A-level Pure Mathematics Revision Cards
Build confidence with 113 revision cards, each breaking a skill into clear steps. Study the worked examples, try five questions, then check your answers.
Explore the available skills. More topics are being added.
Search card titles, sections and categories. Try completing the square or trigonometry
113 cards · 113 available
Algebra and proof44 available · 47 coming soon
Notation and simplifying
2 cards
Expanding expressions
4 cards
Factorising expressions
5 cards
Index laws
7 cards
Surds and fractional indices
4 cards
Linear equations and inequalities
6 cards
Quadratic equations
4 cards
Rearranging formulas
2 cards
Simultaneous equations
2 cards
Solving a linear and quadratic equation simultaneouslyComing soon
Substituting into a circle equationComing soon
Using the discriminant for simultaneous equationsComing soon
Finding a parameter for tangencyComing soon
Inequalities
3 cards
Algebraic methods
0 cards
Using exact values instead of rounded decimalsComing soon
Solving equations by taking square rootsComing soon
Simplifying an algebraic fraction by cancelling factorsComing soon
Finding excluded values in an algebraic fractionComing soon
Adding algebraic fractions with different denominatorsComing soon
Multiplying algebraic fractionsComing soon
Dividing algebraic fractionsComing soon
Direct proof
0 cards
Distinguishing a statement from its converseComing soon
Using a counterexample to disprove a statementComing soon
Writing even and odd integers algebraicallyComing soon
Proving a divisibility statementComing soon
Proving a statement about consecutive integersComing soon
Proving a statement about rational numbersComing soon
Completing a proof by deductionComing soon
Showing that two algebraic expressions are identicalComing soon
Other proof methods
0 cards
Splitting a proof into exhaustive casesComing soon
Proving a result by exhaustionComing soon
Setting up a proof by contradictionComing soon
Proving that a square root is irrationalComing soon
Identifying an error in a proposed proofComing soon
Completing the square
2 cards
Powers and surds
0 cards
Simplifying expressions with fractional indicesComing soon
Combining negative and fractional indicesComing soon
Solving an equation by expressing both sides as powersComing soon
Expanding products containing surdsComing soon
Rationalising a one-term denominatorComing soon
Rationalising a two-term denominatorComing soon
Simplifying an exact surd answerComing soon
Algebraic fractions
0 cards
Combining algebraic fractions before cancellingComing soon
Dividing polynomials before simplifying a fractionComing soon
Solving rational equations and checking restrictionsComing soon
Partial fractions with two distinct linear factorsComing soon
Partial fractions with three distinct linear factorsComing soon
Partial fractions with a repeated linear factorComing soon
Partial fractions with an improper fractionComing soon
Quadratic equations and inequalities
3 cards
Completing the square after taking out a common factorComing soon
Finding a minimum from completed-square formComing soon
Finding a maximum from completed-square formComing soon
Solving quadratic inequalities with a repeated rootComing soon
Solving quadratic inequalities with no real rootsComing soon
Finding parameter values for two real rootsComing soon
Finding parameter values for a repeated rootComing soon
Finding parameter values for no real rootsComing soon
Using the discriminant to test whether a line meets a curveComing soon
Calculus16 available · 74 coming soon
Differentiation basics
0 cards
Finding a derivative from first principlesComing soon
Differentiating a power of the variableComing soon
Differentiating negative powersComing soon
Differentiating fractional powersComing soon
Differentiating a polynomialComing soon
Simplifying an expression before differentiatingComing soon
Finding a gradient at a pointComing soon
Finding a tangent equationComing soon
Finding a normal equationComing soon
Finding where a tangent is parallel to a lineComing soon
Differentiation rules
0 cards
Differentiating the natural exponential functionComing soon
Differentiating an exponential with a general baseComing soon
Differentiating the natural logarithmComing soon
Differentiating sineComing soon
Differentiating cosineComing soon
Differentiating tangentComing soon
Differentiating a power of a linear expressionComing soon
