCSE Pythagoras — 2D, 3D, with worked exam questions.
- [SOHCAHTOA (GCSE)](https://www.maths-help.co.uk/gcse/sohcahtoa/) — GCSE SOHCAHTOA — finding sides and angles in right-angled triangles.
- [Sine rule](https://www.maths-help.co.uk/gcse/sine-rule/) — GCSE sine rule — non-right-angled triangles.
- [Cosine rule](https://www.maths-help.co.uk/gcse/cosine-rule/) — GCSE cosine rule — non-right-angled triangles.
- [Exact values of sin/cos/tan](https://www.maths-help.co.uk/gcse/exact-trig-values/) — GCSE exact trig values — 0, 30, 45, 60, 90 degrees.
- [3D Pythagoras and trigonometry](https://www.maths-help.co.uk/gcse/3d-pythagoras-trig/) — GCSE 3D Pythagoras and trig — cuboid space diagonal, pyramid heights.
- [Circle theorems](https://www.maths-help.co.uk/gcse/circle-theorems/) — GCSE circle theorems — eight key results for proof and calculation.
- [Vectors (GCSE)](https://www.maths-help.co.uk/gcse/vectors/) — GCSE vectors — 2D column vectors, magnitude, geometric proofs.
- [Transformations (GCSE)](https://www.maths-help.co.uk/gcse/transformations-gcse/) — GCSE transformations — translation, reflection, rotation, enlargement.
- [Similarity and congruence](https://www.maths-help.co.uk/gcse/similarity-and-congruence/) — GCSE similarity and congruence — proofs, scale factor, area/volume scale.
- [Loci and construction](https://www.maths-help.co.uk/gcse/loci-and-construction/) — GCSE loci and construction — compass-and-ruler techniques.
- [Bearings](https://www.maths-help.co.uk/gcse/bearings/) — GCSE bearings — three-figure bearing format and Pythagoras/trig combos.
- [Area and perimeter (GCSE)](https://www.maths-help.co.uk/gcse/area-and-perimeter-gcse/) — GCSE area and perimeter — formulas for standard 2D shapes.
- [Volume and surface area](https://www.maths-help.co.uk/gcse/volume-and-surface-area/) — GCSE volume and surface area — full set of 3D formulas.
- [Circle area and circumference](https://www.maths-help.co.uk/gcse/circle-area-circumference/) — GCSE circle area and circumference — full formulas with arc and sector.
- [Probability (GCSE)](https://www.maths-help.co.uk/gcse/probability/) — GCSE probability — single events, AND/OR rules.
- [Tree diagrams](https://www.maths-help.co.uk/gcse/tree-diagrams/) — GCSE tree diagrams — independent and dependent events.
- [Venn diagrams](https://www.maths-help.co.uk/gcse/venn-diagrams/) — GCSE Venn diagrams — set notation and probability calculations.
- [Conditional probability](https://www.maths-help.co.uk/gcse/conditional-probability/) — GCSE conditional probability — formula and Venn diagram method.
- [Cumulative frequency](https://www.maths-help.co.uk/gcse/cumulative-frequency/) — GCSE cumulative frequency — curve, median, quartiles, IQR.
- [Histograms](https://www.maths-help.co.uk/gcse/histograms/) — GCSE histograms — frequency density for unequal class widths.
- [Box plots](https://www.maths-help.co.uk/gcse/box-plots/) — GCSE box plots — five-number summary and comparison.
- [Scatter graphs and correlation](https://www.maths-help.co.uk/gcse/scatter-graphs-correlation/) — GCSE scatter graphs — correlation, line of best fit, predictions.
- [Direct proportion](https://www.maths-help.co.uk/gcse/direct-proportion/) — GCSE direct proportion — y = kx, finding constants, exam questions.
- [Inverse proportion](https://www.maths-help.co.uk/gcse/inverse-proportion/) — GCSE inverse proportion — y = k/x, examples and finding constants.
