GCSE Higher / Extended Revision Cards

Build confidence with 777 revision cards, each breaking a skill into clear steps. Study the worked examples, try five questions, then check your answers.

For GCSE Higher and IGCSE Extended. Exact tier coverage can vary by exam board.

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777 cards · 777 available

Algebra179 available

Algebraic notation

7 cards
Identifying terms and coefficientsKS3 / GCSEOpen Card
Expressions, equations and formulaeKS3 / GCSEOpen Card
Writing algebraic products without a multiplication signKS3 / GCSEOpen Card
Writing algebraic division as a fractionKS3 / GCSEOpen Card

Substitution

3 cards
Substitution into a formulaKS3 / GCSEOpen Card
Substitution involving powers and rootsKS3 / GCSEOpen Card

Function machines

2 cards
Reversing a function machineKS3 / GCSEOpen Card

Simplifying expressions

2 cards
Simplifying by collecting like termsKS3 / GCSEOpen Card
Simplifying powers of algebraic productsKS3 / GCSEOpen Card

Multiplying and dividing algebraic terms

2 cards
Multiplying algebraic termsKS3 / GCSEOpen Card

Expanding brackets

9 cards
Expanding a single bracketUsing arrowsKS3 / GCSEOpen Card
Expanding a single bracketUsing the grid methodKS3 / GCSEOpen Card
Expanding a bracket with a negative multiplierKS3 / GCSEOpen Card
Expanding two bracketsUsing arrowsKS3 / GCSEOpen Card
Expanding two bracketsUsing the grid methodKS3 / GCSEOpen Card
Expanding the square of a bracketKS3 / GCSEOpen Card
Expanding three bracketsUsing arrowsGCSE HigherOpen Card
Expanding three bracketsUsing the grid methodGCSE HigherOpen Card

Factorising with common factors

4 cards
Taking out a common numerical factorKS3 / GCSEOpen Card
Taking out a common algebraic factorKS3 / GCSEOpen Card
Factorising three or more terms into one bracketKS3 / GCSEOpen Card
Factorising expressions using a repeated bracketGCSE HigherOpen Card

Factorising quadratics

9 cards
Factorising quadraticsIn the form KS3 / GCSEOpen Card
Factorising quadratics - shortIn the form KS3 / GCSEOpen Card
Factorising quadraticsIn the form GCSE HigherOpen Card
Factorising quadratics - shortIn the form GCSE HigherOpen Card
Factorising quadraticsIn the form GCSE HigherOpen Card
Factorising quadratics - shortIn the form GCSE HigherOpen Card
Taking out a common factor before factorising a quadraticKS3 / GCSEOpen Card
Factorising perfect-square quadraticsKS3 / GCSEOpen Card

Completing the square

4 cards
Completing the squareIn the form GCSE HigherOpen Card
Completing the squareIn the form GCSE HigherOpen Card
Vertex of a quadraticFrom completed-square formGCSE HigherOpen Card
Finding a quadratic minimum or maximumGCSE HigherOpen Card

Solving quadratic equations

8 cards
Solving a quadratic by factorisingKS3 / GCSEOpen Card
Solving a quadratic after rearrangingGCSE HigherOpen Card
Solving a quadratic by square rootsKS3 / GCSEOpen Card
Solving a quadratic by completing the squareGCSE HigherOpen Card
Quadratic formuladecimal answersGCSE Higher / IGCSE ExtendedOpen Card
Quadratic formulaexact surd answersGCSE Higher / IGCSE ExtendedOpen Card
Interpreting quadratic roots in contextGCSE HigherOpen Card

Algebraic fractions

12 cards
Simplifying algebraic fractions with common termsGCSE Higher / IGCSE ExtendedOpen Card
Simplifying algebraic fractions by factorisingGCSE Higher / IGCSE ExtendedOpen Card
Adding algebraic fractionsWith the same denominatorGCSE Higher / IGCSE ExtendedOpen Card
Subtracting algebraic fractionsWith the same denominatorGCSE Higher / IGCSE ExtendedOpen Card
Adding algebraic fractionsWith different denominatorsGCSE Higher / IGCSE ExtendedOpen Card
Subtracting algebraic fractionsWith different denominatorsGCSE Higher / IGCSE ExtendedOpen Card
Multiplying algebraic fractionsGCSE Higher / IGCSE ExtendedOpen Card
Dividing algebraic fractionsGCSE Higher / IGCSE ExtendedOpen Card
Solving equations containing algebraic fractionsGCSE Higher / IGCSE ExtendedOpen Card
Finding excluded values before cancelling algebraic factorsGCSE Higher / IGCSE ExtendedOpen Card
Taking out a negative factor before cancellingGCSE Higher / IGCSE ExtendedOpen Card
Combining fractions before factorising a numeratorGCSE Higher / IGCSE ExtendedOpen Card

Solving linear equations

12 cards
Solving equationsOne-step addition and subtractionKS3 / GCSEOpen Card
Solving equationsOne-step multiplication and divisionKS3 / GCSEOpen Card
Solving equationsTwo-step equationsKS3 / GCSEOpen Card
Solving equations with a negative coefficientKS3 / GCSEOpen Card
Solving equationsWith one bracketKS3 / GCSEOpen Card
Solving equationsWith several bracketsKS3 / GCSEOpen Card
Solving equationsWith fractionsKS3 / GCSEOpen Card
Solving equationsWith unknowns on both sidesKS3 / GCSEOpen Card
Forming an equation from wordsKS3 / GCSEOpen Card
Forming an equation from a geometric diagramKS3 / GCSEOpen Card
Solving an equation with a decimal coefficientCourse skillOpen Card
Solving an equation by clearing decimals firstCourse skillOpen Card