Using the chain rule with an exponentialComing soon
Using the chain rule with a logarithmComing soon
Using the chain rule with a trigonometric functionComing soon
Using the product ruleComing soon
Using the quotient ruleComing soon
Combining the product and chain rulesComing soon
Combining the quotient and chain rulesComing soon
Differentiating an implicit equationComing soon
Differentiating a parametric curveComing soon
Applying derivatives
0 cards
Finding a second derivativeComing soon
Finding stationary pointsComing soon
Classifying stationary points using the first derivativeComing soon
Classifying stationary points using the second derivativeComing soon
Finding intervals of increase and decreaseComing soon
Finding points of inflectionComing soon
Describing concavity using a second derivativeComing soon
Sketching a derivative from a function graphComing soon
Forming an optimisation functionComing soon
Optimising with a geometric constraintComing soon
Checking endpoints in an optimisation problemComing soon
Solving a connected rates of change problemComing soon
Forming a differential equation from a rate statementComing soon
Integration methods
10 cards
Integrating by substitution with a specified substitutionComing soon
Choosing a substitutionComing soon
Changing limits in a substitutionComing soon
Integrating by parts onceComing soon
Integrating by parts repeatedlyComing soon
Integrating a logarithm by partsComing soon
Integrating using distinct linear partial fractionsComing soon
Integrating using repeated linear partial fractionsComing soon
Definite integrals and areas
6 cards
Reversing integration limitsComing soon
Splitting an integral at an intermediate pointComing soon
Using symmetry to evaluate an integralComing soon
Integrating a parametric curve for an areaComing soon
Differential equations
0 cards
Separating variables in a differential equationComing soon
Finding a general solution by integrationComing soon
Finding a particular solution from an initial conditionComing soon
Solving an exponential growth differential equationComing soon
Solving an exponential decay differential equationComing soon
Interpreting the long-term behaviour of a solutionComing soon
Checking a solution in the original differential equationComing soon
Numerical roots
0 cards
Locating a root using a sign changeComing soon
Identifying when a sign-change argument failsComing soon
Rearranging an equation for iterationComing soon
Carrying out a fixed-point iterationComing soon
Recognising convergence and divergenceComing soon
Drawing a staircase diagramComing soon
Drawing a cobweb diagramComing soon
Applying the Newton-Raphson formulaComing soon
Explaining a failure of Newton-RaphsonComing soon
Choosing a sensible starting valueComing soon
Giving a root to a stated accuracyComing soon
Numerical integration
0 cards
Choosing equal-width stripsComing soon
Applying the trapezium rule to a tableComing soon
Applying the trapezium rule to a functionComing soon
Deciding whether an estimate is too large or too smallComing soon
Improving a numerical area estimateComing soon
Coordinate geometry and vectors7 available · 32 coming soon
Coordinate geometry
7 cards
Straight lines and circles
0 cards
Finding a line through two pointsComing soon
Converting between forms of a straight-line equationComing soon
Finding the intersection of two linesComing soon
Finding a perpendicular bisectorComing soon
Reading the centre and radius of a circleComing soon
Completing the square in a circle equationComing soon
Finding a circle from its centre and a pointComing soon
Finding the endpoints of a diameterComing soon
Finding a tangent to a circleComing soon
Finding intersections of a line and a circleComing soon
Proving a line is tangent to a circleComing soon
Parametric curves
0 cards
Plotting a curve from parametric equationsComing soon
Eliminating a parameter using substitutionComing soon
Eliminating a parameter using a trigonometric identityComing soon
Finding the parameter at an intersectionComing soon
Stating the valid range after eliminating a parameterComing soon
Interpreting the direction of a parametric curveComing soon
Modelling motion using parametric equationsComing soon
Vector methods
0 cards
Writing a vector in component formComing soon
Finding a vector between two pointsComing soon
Finding a vector's magnitude in two dimensionsComing soon
Finding a vector's magnitude in three dimensionsComing soon
