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A-level maths formulae to memorise

These 104 results, from all 24 units that hold one, are not printed in the Pearson Edexcel formula booklet. Learn them with their conditions or be able to derive them. The list does not apply automatically to AQA or OCR booklets.

104 formulae · 24 units.

What the badge means

A Pearson Edexcel candidate sits every paper with the same booklet on the desk: Mathematical Formulae and Statistical Tables, handed out with the question paper. A result it prints can be looked up during the examination; a result it leaves out has to be known or rebuilt, and those are the 104 below. The notes badge each of them where they are stated; this page is that badge counted across the whole library, against the 187 results the notes display in total and the 68 the booklet covers.

What the booklet does print

Anything the booklet prints need not be memorised. For A-level Mathematics the booklet gives mensuration, the arithmetic and binomial series, the compound angle formulae, short tables of derivatives and integrals, the trapezium rule, the probability and standard-deviation formulae, the binomial and normal distributions, the constant acceleration equations, and the statistical tables at the back. Further Maths candidates get two sections more, covering summations, matrix transformations, Maclaurin and Taylor series, vectors, the hyperbolic functions and their calculus, complex numbers, conics, centres of mass, motion in a circle and the further statistics tables.

Two of its omissions are easily missed, and both are on the list below. It prints the compound angle formulae but not the double angle ones. And it prints the sums of the squares and the cubes of the first n integers but not the sum of the integers themselves.

The list

By unit, in the order the course runs. The link on each name goes to that result where it is drawn, badged and given its conditions on the unit’s formulae page; the lesson beside it is where it is derived and used.

ALGEBRA AND FUNCTIONS

• Multiplying powers of the same baseIndices and surds
• Dividing powers of the same baseIndices and surds
• A power raised to a powerIndices and surds
• The square root of a productIndices and surds
• The quadratic formulaQuadratic functions
• The factor theoremPolynomials and the factor theorem

COORDINATE GEOMETRY

• The equation of a straight line through a pointStraight lines
• Perpendicular gradientsStraight lines
• The equation of a circleCircles

SEQUENCES AND SERIES

• The nth term of an arithmetic sequenceArithmetic series
• The nth term of a geometric sequenceGeometric series

TRIGONOMETRY

• The sine ruleTriangles and the sine and cosine rules
• The cosine ruleTriangles and the sine and cosine rules
• The area of a triangleTriangles and the sine and cosine rules
• Tangent as sine over cosineTrigonometric graphs and equations
• The Pythagorean identityTrigonometric graphs and equations
• Arc length in radiansRadians, arcs and small angles
• Sector area in radiansRadians, arcs and small angles
• The secant identityReciprocal and inverse trigonometric functions
• The cosecant identityReciprocal and inverse trigonometric functions
• The double angle formula for sineCompound angles and the harmonic form
• The double angle formulae for cosineCompound angles and the harmonic form
• The double angle formula for tangentCompound angles and the harmonic form

EXPONENTIALS AND LOGARITHMS

• The gradient of an exponentialExponential functions and e
• The definition of a logarithmLogarithms and their laws
• The addition law for logarithmsLogarithms and their laws
• The subtraction law for logarithmsLogarithms and their laws
• The power law for logarithmsLogarithms and their laws

DIFFERENTIATION

• Differentiating a power of xDifferentiating powers of x
• The derivatives of sine and cosineDifferentiating trig, exponentials and logs
• The derivatives of the exponential and the natural logarithmDifferentiating trig, exponentials and logs
• The chain ruleThe product, quotient and chain rules

INTEGRATION

• Integrating a power of xIntegration as antidifferentiation
• Integrating cosineIntegrating standard functions
• Integrating sineIntegrating standard functions
• Integrating the exponentialIntegrating standard functions
• Integrating the reciprocalIntegrating standard functions
• Integrating a derivative over its own functionIntegration by substitution and by parts
• The area under a parametric curveAreas, parametric curves and the limit of a sum

VECTORS

• A directed line segment from position vectorsVectors in two dimensions
• The magnitude of a three-dimensional vectorVectors in three dimensions