- [Compound measures](https://www.maths-help.co.uk/gcse/compound-measures/) — GCSE compound measures — speed, density, pressure with unit conversions.
- [Growth and decay](https://www.maths-help.co.uk/gcse/growth-and-decay/) — GCSE growth and decay — exponential models for finance and decay.
- [Best buys](https://www.maths-help.co.uk/gcse/best-buys/) — GCSE best buys — unit price comparison method.
- [Algebraic fractions](https://www.maths-help.co.uk/a-level/algebraic-fractions/) — A-Level algebraic fractions — simplification and operations.
- [Partial fractions](https://www.maths-help.co.uk/a-level/partial-fractions/) — A-Level partial fractions — decomposition into simpler fractions.
- [Binomial expansion](https://www.maths-help.co.uk/a-level/binomial-expansion/) — A-Level binomial expansion — Pascal's triangle, general term.
- [Sequences and series](https://www.maths-help.co.uk/a-level/sequences-and-series/) — A-Level sequences and series — arithmetic, geometric, sigma.
- [Exponentials and logarithms](https://www.maths-help.co.uk/a-level/exponentials-and-logarithms/) — A-Level exponentials and logarithms — e, ln, change of base.
- [Coordinate geometry](https://www.maths-help.co.uk/a-level/coordinate-geometry/) — A-Level coordinate geometry — gradients and line equations.
- [Equation of a circle](https://www.maths-help.co.uk/a-level/circles-equation/) — A-Level circle equation — centre and radius from completed square form.
- [Parametric equations](https://www.maths-help.co.uk/a-level/parametric-equations/) — A-Level parametric equations — eliminating the parameter, calculus.
- [Trig identities](https://www.maths-help.co.uk/a-level/trig-identities/) — A-Level trig identities — Pythagorean, reciprocal, ratio.
- [Solving trig equations](https://www.maths-help.co.uk/a-level/trig-equations/) — A-Level trig equations — CAST, solutions in a range.
- [R-formula (a sin + b cos)](https://www.maths-help.co.uk/a-level/r-formula/) — A-Level R-formula — combining sin and cos terms.
- [Double-angle formulae](https://www.maths-help.co.uk/a-level/double-angle-formulae/) — A-Level double-angle formulae — sin, cos, tan of 2x.
- [Differentiation](https://www.maths-help.co.uk/a-level/differentiation/) — A-Level differentiation — power rule, polynomial.
- [Product rule](https://www.maths-help.co.uk/a-level/product-rule/) — A-Level product rule — differentiation of products.
- [Quotient rule](https://www.maths-help.co.uk/a-level/quotient-rule/) — A-Level quotient rule — differentiation of quotients.
- [Chain rule](https://www.maths-help.co.uk/a-level/chain-rule/) — A-Level chain rule — composite differentiation.
- [Integration](https://www.maths-help.co.uk/a-level/integration/) — A-Level integration — power rule, definite integrals as area.
- [Integration by parts](https://www.maths-help.co.uk/a-level/integration-by-parts/) — A-Level integration by parts — when and how.
- [Integration by substitution](https://www.maths-help.co.uk/a-level/integration-by-substitution/) — A-Level integration by substitution — reverse chain rule.
- [Numerical methods (Newton-Raphson, trapezium)](https://www.maths-help.co.uk/a-level/numerical-methods/) — A-Level numerical methods — Newton-Raphson, trapezium rule.
- [Vectors (A-Level)](https://www.maths-help.co.uk/a-level/vectors/) — A-Level vectors — 2D and 3D, dot product, magnitude.
- [Proof](https://www.maths-help.co.uk/a-level/proof/) — A-Level proof — deduction, exhaustion, contradiction.
- [Sampling methods](https://www.maths-help.co.uk/a-level/sampling/) — A-Level sampling — random, systematic, stratified.
- [Probability (A-Level)](https://www.maths-help.co.uk/a-level/probability-alevel/) — A-Level probability — conditional, independence, formulae.