Finding a unit vectorComing soon
Finding a direction angleComing soon
Adding and subtracting vectorsComing soon
Multiplying a vector by a scalarComing soon
Finding a position vector from a routeComing soon
Dividing a line segment in a ratioComing soon
Proving that vectors are parallelComing soon
Proving that points are collinearComing soon
Finding a distance using position vectorsComing soon
Interpreting a vector model in contextComing soon
Exponentials and logarithms4 available · 21 coming soon
Exponential prerequisites
3 cards
Exponential foundations
1 card
Exponential and logarithmic functions
0 cards
Sketching an exponential growth graphComing soon
Sketching an exponential decay graphComing soon
Sketching the natural exponential functionComing soon
Converting exponential form to logarithmic formComing soon
Converting logarithmic form to exponential formComing soon
Evaluating simple logarithms exactlyComing soon
Expanding a logarithm using lawsComing soon
Combining logarithms into one expressionComing soon
Solving an exponential equation using logarithmsComing soon
Solving a logarithmic equation and checking its domainComing soon
Using a change of logarithm baseComing soon
Sketching the natural logarithm functionComing soon
Exponential models
0 cards
Finding an exponential model from two pointsComing soon
Interpreting an exponential rate constantComing soon
Finding doubling timeComing soon
Finding half-lifeComing soon
Linearising a power model using logarithmsComing soon
Linearising an exponential model using logarithmsComing soon
Recovering model parameters from a straight-line graphComing soon
Interpreting a model's restrictionsComing soon
Comparing predicted and observed valuesComing soon
Functions and graphs31 available · 29 coming soon
Function notation and representations
4 cards
Piecewise functions
2 cards
Recognising polynomial structure
2 cards
Degree and leading coefficient
4 cards
Zeros and factors
4 cards
End behaviour
1 card
Division and theorems
3 cards
Polynomial equations and structure
0 cards
Expanding a product of a linear and quadratic factorComing soon
Factorising a cubic after finding one rootComing soon
Factorising a quartic using a quadratic substitutionComing soon
Finding a coefficient using the factor theoremComing soon
Finding a coefficient using the remainder theoremComing soon
Dividing a polynomial with missing powersComing soon
Sketching a polynomial from its real factorsComing soon
Using multiplicity to decide whether a curve crosses or touchesComing soon
Finding a polynomial from its roots and a pointComing soon
Quadratic functions
3 cards
Rates of change
2 cards
Symmetry
1 card
Domain and range
0 cards
Finding the domain of a rational functionComing soon
Finding the domain of a square-root functionComing soon
Finding the range of a quadratic functionComing soon
Restricting a domain to make a function one-to-oneComing soon
Reading the domain and range from a graphComing soon
Composite and inverse functions
0 cards
Evaluating a composite functionComing soon
Finding an algebraic composite functionComing soon
Finding the domain of a composite functionComing soon
Finding an inverse of a linear functionComing soon
Finding an inverse of a rational functionComing soon
Finding an inverse of a restricted quadratic functionComing soon
Relating inverse domain and rangeComing soon
Reflecting a graph to sketch an inverseComing soon
Modulus and reciprocal graphs
0 cards
Sketching a modulus of a linear expressionComing soon
Sketching the modulus of a functionComing soon
Replacing the input by its modulusComing soon
Solving a modulus equation graphicallyComing soon
Solving a modulus inequalityComing soon
Identifying asymptotes of a reciprocal graphComing soon
Sketching a translated reciprocal functionComing soon
Sequences and binomial expansion0 available · 37 coming soon
Arithmetic sequences and series
0 cards
Finding a common differenceComing soon
Finding an arithmetic
Finding the position of a term in an arithmetic sequenceComing soon
Finding missing terms in an arithmetic sequenceComing soon
Finding an arithmetic sumComing soon
Finding the number of terms from an arithmetic sumComing soon
Solving an arithmetic sequence problem in contextComing soon
Geometric sequences and series
0 cards
Finding a common ratioComing soon
Finding a geometric
Finding the position of a geometric termComing soon