Rearranging formulae

8 cards
Rearranging a one-step formulaKS3 / GCSEOpen Card
Rearranging a two-step formulaKS3 / GCSEOpen Card
Rearranging a formula containing bracketsKS3 / GCSEOpen Card
Rearranging a formula containing a square or rootKS3 / GCSEOpen Card
Rearranging when the subject appears twiceGCSE HigherOpen Card
Rearranging a formula containing algebraic fractionsGCSE Higher / IGCSE ExtendedOpen Card
Rearranging a formula containing a reciprocalGCSE Higher / IGCSE ExtendedOpen Card
Rearranging a formula where the subject occurs in both numerator and denominatorGCSE Higher / IGCSE ExtendedOpen Card

Simultaneous equations

11 cards
Simultaneous equations by eliminationmatching coefficientsKS3 / GCSEOpen Card
Simultaneous equations by eliminationmultiply one equationKS3 / GCSEOpen Card
Simultaneous equations by eliminationmultiply both equationsKS3 / GCSEOpen Card
Simultaneous equations by substitutionKS3 / GCSEOpen Card
Forming simultaneous equations from a contextKS3 / GCSEOpen Card
Solving linear and quadratic simultaneous equationsGCSE HigherOpen Card
Solving a line and circle simultaneouslyGCSE HigherOpen Card
Reading simultaneous solutions from graphsKS3 / GCSEOpen Card
Choosing a multiple before eliminating an unknownCourse skillOpen Card
Forming simultaneous equations from a price problemCourse skillOpen Card
Interpreting both intersections of a line and a quadraticGCSE Higher / IGCSE ExtendedOpen Card

Inequalities

19 cards
Reading inequality notationKS3 / GCSEOpen Card
Plotting inequalities on a number lineKS3 / GCSEOpen Card
Solving linear inequalitiesKS3 / GCSEOpen Card
Solving compound inequalitiesWith unknowns in all three partsGCSE HigherOpen Card
Finding integer solutions to an inequalityKS3 / GCSEOpen Card
Writing a solution using set notationGCSE Higher / IGCSE ExtendedOpen Card
Drawing an inequality boundary lineGCSE HigherOpen Card
Shading a region for one linear inequalityGCSE HigherOpen Card
Combining regions from several inequalitiesGCSE HigherOpen Card
Quadratic inequalities by drawing the graphGCSE HigherOpen Card
Finding an integer solution when the boundary is fractionalCourse skillOpen Card
Distinguishing a strict and inclusive inequality in contextCourse skillOpen Card
Intersecting two solution intervalsCourse skillOpen Card
Identifying when two inequalities have no common solutionCourse skillOpen Card
Quadratic inequalities by testing valuesGCSE Higher / IGCSE ExtendedOpen Card
Quadratic inequalities after rearranging to zeroGCSE Higher / IGCSE ExtendedOpen Card
Inequalities: dividing by a negativeKS3 / GCSEOpen Card
Inequalities: multiplying by a negativeKS3 / GCSEOpen Card

Sequences

15 cards
Continuing a sequence from a term-to-term ruleKS3 / GCSEOpen Card
Generating terms from a position-to-term ruleKS3 / GCSEOpen Card
Recognising triangular-number sequencesKS3 / GCSEOpen Card
Recognising square-number sequencesKS3 / GCSEOpen Card
Recognising cube-number sequencesKS3 / GCSEOpen Card
Continuing Fibonacci-type sequencesKS3 / GCSEOpen Card
The th term of an increasing linear sequenceKS3 / GCSEOpen Card
The th term of a decreasing linear sequenceKS3 / GCSEOpen Card
Finding a term from the th-term ruleKS3 / GCSEOpen Card
Deciding whether a number is in a sequenceKS3 / GCSEOpen Card
The th term of a quadratic sequenceGCSE HigherOpen Card
Continuing a geometric sequenceKS3 / GCSEOpen Card
Geometric sequences involving surdsGCSE HigherOpen Card
Using a recursive sequence ruleKS3 / GCSEOpen Card

Coordinates and straight-line graphs

18 cards
Plotting coordinates in four quadrantsKS3 / GCSEOpen Card
Reading coordinates from a graphKS3 / GCSEOpen Card
Midpoint of a line segmentKS3 / GCSEOpen Card
Length between two coordinatesKS3 / GCSEOpen Card
Plotting horizontal and vertical linesKS3 / GCSEOpen Card
Plotting a straight line from a tableKS3 / GCSEOpen Card
Finding gradient from a graphKS3 / GCSEOpen Card
Finding gradient from two pointsKS3 / GCSEOpen Card
Writing a line equation from a graphKS3 / GCSEOpen Card
Finding a line equation from a point and gradientKS3 / GCSEOpen Card
Finding a line equation through two pointsKS3 / GCSEOpen Card
Identifying parallel linesKS3 / GCSEOpen Card
Finding an equation of a parallel lineKS3 / GCSEOpen Card
Finding a perpendicular gradientGCSE HigherOpen Card
Finding an equation of a perpendicular lineGCSE HigherOpen Card
Finding intercepts algebraicallyKS3 / GCSEOpen Card

Curved graphs

19 cards
Plotting a quadratic graphKS3 / GCSEOpen Card
Reading roots of a quadratic graphKS3 / GCSEOpen Card
Reading a quadratic turning pointKS3 / GCSEOpen Card
Finding the axis of symmetry of a quadraticKS3 / GCSEOpen Card
Sketching a quadratic from its factorsKS3 / GCSEOpen Card
Recognising and sketching a cubic graphKS3 / GCSEOpen Card
Recognising and sketching a reciprocal graphKS3 / GCSEOpen Card
Recognising and sketching an exponential graphGCSE HigherOpen Card
Recognising the sine graphGCSE HigherOpen Card
Recognising the cosine graphGCSE HigherOpen Card
Recognising the tangent graphGCSE HigherOpen Card
Solving an equation using a graphKS3 / GCSEOpen Card
Solving an equation by adding a line to a graphKS3 / GCSEOpen Card
Interpreting graphs in an unfamiliar contextKS3 / GCSEOpen Card
Finding an average gradient on a curveGCSE HigherOpen Card
Estimating a gradient at a pointGCSE HigherOpen Card
Estimating an area under a graphGCSE HigherOpen Card
Equation of a circle centred at the originGCSE HigherOpen Card
Equation of a tangent to a circleGCSE HigherOpen Card

