Maths › Equations

A-level Maths formulae by unit

Formulae and standard results used in the lessons, grouped by unit and linked to their conditions and to the lessons that state them. Badges show whether a result appears in the Pearson Edexcel formula booklet. AQA and OCR candidates should check the booklet for their own qualification.

A result the Edexcel formulae booklet prints is marked as such; one it does not print is marked to learn; and a result badged derived in the lesson is a working line the notes build in front of you rather than a standard result to memorise.

Only want the ones you have to memorise? All 104 of them, across every unit, are on the formulae to memorise.

The units

Which lesson states it

Every lesson in the library that displays a result, listed under its unit. If you know roughly what the formula is about but not where it lives, this is the way in; if you know what it looks like but not what it is called, the search box holds all 187 of them by their own symbols.

• Indices and surdsAlgebra and functions4 results, 4 to learn
• Quadratic functionsAlgebra and functions2 results, 1 to learn
• Polynomials and the factor theoremAlgebra and functions1 result, 1 to learn
• Straight linesCoordinate geometry2 results, 2 to learn
• CirclesCoordinate geometry1 result, 1 to learn
• The binomial expansionSequences and series2 results
• The general binomial expansionSequences and series2 results
• Arithmetic seriesSequences and series2 results, 1 to learn
• Geometric seriesSequences and series3 results, 1 to learn
• Triangles and the sine and cosine rulesTrigonometry3 results, 3 to learn
• Trigonometric graphs and equationsTrigonometry2 results, 2 to learn
• Radians, arcs and small anglesTrigonometry3 results, 2 to learn
• Reciprocal and inverse trigonometric functionsTrigonometry2 results, 2 to learn
• Compound angles and the harmonic formTrigonometry6 results, 3 to learn
• Exponential functions and eExponentials and logarithms1 result, 1 to learn
• Logarithms and their lawsExponentials and logarithms4 results, 4 to learn
• The derivative from first principlesDifferentiation1 result
• Differentiating powers of xDifferentiation1 result, 1 to learn
• Differentiating trig, exponentials and logsDifferentiation2 results, 2 to learn
• The product, quotient and chain rulesDifferentiation2 results, 1 to learn
• Implicit and parametric differentiationDifferentiation1 result
• Integration as antidifferentiationIntegration1 result, 1 to learn
• Integrating standard functionsIntegration4 results, 4 to learn
• Integration by substitution and by partsIntegration2 results, 1 to learn
• Integrating rational functionsIntegration1 result
• Areas, parametric curves and the limit of a sumIntegration2 results, 1 to learn
• Solving differential equationsIntegration1 result
• Locating roots and iterationNumerical methods1 result
• The Newton-Raphson methodNumerical methods1 result
• The trapezium ruleNumerical methods2 results
• Vectors in two dimensionsVectors1 result, 1 to learn
• Vectors in three dimensionsVectors1 result, 1 to learn
• Sampling and the large data setStatistics1 result, 1 to learn
• Measures of location and spreadStatistics3 results, 2 to learn
• Representing and interpreting dataStatistics2 results, 2 to learn
• Probability and Venn diagramsStatistics1 result
• Conditional probabilityStatistics1 result, 1 to learn
• The binomial distributionStatistics2 results, 1 to learn
• The normal distributionStatistics2 results, 2 to learn
• Hypothesis testing: correlation and the normalStatistics1 result
• Kinematics with constant accelerationMechanics3 results
• Kinematics with variable accelerationMechanics1 result, 1 to learn
• Forces and Newton's lawsMechanics1 result, 1 to learn
• ProjectilesMechanics1 result
• Friction and inclined planesMechanics2 results, 1 to learn
• MomentsMechanics1 result, 1 to learn
• Proof by induction: sums and seriesFurther proof1 result
• Modulus, argument and lociComplex numbers1 result, 1 to learn
• De Moivre's theorem and trigonometric identitiesComplex numbers1 result
• Roots of polynomialsFurther algebra and series1 result, 1 to learn
• Summing series and the method of differencesFurther algebra and series2 results, 1 to learn
• Maclaurin seriesFurther algebra and series2 results
• Lines and planes in three dimensionsFurther vectors2 results, 2 to learn
• Intersections, angles and distancesFurther vectors1 result
• Volumes of revolutionFurther calculus1 result, 1 to learn