- [Discrete random variables](https://www.maths-help.co.uk/a-level/discrete-distributions/) — A-Level discrete random variables — expected value, variance.
- [Binomial distribution](https://www.maths-help.co.uk/a-level/binomial-distribution/) — A-Level binomial distribution — formula and calculator usage.
- [Normal distribution](https://www.maths-help.co.uk/a-level/normal-distribution/) — A-Level normal distribution — standardising, calculator probabilities.
- [Hypothesis testing](https://www.maths-help.co.uk/a-level/hypothesis-testing/) — A-Level hypothesis testing — null, alternative, p-value.
- [Correlation and regression](https://www.maths-help.co.uk/a-level/correlation-regression/) — A-Level correlation and regression — Pearson r, regression line.
- [Z-scores (standardising)](https://www.maths-help.co.uk/a-level/z-scores/) — A-Level z-scores — standardising values for normal distribution.
- [SUVAT (constant acceleration)](https://www.maths-help.co.uk/a-level/suvat/) — A-Level SUVAT — five constant-acceleration equations.
- [Kinematics graphs](https://www.maths-help.co.uk/a-level/kinematics-graphs/) — A-Level kinematics graphs — gradient and area interpretations.
- [Calculus in kinematics](https://www.maths-help.co.uk/a-level/calculus-kinematics/) — A-Level calculus kinematics — variable acceleration.
- [Newton's laws of motion](https://www.maths-help.co.uk/a-level/newtons-laws/) — A-Level Newton's laws — F = ma applications.
- [Forces in equilibrium](https://www.maths-help.co.uk/a-level/forces-equilibrium/) — A-Level forces equilibrium — resolving in two directions.
- [Friction](https://www.maths-help.co.uk/a-level/friction/) — A-Level friction — coefficient of friction, limiting equilibrium.
- [Connected particles](https://www.maths-help.co.uk/a-level/connected-particles/) — A-Level connected particles — equation per particle.
- [Projectiles](https://www.maths-help.co.uk/a-level/projectiles/) — A-Level projectiles — range, height, time of flight.
- [Moments](https://www.maths-help.co.uk/a-level/moments/) — A-Level moments — equilibrium of rigid bodies.
- [Momentum and impulse](https://www.maths-help.co.uk/a-level/momentum-and-impulse/) — A-Level momentum and impulse — conservation laws.
- [Complex numbers](https://www.maths-help.co.uk/further-maths/complex-numbers/) — Further Maths complex numbers — definition, Argand diagram.
- [Complex arithmetic](https://www.maths-help.co.uk/further-maths/complex-arithmetic/) — Further Maths complex arithmetic — sum, product, quotient.
- [Modulus and argument](https://www.maths-help.co.uk/further-maths/modulus-argument/) — Further Maths modulus and argument — geometric view.
- [Polar form](https://www.maths-help.co.uk/further-maths/polar-form-complex/) — Further Maths polar form complex numbers — Euler's formula.
- [de Moivre's theorem](https://www.maths-help.co.uk/further-maths/de-moivre/) — Further Maths de Moivre — powers and roots of complex numbers.
- [Roots of unity](https://www.maths-help.co.uk/further-maths/roots-of-unity/) — Further Maths roots of unity — n-th roots of 1.
- [Matrices (introduction)](https://www.maths-help.co.uk/further-maths/matrices-introduction/) — Further Maths matrices introduction — definition, sum, scalar.
- [Matrix arithmetic](https://www.maths-help.co.uk/further-maths/matrix-arithmetic/) — Further Maths matrix multiplication — non-commutative product.
- [Determinant and inverse](https://www.maths-help.co.uk/further-maths/matrix-determinant-inverse/) — Further Maths matrix determinant inverse — 2×2 and 3×3.
- [Matrices as transformations](https://www.maths-help.co.uk/further-maths/matrix-transformations/) — Further Maths matrix transformations — geometric interpretation.
- [Eigenvalues and eigenvectors](https://www.maths-help.co.uk/further-maths/matrix-eigenvalues-eigenvectors/) — Further Maths eigenvalues eigenvectors — characteristic equation.