Graph transformations

2 cards

Functions

4 cards
Solving an equation in function notationGCSE HigherOpen Card
Finding a composite functionGCSE HigherOpen Card
Finding an inverse functionGCSE HigherOpen Card

Iteration

3 cards
Using an iteration formulaGCSE HigherOpen Card
Rearranging an equation for iterationGCSE HigherOpen Card
Interpreting convergence of iterationGCSE HigherOpen Card

Algebraic proof

6 cards
Disproving a statement with a counterexampleKS3 / GCSEOpen Card
Writing expressions for even and odd integersKS3 / GCSEOpen Card
Writing expressions for consecutive integersKS3 / GCSEOpen Card
Proving a divisibility statement algebraicallyGCSE HigherOpen Card
Proving a statement about parityGCSE HigherOpen Card
Proving two expressions are equivalentKS3 / GCSEOpen Card
Number147 available

Place value and ordering

8 cards
Place value in whole numbersKS3 / GCSEOpen Card
Reading and writing large numbersKS3 / GCSEOpen Card
Ordering integers on a number lineKS3 / GCSEOpen Card
Comparing numbers using inequality symbolsKS3 / GCSEOpen Card
Multiplying by powers of tenKS3 / GCSEOpen Card

Written calculations and negative numbers

24 cards
Dividing decimals by whole numbersKS3 / GCSEOpen Card
Interpreting remainders in contextKS3 / GCSEOpen Card
Adding and subtracting negative numbersKS3 / GCSEOpen Card
Multiplying with negative numbersKS3 / GCSEOpen Card
Dividing with negative numbersKS3 / GCSEOpen Card
Calculations with negative decimalsKS3 / GCSEOpen Card
Calculations with negative fractionsKS3 / GCSEOpen Card
Order of operations (BIDMAS)KS3 / GCSEOpen Card
Inverse operations to check a calculationKS3 / GCSEOpen Card
Interpreting bank balances and transactionsKS3 / GCSEOpen Card
Multiplying decimals using an integer calculationCourse skillOpen Card
Dividing decimals by scaling both numbersCourse skillOpen Card
Choosing how to round a remainder in a word problemCourse skillOpen Card

Factors, multiples and counting

12 cards
Prime factorisation using a factor treeKS3 / GCSEOpen Card
Writing prime factorisation in index formKS3 / GCSEOpen Card
Highest common factor by listingKS3 / GCSEOpen Card
Highest common factor from prime factorsKS3 / GCSEOpen Card
Lowest common multiple by listingKS3 / GCSEOpen Card
Lowest common multiple from prime factorsKS3 / GCSEOpen Card
Finding missing digits using divisibilityKS3 / GCSEOpen Card
Systematic listing without repetitionKS3 / GCSEOpen Card
Product rule for countingGCSE HigherOpen Card

Powers and roots

18 cards
Powers of positive integersKS3 / GCSEOpen Card
Powers of negative numbersKS3 / GCSEOpen Card
Multiplying powers with the same baseKS3 / GCSEOpen Card
Dividing powers with the same baseKS3 / GCSEOpen Card
Fractional indices as rootsGCSE HigherOpen Card
Fractional indices with a numeratorGCSE HigherOpen Card
Negative fractional indicesGCSE HigherOpen Card
Estimating powers and higher rootsGCSE HigherOpen Card

Fractions

37 cards
Reading fractions from diagramsKS3 / GCSEOpen Card
Numerators and denominatorsKS3 / GCSEOpen Card
Comparing fractionsWith the same denominatorKS3 / GCSEOpen Card
Comparing fractionsWith different denominatorsKS3 / GCSEOpen Card
Adding fractionsWith the same denominatorKS3 / GCSEOpen Card
Adding fractionsWith different denominatorsKS3 / GCSEOpen Card
Subtracting fractionsWith the same denominatorKS3 / GCSEOpen Card
Subtracting fractionsWith different denominatorsKS3 / GCSEOpen Card
Multiplying a fraction by a whole numberKS3 / GCSEOpen Card
Dividing a fraction by a whole numberKS3 / GCSEOpen Card
Dividing a whole number by a fractionKS3 / GCSEOpen Card
Fractions greater than oneKS3 / GCSEOpen Card
Improper fractions to mixed numbersKS3 / GCSEOpen Card
Mixed numbers to improper fractionsKS3 / GCSEOpen Card
Fraction of an amountbar modelKS3 / GCSEOpen Card
Fraction of an amountcalculationKS3 / GCSEOpen Card
Reverse fractions of an amountbar modelKS3 / GCSEOpen Card
Reverse fractions of an amountcalculationKS3 / GCSEOpen Card
Expressing one amount as a fraction of anotherKS3 / GCSEOpen Card
Finding the fraction remainingKS3 / GCSEOpen Card
Successive fractions of a remaining amountKS3 / GCSEOpen Card
Cancelling common factors before multiplying fractionsKS3 / GCSEOpen Card
Cancelling common factors before dividing fractionsKS3 / GCSEOpen Card
Adding mixed numbers with a carry into the whole partKS3 / GCSEOpen Card
Subtracting mixed numbers by borrowing one wholeKS3 / GCSEOpen Card
Finding a missing fraction in a sumKS3 / GCSEOpen Card
Finding a missing fraction in a differenceKS3 / GCSEOpen Card