STATISTICS

• The size of a stratified sampleSampling and the large data set
• The mean of a data setMeasures of location and spread
• The effect of coding on the mean and the standard deviationMeasures of location and spread
• Frequency densityRepresenting and interpreting data
• The outlier ruleRepresenting and interpreting data
• Conditional probabilityConditional probability
• The discrete uniform distributionThe binomial distribution
• The standard normal scoreThe normal distribution
• The normal approximation to the binomialThe normal distribution

MECHANICS

• Velocity and acceleration by differentiationKinematics with variable acceleration
• Newton's second lawForces and Newton's laws
• The friction inequalityFriction and inclined planes
• The moment of a forceMoments

COMPLEX NUMBERS

• Modulus-argument formModulus, argument and loci

FURTHER ALGEBRA AND SERIES

• The roots of a cubic and its coefficientsRoots of polynomials
• The sum of the first n integersSumming series and the method of differences

FURTHER VECTORS

• The vector equation of a lineLines and planes in three dimensions
• The scalar product equation of a planeLines and planes in three dimensions

FURTHER CALCULUS

• The volume of revolution about the x-axisVolumes of revolution
• The mean value of a functionMean values and improper integrals

HYPERBOLIC FUNCTIONS

• The definitions of cosh and sinhHyperbolic functions and identities

POLAR COORDINATES

• Polar and Cartesian coordinatesPolar curves

DIFFERENTIAL EQUATIONS

• The integrating factorFirst order equations and integrating factors
• The auxiliary equationSecond order equations

FURTHER PURE 1

• The t-formulaeThe t-formulae
• Taylor's series about a pointTaylor series
• Leibniz's theoremLeibniz's theorem and the Weierstrass substitution
• Finite difference approximations to a derivativeNumerical methods for differential equations
• Simpson's ruleNumerical methods for differential equations

FURTHER STATISTICS 1

• The mean and variance of a discrete uniform distributionDiscrete random variables and expectation
• The expected frequency in a contingency tableContingency tables
• Yates' continuity correctionContingency tables

FURTHER PURE 2

• The characteristic equationEigenvalues and eigenvectors
• Diagonalising a matrixDiagonalisation and the Cayley-Hamilton theorem
• Fermat's little theoremModular arithmetic and Fermat's little theorem

FURTHER STATISTICS 2

• Probability from a density functionContinuous random variables: density and distribution functions
• The density as the derivative of the distribution functionContinuous random variables: density and distribution functions
• Total probability for a mixed distributionContinuous random variables: density and distribution functions
• The exponential distribution functionContinuous random variables: density and distribution functions
• The exponential densityContinuous random variables: density and distribution functions
• The memoryless propertyContinuous random variables: density and distribution functions
• The mean and variance of an exponential distributionMean, variance and skewness of continuous variables
• The distribution function of a continuous uniform distributionThe continuous uniform distribution
• A linear combination of normal variablesCombinations of normal random variables
• The unbiased estimate of a population varianceEstimators, standard error and confidence intervals
• A confidence interval for a meanEstimators, standard error and confidence intervals

FURTHER MECHANICS 1

• Impulse and momentumMomentum and impulse
• Conservation of linear momentumMomentum and impulse
• Impulse as a vectorImpulse and momentum as vectors
• Kinetic and gravitational potential energyWork, energy and power
• Power as force times velocityWork, energy and power
• Hooke's lawHooke's law and elastic strings
• Elastic potential energyElastic potential energy
• Newton's law of restitutionDirect impact and Newton's law of restitution

FURTHER MECHANICS 2

• The angle of a banked trackAngular speed and horizontal circular motion
• The centre of mass of a discrete distributionCentre of mass of a discrete distribution
• The centre of mass of a lamina by integrationCentres of mass by integration
• The centre of mass of a solid of revolutionCentres of mass by integration
• Newton's second law with a variable forceNewton's laws with a variable force
• The defining equation of simple harmonic motionSimple harmonic motion
• Speed in simple harmonic motionSimple harmonic motion
• The two forms of accelerationFurther kinematics: acceleration as a function of x, t or v

DECISION MATHEMATICS 2

• The improvement indexThe stepping-stone method

The counts are read off the notes themselves rather than typed, so a result that changes badge changes this page. Every result the library displays, printed or not, is indexed on the equation index; if you know what a formula looks like but not what it is called, the search box holds all 187 of them by their own symbols. The flashcard decks drill the same results.