- [Proof by induction](https://www.maths-help.co.uk/further-maths/proof-by-induction/) — Further Maths induction — base + inductive step.
- [Hyperbolic functions](https://www.maths-help.co.uk/further-maths/hyperbolic-functions/) — Further Maths hyperbolic functions — sinh, cosh, tanh.
- [Hyperbolic identities](https://www.maths-help.co.uk/further-maths/hyperbolic-identities/) — Further Maths hyperbolic identities — analogues of trig identities.
- [Differentiating hyperbolics](https://www.maths-help.co.uk/further-maths/differentiation-of-hyperbolic/) — Further Maths differentiating hyperbolics — derivatives.
- [Integration using partial fractions](https://www.maths-help.co.uk/further-maths/integration-using-partial-fractions/) — Further Maths integration partial fractions — method.
- [First-order separable ODEs](https://www.maths-help.co.uk/further-maths/first-order-separable/) — Further Maths first-order separable ODE — method.
- [Integrating factor](https://www.maths-help.co.uk/further-maths/integrating-factor/) — Further Maths integrating factor — linear first-order ODE.
- [Second-order linear homogeneous ODE](https://www.maths-help.co.uk/further-maths/second-order-linear-homogeneous/) — Further Maths second-order linear homogeneous ODE — auxiliary equation.
- [Polar coordinates](https://www.maths-help.co.uk/further-maths/polar-coordinates/) — Further Maths polar coordinates — conversion to/from Cartesian.
- [Area enclosed by a polar curve](https://www.maths-help.co.uk/further-maths/polar-curves-area/) — Further Maths polar curve area — formula.
- [Maclaurin and Taylor series](https://www.maths-help.co.uk/further-maths/maclaurin-and-taylor/) — Further Maths Maclaurin and Taylor series — power series expansion.
- [Number sequences (11+ style)](https://www.maths-help.co.uk/eleven-plus/number-sequences-11plus/) — 11+ number sequences — arithmetic, alternating, recursive patterns.
- [Word problems (11+)](https://www.maths-help.co.uk/eleven-plus/word-problems-11plus/) — 11+ word problems — multi-step strategies.
- [Mental arithmetic strategies](https://www.maths-help.co.uk/eleven-plus/mental-arithmetic-strategies/) — 11+ mental arithmetic — partition, round-and-adjust, near doubles.
- [Times tables speed drills](https://www.maths-help.co.uk/eleven-plus/times-tables-speed-drills/) — 11+ times tables — speed targets and drills.
- [Ratio word problems (11+)](https://www.maths-help.co.uk/eleven-plus/ratio-word-problems-11plus/) — 11+ ratio word problems — sharing, scaling.
- [Percentages word problems (11+)](https://www.maths-help.co.uk/eleven-plus/percentages-word-problems-11plus/) — 11+ percentages word problems — discount, profit, loss.
- [Fractions of amounts (11+)](https://www.maths-help.co.uk/eleven-plus/fractions-of-amounts-11plus/) — 11+ fractions of amounts — speed methods.
- [Time and money problems](https://www.maths-help.co.uk/eleven-plus/time-and-money-11plus/) — 11+ time and money — 24-hour clock and durations.
- [Area and perimeter word problems](https://www.maths-help.co.uk/eleven-plus/area-and-perimeter-word-problems/) — 11+ area perimeter word problems — compound shapes.
- [CEM vs GL Assessment](https://www.maths-help.co.uk/eleven-plus/cem-vs-gl-assessment/) — 11+ CEM vs GL Assessment — differences explained.
- [Exam-day strategy](https://www.maths-help.co.uk/eleven-plus/exam-day-strategy-11plus/) — 11+ exam day strategy — pacing and technique.
- [Regional tests overview](https://www.maths-help.co.uk/eleven-plus/regional-tests-overview/) — 11+ regional tests — Kent, Bucks, Essex, Birmingham, GLA.