Finding missing terms in a geometric sequenceComing soon
Summing a finite geometric seriesComing soon
Testing whether a geometric series convergesComing soon
Finding a sum to infinityComing soon
Finding an unknown using a sum to infinityComing soon
Modelling compound growth with a geometric sequenceComing soon
Recurrence relations and notation
0 cards
Generating terms from a recurrence relationComing soon
Finding a recurrence relation from termsComing soon
Classifying a sequence as increasing or decreasingComing soon
Identifying a periodic sequenceComing soon
Finding a possible limiting value of a recurrenceComing soon
Expanding a sum written in sigma notationComing soon
Writing a series in sigma notationComing soon
Splitting and combining sumsComing soon
Binomial expansion
0 cards
Using factorial notationComing soon
Calculating a binomial coefficientComing soon
Building a row of Pascal's triangleComing soon
Expanding a binomial with a positive integer powerComing soon
Finding a specified term in a binomial expansionComing soon
Finding a coefficient in a binomial expansionComing soon
Finding a constant term in a binomial expansionComing soon
Expanding a binomial with a negative powerComing soon
Expanding a binomial with a fractional powerComing soon
Factorising out a constant before a binomial expansionComing soon
Stating the interval of validity of a binomial expansionComing soon
Using a binomial expansion for an approximationComing soon
Multiplying a binomial expansion by another expressionComing soon
Trigonometry11 available · 50 coming soon
Right-angled trigonometry
7 cards
Right-triangle trigonometry
1 card
Pythagoras’ theorem
3 cards
Radians and exact values
0 cards
Converting degrees to radiansComing soon
Converting radians to degreesComing soon
Finding an arc length in radiansComing soon
Finding a sector area in radiansComing soon
Finding an angle from an arc or sectorComing soon
Finding the area of a segmentComing soon
Using the unit circle to determine a signComing soon
Finding exact trigonometric values in radiansComing soon
Finding a related acute angleComing soon
Triangles and applications
0 cards
Finding a side using the sine ruleComing soon
Finding an angle using the sine ruleComing soon
Finding both triangles in the ambiguous sine-rule caseComing soon
Finding a side using the cosine ruleComing soon
Finding an angle using the cosine ruleComing soon
Finding triangle area using two sides and the included angleComing soon
Solving a bearings problem with trigonometryComing soon
Trigonometric graphs and inverses
0 cards
Sketching a sine graphComing soon
Sketching a cosine graphComing soon
Sketching a tangent graphComing soon
Finding amplitude and periodComing soon
Finding a phase shiftComing soon
Finding a trigonometric equation from a graphComing soon
Evaluating an inverse trigonometric functionComing soon
Stating inverse trigonometric domains and rangesComing soon
Sketching reciprocal trigonometric graphsComing soon
Identities and equations
0 cards
Using the tangent identityComing soon
Using the sine-squared plus cosine-squared identityComing soon
Using a secant identityComing soon
Using a cosecant identityComing soon
Proving a trigonometric identityComing soon
Solving a sine equation on an intervalComing soon
Solving a cosine equation on an intervalComing soon
Solving a tangent equation on an intervalComing soon
Solving an equation with a multiple angleComing soon
Solving an equation with a shifted angleComing soon
Solving a quadratic in a trigonometric functionComing soon
Solving a trigonometric equation by factorisingComing soon
Checking for solutions lost through divisionComing soon
Compound angles and approximations
0 cards
Expanding the sine of a sum or differenceComing soon
Expanding the cosine of a sum or differenceComing soon
Expanding the tangent of a sum or differenceComing soon
Using the sine double-angle formulaComing soon
Choosing a cosine double-angle formulaComing soon
Using the tangent double-angle formulaComing soon
Writing a sine-cosine combination as a single sineComing soon
Writing a sine-cosine combination as a single cosineComing soon
Finding a maximum or minimum from harmonic formComing soon
Solving an equation using harmonic formComing soon
Using small-angle approximationsComing soon
Stating when a small-angle approximation is validComing soon
No cards available yet
Switch to All cards to browse the topics that are coming soon.