Fractions, decimals and percentages

11 cards
Fractions to terminating decimalsKS3 / GCSEOpen Card
Terminating decimals to fractionsKS3 / GCSEOpen Card
Ordering fractions, decimals and percentagesKS3 / GCSEOpen Card
Recognising recurring decimal notationGCSE HigherOpen Card
Pure recurring decimals to fractionsGCSE HigherOpen Card
Mixed recurring decimals to fractionsGCSE HigherOpen Card
Fractions to recurring decimalsGCSE HigherOpen Card

Accuracy and estimation

16 cards
Rounding to the nearest ten, hundred or thousandKS3 / GCSEOpen Card
Rounding to decimal placesKS3 / GCSEOpen Card
Rounding to significant figuresKS3 / GCSEOpen Card
Checking the size of a calculator answerKS3 / GCSEOpen Card
Rounding sensibly in contextKS3 / GCSEOpen Card
Error intervals after roundingKS3 / GCSEOpen Card
Error intervals after truncationKS3 / GCSEOpen Card
Reading lower and upper boundsKS3 / GCSEOpen Card
Bounds in multi-step calculationsGCSE HigherOpen Card
Justifying a degree of accuracyGCSE HigherOpen Card

Standard form

9 cards
Writing large numbers in standard formKS3 / GCSEOpen Card
Writing small numbers in standard formKS3 / GCSEOpen Card
Standard form to ordinary numbersKS3 / GCSEOpen Card
Ordering numbers in standard formKS3 / GCSEOpen Card
Multiplying numbers in standard formKS3 / GCSEOpen Card
Dividing numbers in standard formKS3 / GCSEOpen Card
Adding numbers in standard formKS3 / GCSEOpen Card
Subtracting numbers in standard formKS3 / GCSEOpen Card
Interpreting standard form on a calculatorKS3 / GCSEOpen Card

Surds and exact values

9 cards
Simplifying a single surdGCSE HigherOpen Card
Expanding brackets containing surdsGCSE HigherOpen Card
Rationalising a single-term denominatorGCSE HigherOpen Card
Rationalising a two-term denominatorGCSE HigherOpen Card
Working with exact multiples of piGCSE HigherOpen Card

Rounding, estimation and bounds

3 cards
Finding a bound from truncationCourse skillOpen Card
Writing a truncation error intervalCourse skillOpen Card
Checking whether an estimate is an overestimate or underestimateCourse skillOpen Card
Ratio, proportion and rates of change107 available

Ratio notation and sharing

22 cards
Writing a ratio from quantitiesKS3 / GCSEOpen Card
Simplifying an integer ratioKS3 / GCSEOpen Card
Simplifying a ratio involving decimalsKS3 / GCSEOpen Card
Simplifying a ratio involving fractionsKS3 / GCSEOpen Card
Converting units before simplifying a ratioKS3 / GCSEOpen Card
Sharing an amount in a two-part ratioKS3 / GCSEOpen Card
Sharing an amount in a three-part ratioKS3 / GCSEOpen Card
Finding the whole from one ratio shareKS3 / GCSEOpen Card
Finding shares from the difference between themKS3 / GCSEOpen Card
Combining two linked ratiosKS3 / GCSEOpen Card
Changing a ratio after adding quantitiesKS3 / GCSEOpen Card
Changing a ratio after removing quantitiesKS3 / GCSEOpen Card
Converting a part-to-part ratio into fractionsKS3 / GCSEOpen Card
Converting fractions into a ratioKS3 / GCSEOpen Card
Distinguishing part-to-part and part-to-whole ratiosKS3 / GCSEOpen Card
Solving an equality of ratiosKS3 / GCSEOpen Card
Finding a ratio after adding to one quantityKS3 / GCSEOpen Card
Finding a ratio after removing from one quantityKS3 / GCSEOpen Card
Sharing an amount when the ratio contains decimalsKS3 / GCSEOpen Card
Checking a ratio allocation against a totalKS3 / GCSEOpen Card

Proportion in context

14 cards
Mixing quantities in a given ratioKS3 / GCSEOpen Card
Concentrations and dilutionKS3 / GCSEOpen Card
Actual distances from a mapKS3 / GCSEOpen Card
Map distances from actual distancesKS3 / GCSEOpen Card
Converting currencies from a given rateKS3 / GCSEOpen Card
Inverse proportion in worker-time problemsKS3 / GCSEOpen Card
Comparing two direct-proportion modelsKS3 / GCSEOpen Card
Distinguishing direct proportion from a non-zero-intercept lineKS3 / GCSEOpen Card
Finding a constant in an inverse-square modelGCSE Higher / IGCSE ExtendedOpen Card

Percentages

16 cards
Finding 10%, 5% and 1% mentallyKS3 / GCSEOpen Card
Finding a percentage by combining simple percentagesKS3 / GCSEOpen Card
Finding a percentage using a multiplierKS3 / GCSEOpen Card
Finding percentages greater than 100%KS3 / GCSEOpen Card
Expressing one amount as a percentage of anotherKS3 / GCSEOpen Card
Finding a percentage increaseKS3 / GCSEOpen Card
Finding a percentage decreaseKS3 / GCSEOpen Card
Increasing an amount by a percentageKS3 / GCSEOpen Card
Decreasing an amount by a percentageKS3 / GCSEOpen Card
Finding an original amount after an increaseKS3 / GCSEOpen Card
Finding an original amount after a decreaseKS3 / GCSEOpen Card
Comparing quantities using percentagesKS3 / GCSEOpen Card
Calculating profit as a percentage of costKS3 / GCSEOpen Card
Calculating loss as a percentage of costKS3 / GCSEOpen Card
Calculating VAT from a stated rateKS3 / GCSEOpen Card
Calculating simple interestKS3 / GCSEOpen Card