- [KS1 SATs (Year 2) overview](https://www.maths-help.co.uk/sats/ks1-sats-overview/) — KS1 SATs Year 2 — current status, structure, content.
- [KS2 SATs (Year 6) overview](https://www.maths-help.co.uk/sats/ks2-sats-overview/) — KS2 SATs Year 6 — three-paper structure.
- [Arithmetic paper strategy](https://www.maths-help.co.uk/sats/arithmetic-paper-strategy/) — KS2 SATs arithmetic paper — pacing strategy and method.
- [Reasoning paper strategy](https://www.maths-help.co.uk/sats/reasoning-paper-strategy/) — KS2 SATs reasoning papers — multi-step strategy.
- [Scaled scores explained](https://www.maths-help.co.uk/sats/scaled-scores-explained/) — KS2 SATs scaled scores — 100 expected standard, 110+ greater depth.
- [Common arithmetic question types](https://www.maths-help.co.uk/sats/common-question-types-arithmetic/) — KS2 SATs arithmetic — recurring question types.
- [Common reasoning question types](https://www.maths-help.co.uk/sats/common-question-types-reasoning/) — KS2 SATs reasoning — recurring word problem types.
- [KS1 SATs in 2026](https://www.maths-help.co.uk/sats/ks1-sats-2026-changes/) — KS1 SATs 2026 — current status.
- [KS2 SATs in 2026](https://www.maths-help.co.uk/sats/ks2-sats-2026-changes/) — KS2 SATs 2026 — paper structure and recent changes.
- [SATs revision checklist](https://www.maths-help.co.uk/sats/sats-revision-checklist/) — KS2 SATs revision — 6-week checklist.
- [Functional Skills overview](https://www.maths-help.co.uk/functional-skills/functional-skills-overview/) — Functional Skills Maths overview — levels, exam boards, GCSE comparison.
- [Entry Level topics](https://www.maths-help.co.uk/functional-skills/entry-level-1-2-3-topics/) — Functional Skills Entry Level 1, 2, 3 — pre-Level-1 maths.
- [Level 1 topics](https://www.maths-help.co.uk/functional-skills/level-1-topics/) — Functional Skills Level 1 maths — full topic list.
- [Level 2 topics](https://www.maths-help.co.uk/functional-skills/level-2-topics/) — Functional Skills Level 2 maths — full topic list.
- [Money and budgeting (FS)](https://www.maths-help.co.uk/functional-skills/money-budgeting-fs/) — Functional Skills money budgeting — UK contexts.
- [Time and timetables](https://www.maths-help.co.uk/functional-skills/time-and-timetables-fs/) — Functional Skills time and timetables — 24-hour clock.
- [Measures and conversions](https://www.maths-help.co.uk/functional-skills/measures-conversions-fs/) — Functional Skills measure conversions — metric and imperial.
- [Percentages (FS)](https://www.maths-help.co.uk/functional-skills/percentages-fs/) — Functional Skills percentages — discount, VAT, interest.
- [Fractions (FS)](https://www.maths-help.co.uk/functional-skills/fractions-fs/) — Functional Skills fractions — Level 1 and Level 2 topics.
- [Ratio and proportion (FS)](https://www.maths-help.co.uk/functional-skills/ratio-and-proportion-fs/) — Functional Skills ratio proportion — sharing, scaling.
- [Statistics interpretation](https://www.maths-help.co.uk/functional-skills/statistics-interpretation-fs/) — Functional Skills statistics — mean, median, mode, charts.
- [Simple probability (FS)](https://www.maths-help.co.uk/functional-skills/simple-probability-fs/) — Functional Skills simple probability — basic concepts.
- [Exam-board comparison](https://www.maths-help.co.uk/functional-skills/exam-boards-comparison/) — Functional Skills exam boards — Pearson, City & Guilds, NCFE.
- [Common exam question patterns](https://www.maths-help.co.uk/functional-skills/common-exam-questions-fs/) — Functional Skills common exam questions — patterns and tips.