• Mean values and improper integralsFurther calculus1 result, 1 to learn
• Calculus with inverse trigonometric functionsFurther calculus2 results
• Hyperbolic functions and identitiesHyperbolic functions1 result, 1 to learn
• Calculus with hyperbolic functionsHyperbolic functions1 result
• Polar curvesPolar coordinates1 result, 1 to learn
• Areas with polar coordinatesPolar coordinates1 result
• First order equations and integrating factorsDifferential equations1 result, 1 to learn
• Second order equationsDifferential equations1 result, 1 to learn
• The t-formulaeFurther Pure 11 result, 1 to learn
• Taylor seriesFurther Pure 11 result, 1 to learn
• Leibniz's theorem and the Weierstrass substitutionFurther Pure 11 result, 1 to learn
• Conic sectionsFurther Pure 11 result
• The vector product and the scalar triple productFurther Pure 11 result
• Numerical methods for differential equationsFurther Pure 12 results, 2 to learn
• Discrete random variables and expectationFurther Statistics 13 results, 1 to learn
• The Poisson distributionFurther Statistics 11 result
• Geometric and negative binomial distributionsFurther Statistics 13 results
• The Central Limit TheoremFurther Statistics 11 result
• Goodness-of-fit testsFurther Statistics 11 result
• Contingency tablesFurther Statistics 13 results, 2 to learn
• Probability generating functionsFurther Statistics 14 results
• Reduction formulaeFurther Pure 21 result
• Arc length and surface areaFurther Pure 21 result
• Eigenvalues and eigenvectorsFurther Pure 21 result, 1 to learn
• Diagonalisation and the Cayley-Hamilton theoremFurther Pure 21 result, 1 to learn
• Modular arithmetic and Fermat's little theoremFurther Pure 21 result, 1 to learn
• Least squares regression and residualsFurther Statistics 22 results
• Continuous random variables: density and distribution functionsFurther Statistics 26 results, 6 to learn
• Mean, variance and skewness of continuous variablesFurther Statistics 22 results, 1 to learn
• The continuous uniform distributionFurther Statistics 22 results, 1 to learn
• Correlation coefficients: product moment and SpearmanFurther Statistics 22 results
• Combinations of normal random variablesFurther Statistics 22 results, 1 to learn
• Estimators, standard error and confidence intervalsFurther Statistics 23 results, 2 to learn
• Comparing two normal meansFurther Statistics 21 result
• Testing variances: chi-squared and the F-distributionFurther Statistics 22 results
• Confidence intervals and tests with the t-distributionFurther Statistics 22 results
• Momentum and impulseFurther Mechanics 12 results, 2 to learn
• Impulse and momentum as vectorsFurther Mechanics 11 result, 1 to learn
• Work, energy and powerFurther Mechanics 12 results, 2 to learn
• Hooke's law and elastic stringsFurther Mechanics 11 result, 1 to learn
• Elastic potential energyFurther Mechanics 11 result, 1 to learn
• Direct impact and Newton's law of restitutionFurther Mechanics 11 result, 1 to learn
• Angular speed and horizontal circular motionFurther Mechanics 22 results, 1 to learn
• Motion in a vertical circleFurther Mechanics 21 result
• Centre of mass of a discrete distributionFurther Mechanics 21 result, 1 to learn
• Centres of mass of plane figures and frameworksFurther Mechanics 27 results
• Centres of mass by integrationFurther Mechanics 22 results, 2 to learn
• Newton's laws with a variable forceFurther Mechanics 21 result, 1 to learn
• Simple harmonic motionFurther Mechanics 22 results, 2 to learn
• Oscillations on strings and springsFurther Mechanics 21 result
• Further kinematics: acceleration as a function of x, t or vFurther Mechanics 21 result, 1 to learn
• Linear programming: formulation and graphical solutionDecision Mathematics 11 result
• The stepping-stone methodDecision Mathematics 21 result, 1 to learn

187 results across 27 units, 104 of them to learn outright. Proof and Matrices display no standard result: they are argument and procedure rather than formulae. See also the key ideas and key definitions.

Two things this page raises

Every result above is published in three forms from one source: the typeset formula, a MathML version a screen reader can step through, and a plain-text line for copying. What that means in practice, and where the library still falls short, is on the accessibility page. The badge beside each result refers to the Edexcel booklet only; the FAQ says which board the notes follow and what changes for the other three.