Repeated change and finance

12 cards
Compound interest over a fixed number of periodsKS3 / GCSEOpen Card
Depreciation over a fixed number of periodsKS3 / GCSEOpen Card
Population growth using repeated percentagesKS3 / GCSEOpen Card
Successive percentage changesKS3 / GCSEOpen Card
Finding an original value before compound changeKS3 / GCSEOpen Card
Finding a repeated percentage rateGCSE HigherOpen Card
Finding how many periods a target takesKS3 / GCSEOpen Card
Writing a growth or decay formulaKS3 / GCSEOpen Card
Using an iterative financial processGCSE HigherOpen Card
Gross pay from hourly ratesKS3 / GCSEOpen Card
Net pay from stated deductionsKS3 / GCSEOpen Card

Direct and inverse proportion

14 cards
Recognising direct proportion from a tableKS3 / GCSEOpen Card
Recognising direct proportion from a graphKS3 / GCSEOpen Card
Using a direct proportion equationKS3 / GCSEOpen Card
Direct proportion to a squareGCSE HigherOpen Card
Direct proportion to a cubeGCSE HigherOpen Card
Direct proportion to a square rootGCSE HigherOpen Card
Recognising inverse proportion from a tableKS3 / GCSEOpen Card
Recognising inverse proportion from a graphKS3 / GCSEOpen Card
Using an inverse proportion equationKS3 / GCSEOpen Card
Forming from given valuesGCSE HigherOpen Card
Inverse proportion to a squareGCSE HigherOpen Card
Inverse proportion to a cubeGCSE HigherOpen Card
Proportional change without finding the constantGCSE HigherOpen Card

Units and compound measures

19 cards
Converting between volume and capacityKS3 / GCSEOpen Card
Converting between hours and decimal hoursKS3 / GCSEOpen Card
Speed from distance and timeKS3 / GCSEOpen Card
Distance from speed and timeKS3 / GCSEOpen Card
Time from distance and speedKS3 / GCSEOpen Card
Average speed over a whole journeyKS3 / GCSEOpen Card
Density from mass and volumeKS3 / GCSEOpen Card
Mass from density and volumeKS3 / GCSEOpen Card
Volume from mass and densityKS3 / GCSEOpen Card
Pressure from force and areaKS3 / GCSEOpen Card
Force from pressure and areaKS3 / GCSEOpen Card
Area from force and pressureKS3 / GCSEOpen Card
Unit prices and rates of payKS3 / GCSEOpen Card

Motion graphs and rates

10 cards
Reading a distance-time graphKS3 / GCSEOpen Card
Drawing a distance-time graphKS3 / GCSEOpen Card
Speed from a distance-time graphKS3 / GCSEOpen Card
Comparing journeys on a distance-time graphKS3 / GCSEOpen Card
Reading a velocity-time graphKS3 / GCSEOpen Card
Acceleration from a velocity-time graphGCSE Higher / IGCSE ExtendedOpen Card
Distance from a velocity-time graphGCSE Higher / IGCSE ExtendedOpen Card
Drawing a velocity-time graphKS3 / GCSEOpen Card
Average rate of change in contextGCSE HigherOpen Card
Instantaneous rate of change in contextGCSE HigherOpen Card
Geometry and measures220 available

Angle facts

39 cards
Angles on a straight line with algebraGCSE / IGCSEOpen Card
Vertically opposite anglesKS3 / GCSEOpen Card
Vertically opposite angles with algebraGCSE / IGCSEOpen Card
Corresponding angles in parallel linesKS3 / GCSEOpen Card
Alternate angles in parallel linesKS3 / GCSEOpen Card
Co-interior angles in parallel linesKS3 / GCSEOpen Card
Angles in parallel lines with algebraGCSE / IGCSEOpen Card
Angles in a triangle with algebraGCSE / IGCSEOpen Card
Angles in an isosceles triangleKS3 / GCSEOpen Card
Angles in an isosceles triangle with algebraGCSE / IGCSEOpen Card
Angles in an equilateral triangleKS3 / GCSEOpen Card
Angles in an equilateral triangle with algebraGCSE / IGCSEOpen Card
Triangle angle facts: summaryGCSE / IGCSEOpen Card
Angles in a quadrilateral with algebraGCSE / IGCSEOpen Card
Angles in parallelograms and rhombusesGCSE / IGCSEOpen Card
Angles in parallelograms and rhombuses with algebraGCSE / IGCSEOpen Card
Angles in a trapezium with algebraGCSE / IGCSEOpen Card
Angles in a kite with algebraGCSE / IGCSEOpen Card
Angles in rectangles and squaresGCSE / IGCSEOpen Card
Angles in rectangles and squares with algebraGCSE / IGCSEOpen Card
Quadrilateral properties: summaryGCSE / IGCSEOpen Card
Exterior angle of a triangleKS3 / GCSEOpen Card
Number of sides from an exterior angleKS3 / GCSEOpen Card
Number of sides from an interior angleKS3 / GCSEOpen Card
Giving reasons in an angle proofKS3 / GCSEOpen Card
Sum of interior angles of a polygonKS3 / GCSEOpen Card
Interior angles of a regular polygonKS3 / GCSEOpen Card
Interior angles of an irregular polygonGCSE / IGCSEOpen Card
Exterior angles of a polygon add to 360°KS3 / GCSEOpen Card
Exterior angles of a regular polygonKS3 / GCSEOpen Card
Exterior angles of an irregular polygonGCSE / IGCSEOpen Card
Number of sides of a regular polygonGCSE / IGCSEOpen Card
Angles in a polygon with algebraGCSE / IGCSEOpen Card

Circle theorems

14 cards
The angle at the centre is twice the angle at the circumference standing on the same arcGCSE HigherOpen Card
The angle subtended by a diameter at the circumference is a right angleGCSE HigherOpen Card
Angles subtended by the same chord, with their vertices in the same segment, are equalGCSE HigherOpen Card
Opposite angles in a cyclic quadrilateral add to 180°GCSE HigherOpen Card
An exterior angle of a cyclic quadrilateral equals the opposite interior angleGCSE Higher / IGCSE ExtendedOpen Card
A tangent is perpendicular to the radius at the point of contactGCSE HigherOpen Card
The two tangent segments from the same external point to a circle have equal lengthsGCSE HigherOpen Card
Alternate segment theorem: the tangent–chord angle equals the angle in the alternate segmentGCSE HigherOpen Card
The perpendicular from the centre of a circle to a chord bisects the chordGCSE HigherOpen Card
Radii of the same circle are equal, forming an isosceles triangleGCSE Higher / IGCSE ExtendedOpen Card
In the same circle, equal chords subtend equal angles at the centre and equal minor arcsGCSE Higher / IGCSE ExtendedOpen Card
Equal chords of the same circle are the same perpendicular distance from the centreGCSE Higher / IGCSE ExtendedOpen Card
Combining circle theorems with reasonsGCSE HigherOpen Card

Perimeter and area

22 cards
Perimeter of a compound rectilinear shapeKS3 / GCSEOpen Card
Area of a compound shapeTwo rectangles attachedKS3 / GCSEOpen Card
Area of a compound shapeA rectangle and a triangleGCSE / IGCSEOpen Card
Area of a compound shapeMultiple shapesKS3 / GCSEOpen Card
Finding a missing length from an areaKS3 / GCSEOpen Card
Radius or diameter from a circumferenceKS3 / GCSEOpen Card
Radius from the area of a circleKS3 / GCSEOpen Card
Area of a semicircle or quadrantKS3 / GCSEOpen Card
Perimeter of a semicircle or quadrantKS3 / GCSEOpen Card
Sector angle from its areaKS3 / GCSEOpen Card
Sector angle from its arc lengthKS3 / GCSEOpen Card

Geometric language and shapes

21 cards
Points, lines, line segments and raysKS3 / GCSEOpen Card
Parallel and perpendicular linesKS3 / GCSEOpen Card
Naming angles using three lettersKS3 / GCSEOpen Card
Classifying acute, obtuse and reflex anglesKS3 / GCSEOpen Card
Classifying triangles by sidesKS3 / GCSEOpen Card
Classifying triangles by anglesKS3 / GCSEOpen Card
Properties of a parallelogramKS3 / GCSEOpen Card
Regular and irregular polygonsKS3 / GCSEOpen Card
Order of rotational symmetryKS3 / GCSEOpen Card
Circle vocabularyradius, diameter and chordKS3 / GCSEOpen Card
Circle vocabularytangent, arc, sector and segmentKS3 / GCSEOpen Card
Faces, edges and vertices of solidsKS3 / GCSEOpen Card
Identifying prisms and pyramidsKS3 / GCSEOpen Card

Constructions, loci and bearings

19 cards
Measuring an angle with a protractorKS3 / GCSEOpen Card
Constructing a triangle from three sidesKS3 / GCSEOpen Card
Constructing a triangle from two sides and an angleKS3 / GCSEOpen Card
Constructing a perpendicular bisectorKS3 / GCSEOpen Card
Constructing an angle bisectorKS3 / GCSEOpen Card
Constructing a perpendicular from a point on a lineKS3 / GCSEOpen Card
Constructing a perpendicular from a point off a lineKS3 / GCSEOpen Card
Constructing a 60-degree angleKS3 / GCSEOpen Card
Locus a fixed distance from a pointKS3 / GCSEOpen Card
Locus a fixed distance from a line segmentKS3 / GCSEOpen Card
Locus equidistant from two pointsKS3 / GCSEOpen Card
Locus equidistant from two intersecting linesKS3 / GCSEOpen Card
Combining loci to find regionKS3 / GCSEOpen Card
Reading three-figure bearingsKS3 / GCSEOpen Card
Drawing three-figure bearingsKS3 / GCSEOpen Card
Bearings using parallel-line angle factsKS3 / GCSEOpen Card

Transformations and coordinates

15 cards
Finding the centre of enlargementKS3 / GCSEOpen Card
Combining transformationsGCSE HigherOpen Card
Reading a plan or elevationKS3 / GCSEOpen Card
Drawing plans and elevationsKS3 / GCSEOpen Card
Completing a shape from coordinatesKS3 / GCSEOpen Card
Enlargementspositive scale factorsGCSE / IGCSEOpen Card
Enlargementsnegative scale factorsHigherOpen Card
EnlargementsPositive and negative fractional scale factorsHigherOpen Card

Congruence and similarity

17 cards
Recognising congruent trianglesKS3 / GCSEOpen Card
Proving triangles congruentKS3 / GCSEOpen Card
Recognising similar shapesKS3 / GCSEOpen Card
Finding a length scale factorKS3 / GCSEOpen Card
Finding a missing length in similar shapesKS3 / GCSEOpen Card
Finding an area scale factorGCSE HigherOpen Card
Finding a volume scale factorGCSE HigherOpen Card
Length scale factor from an area ratioGCSE HigherOpen Card
Length scale factor from a volume ratioGCSE HigherOpen Card
Deciding whether an area ratio or length ratio is requiredGCSE Higher / IGCSE ExtendedOpen Card
Deciding whether a volume ratio or length ratio is requiredGCSE Higher / IGCSE ExtendedOpen Card
Finding a missing length in overlapping similar trianglesCourse skillOpen Card

Volume and surface area

21 cards
Volume of a triangular prismKS3 / GCSEOpen Card
Volume of a prism with a compound cross-sectionKS3 / GCSEOpen Card
Finding a missing dimension of a prismKS3 / GCSEOpen Card
Volume of a composite solidKS3 / GCSEOpen Card
Surface area of a cylinderKS3 / GCSEOpen Card
Surface area of a hemisphereKS3 / GCSEOpen Card
Surface area of a composite solidKS3 / GCSEOpen Card
Finding a cone's slant height before its surface areaCourse skillOpen Card
Finding a cone's perpendicular height from its slant heightCourse skillOpen Card
Finding a missing radius in a composite solidCourse skillOpen Card

Pythagoras

4 cards
Identifying the hypotenuseKS3 / GCSEOpen Card
Pythagoras with exact surd lengthsGCSE Higher / IGCSE ExtendedOpen Card
Checking whether a triangle is right-angledKS3 / GCSEOpen Card
Pythagoras in three dimensionsGCSE HigherOpen Card

Pythagoras’ theorem

3 cards
Pythagoras - finding the hypotenuseGCSE / IGCSEOpen Card
Pythagoras - finding a shorter sideGCSE / IGCSEOpen Card
Repeated use of PythagorasGCSE / IGCSEOpen Card

Right-angled trigonometry

15 cards
Identifying opposite and adjacent sidesKS3 / GCSEOpen Card
Choosing sine, cosine or tangentGCSE / IGCSEOpen Card
Finding an angle using inverse sineKS3 / GCSEOpen Card
Finding an angle using inverse cosineKS3 / GCSEOpen Card
Finding an angle using inverse tangentKS3 / GCSEOpen Card
Trigonometry in three dimensionsGCSE HigherOpen Card
Finding a length with the sine ratioGCSE / IGCSEOpen Card
Finding a length with the cosine ratioGCSE / IGCSEOpen Card
Finding a length with the tangent ratioGCSE / IGCSEOpen Card
Repeated use of right-angled trigonometryGCSE / IGCSEOpen Card

Non-right-angled trigonometry

11 cards
Sine rulefinding an angleGCSE HigherOpen Card
Sine rulerecognising an obtuse-angle alternativeGCSE HigherOpen Card
Cosine rulefinding a sideGCSE HigherOpen Card
Cosine rulefinding an angleGCSE HigherOpen Card
Choosing between sine and cosine rulesGCSE HigherOpen Card
Area of a triangle using one half GCSE HigherOpen Card
Finding a side from one half GCSE HigherOpen Card
Finding an angle from one half GCSE HigherOpen Card
Bearings using non-right-angled trigonometryGCSE HigherOpen Card
Area of a segment of a circleGCSE HigherOpen Card

Vectors

19 cards
Multiplying a vector by a scalarKS3 / GCSEOpen Card
Finding a route using vectorsKS3 / GCSEOpen Card
Vectors dividing a line in a ratioGCSE HigherOpen Card
Recognising scalar multiples in vector proofsGCSE Higher / IGCSE ExtendedOpen Card
Proving vectors are parallelGCSE HigherOpen Card
Proving points are collinearGCSE HigherOpen Card
Finding one unknown for collinear pointsGCSE Higher / IGCSE ExtendedOpen Card
Proving collinearity with a single parameterGCSE Higher / IGCSE ExtendedOpen Card
Expressing a point on a line using a parameterGCSE Higher / IGCSE ExtendedOpen Card
Comparing coefficients of independent vectorsGCSE Higher / IGCSE ExtendedOpen Card
Forming two vector routes to an intersectionGCSE Higher / IGCSE ExtendedOpen Card
Solving vector proofs with lambda and muGCSE Higher / IGCSE ExtendedOpen Card
Interpreting vector parameters as ratiosGCSE Higher / IGCSE ExtendedOpen Card
Probability45 available

Probability language and single events

8 cards
Using the probability scaleKS3 / GCSEOpen Card
Writing probability as a fraction, decimal or percentageKS3 / GCSEOpen Card
Recognising equally likely outcomesKS3 / GCSEOpen Card
Calculating a theoretical probabilityKS3 / GCSEOpen Card
Finding a complementary probabilityKS3 / GCSEOpen Card
Finding a missing probabilityKS3 / GCSEOpen Card
Probabilities of mutually exclusive eventsKS3 / GCSEOpen Card
Recognising exhaustive outcomesKS3 / GCSEOpen Card

Experiments and expected outcomes

7 cards
Recording outcomes in a frequency tableKS3 / GCSEOpen Card
Calculating relative frequencyKS3 / GCSEOpen Card
Estimating probability from experimental resultsKS3 / GCSEOpen Card
Estimating an expected frequencyKS3 / GCSEOpen Card
Comparing experimental and theoretical probabilityKS3 / GCSEOpen Card
Explaining the effect of sample sizeKS3 / GCSEOpen Card
Assessing fairness from resultsKS3 / GCSEOpen Card

Lists, tables and sets

13 cards
Systematic lists of combined outcomesKS3 / GCSEOpen Card
Drawing a sample-space diagramKS3 / GCSEOpen Card
Using a sample-space diagram to calculate probabilityKS3 / GCSEOpen Card
Completing a two-way tableKS3 / GCSEOpen Card
Probability from a two-way tableKS3 / GCSEOpen Card
Completing a frequency treeKS3 / GCSEOpen Card
Probability from a frequency treeKS3 / GCSEOpen Card
Placing values in a two-set Venn diagramKS3 / GCSEOpen Card
Finding a missing frequency in a Venn diagramKS3 / GCSEOpen Card
Reading union and intersection notationKS3 / GCSEOpen Card
Reading complement notationKS3 / GCSEOpen Card
Shading regions in a two-set Venn diagramKS3 / GCSEOpen Card
Probability from a Venn diagramKS3 / GCSEOpen Card

Combined events and trees

12 cards
Recognising independent eventsKS3 / GCSEOpen Card
Drawing a probability tree with replacementKS3 / GCSEOpen Card
Multiplying probabilities along one branchKS3 / GCSEOpen Card
Adding probabilities across alternative branchesKS3 / GCSEOpen Card
Probability of exactly one successKS3 / GCSEOpen Card
Probability of at least one successKS3 / GCSEOpen Card
Drawing a probability tree without replacementKS3 / GCSEOpen Card
Probabilities from dependent eventsKS3 / GCSEOpen Card
Working backwards to find missing tree probabilityKS3 / GCSEOpen Card
Finding at least one success using a complementCourse skillOpen Card
Finding exactly two successes in three trialsCourse skillOpen Card
Comparing with-replacement and without-replacement probabilitiesCourse skillOpen Card

Conditional probability

5 cards
Conditional probability from a two-way tableGCSE HigherOpen Card
Conditional probability from a Venn diagramGCSE HigherOpen Card
Conditional probability from a tree diagramGCSE HigherOpen Card
Conditional probability using expected frequenciesGCSE HigherOpen Card
Identifying the correct conditional sample spaceGCSE HigherOpen Card
Statistics79 available

Data and sampling

11 cards
Categorical and numerical dataKS3 / GCSEOpen Card
Discrete and continuous dataKS3 / GCSEOpen Card
Primary and secondary dataKS3 / GCSEOpen Card
Identifying biased samplesKS3 / GCSEOpen Card
Simple random samplingGCSE Foundation / IGCSE CoreOpen Card
Systematic samplingGCSE Foundation / IGCSE CoreOpen Card
Stratified sampling calculationsGCSE Higher / IGCSE ExtendedOpen Card
Critiquing questionnaire questionsKS3 / GCSEOpen Card
Interpreting a sample’s limitationsGCSE Foundation / IGCSE CoreOpen Card
Estimating a population quantity from a sampleGCSE Foundation / IGCSE CoreOpen Card

Tables and basic charts

20 cards
Constructing a frequency tableKS3 / GCSEOpen Card
Grouping data into class intervalsKS3 / GCSEOpen Card
Interpreting a pictogram keyKS3 / GCSEOpen Card
Reading a vertical line chartKS3 / GCSEOpen Card
Drawing a vertical line chartKS3 / GCSEOpen Card
Reading a comparative bar chartKS3 / GCSEOpen Card
Calculating pie-chart anglesKS3 / GCSEOpen Card
Finding frequencies from a pie chartKS3 / GCSEOpen Card
Reading a stem-and-leaf diagramKS3 / GCSEOpen Card
Drawing a stem-and-leaf diagramKS3 / GCSEOpen Card
Comparing back-to-back stem-and-leaf diagramsKS3 / GCSEOpen Card
Reading a time-series graphKS3 / GCSEOpen Card
Drawing a time-series graphKS3 / GCSEOpen Card
Choosing a suitable statistical diagramKS3 / GCSEOpen Card
Spotting misleading graphsKS3 / GCSEOpen Card

Averages and spread

19 cards
Finding the mean from a listKS3 / GCSEOpen Card
Finding the median from an odd number of valuesKS3 / GCSEOpen Card
Finding the median from an even number of valuesKS3 / GCSEOpen Card
Finding the mode from a listKS3 / GCSEOpen Card
Finding the range from a listKS3 / GCSEOpen Card
Finding a missing value from the meanKS3 / GCSEOpen Card
Combining means from two groupsKS3 / GCSEOpen Card
Finding the mean from a frequency tableKS3 / GCSEOpen Card
Finding the median from a frequency tableKS3 / GCSEOpen Card
Finding the mode from a frequency tableKS3 / GCSEOpen Card
Estimating the mean from grouped dataKS3 / GCSEOpen Card
Identifying a median classKS3 / GCSEOpen Card
Choosing an appropriate averageKS3 / GCSEOpen Card
Effect of an outlier on averages and rangeKS3 / GCSEOpen Card
Comparing two distributions using average and spreadKS3 / GCSEOpen Card
Finding a missing frequency from a meanCourse skillOpen Card
Finding the change in mean after replacing a valueCourse skillOpen Card
Finding a combined mean when group sizes differCourse skillOpen Card

Scatter graphs

8 cards
Describing direction and strength of correlationKS3 / GCSEOpen Card
Explaining why correlation does not prove causationKS3 / GCSEOpen Card
Drawing a line of best fitKS3 / GCSEOpen Card
Making an interpolated predictionKS3 / GCSEOpen Card
Making an extrapolated predictionKS3 / GCSEOpen Card
Explaining the risk of extrapolationKS3 / GCSEOpen Card
Identifying an outlier on a scatter graphKS3 / GCSEOpen Card

Cumulative frequency and box plots

9 cards
Completing a cumulative-frequency tableGCSE HigherOpen Card
Plotting a cumulative-frequency graphGCSE HigherOpen Card
Estimating a median from cumulative frequencyGCSE HigherOpen Card
Estimating quartiles from cumulative frequencyGCSE HigherOpen Card
Estimating a frequency above or below a valueGCSE HigherOpen Card
Estimating an interquartile rangeGCSE HigherOpen Card
Drawing a box plot from five summary valuesGCSE HigherOpen Card
Reading values from a box plotGCSE HigherOpen Card

Histograms

10 cards
Calculating class widthGCSE Higher / IGCSE ExtendedOpen Card
Calculating frequency densityGCSE Higher / IGCSE ExtendedOpen Card
Drawing a histogram with unequal class widthsGCSE Higher / IGCSE ExtendedOpen Card
Finding a frequency from density and class widthGCSE Higher / IGCSE ExtendedOpen Card
Finding a missing frequency-density scaleGCSE Higher / IGCSE ExtendedOpen Card
Finding a missing frequency from a histogramGCSE Higher / IGCSE ExtendedOpen Card
Estimating frequency within part of a classGCSE Higher / IGCSE ExtendedOpen Card
Comparing histograms and bar chartsGCSE Higher / IGCSE ExtendedOpen Card
Estimating a median position within a histogram classGCSE Higher / IGCSE ExtendedOpen Card
Recovering total frequency from an unlabelled histogram scaleGCSE Higher / IGCSE ExtendedOpen Card

Statistical diagrams

2 cards
Finding the total from one known pie-chart sectorKS3 / GCSEOpen Card
Completing a pie-chart table from one known rowKS3 / GCSEOpen Card