Flashcards
Flashcards
Only what earns marks: exact values, the standard results the formulae booklet does not print, definitions in precise wording, and the slips that lose marks. Grade yourself and the deck schedules each card for just before you would otherwise forget it.
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What is in the collection
Every card, by deck, each one linking to the lesson that teaches it. Open a deck to see what it covers.
Exact trig valuesThe degree-and-radian values the paper expects without a calculator.14 cards
- Exact valueResult
- Exact valueResult
- Exact valueResult
- Exact valueResult
- Exact valueResult
- Exact valueResult
- Exact valueResult
- Exact valueResult
- Exact valueResult
- Degrees to radiansResult
- Degrees to radiansResult
- Degrees to radiansResult
- Degrees to radiansResult
- Without a calculator, state the exact value of cos 30° × tan 60°.Check
Differentiation: standard resultsThe derivatives the formulae booklet does not hand you.14 cards
- Power ruleResult
- ExponentialResult
- Natural logResult
- Sine (x in radians)Result
- Cosine (x in radians)Result
- General exponentialResult
- Chain ruleResult
- Product ruleResult
- State how to connect two rates of changeRecall
- State how to classify a stationary pointRecall
- differentiation from first principlesDefine
- Differentiate y = 3 ln x − cos 2x.Check
- Implicit and parametricResult
- The derivative of cos x is sin x.Spot the error
Integration: standard resultsThe integrals to produce on sight, constant of integration included.12 cards
- Power rule (n ≠ −1)Result
- The n = −1 caseResult
- Exponential (k ≠ 0)Result
- Sine (x in radians)Result
- Cosine (x in radians)Result
- Log integralResult
- State how to choose u when integrating by partsRecall
- State what to do when part of an area lies below the x-axisRecall
- Find the integral of 6e3x with respect to x.Check
- Area under a parametric curveResult
- State how to solve a separable differential equationRecall
- The integral of sin x is cos x.Spot the error
Indices and log lawsThe rewriting rules everything in algebra leans on.10 cards
- Laws of indicesResult
- Negative and fractional indicesResult
- Exponential and log undo each otherResult
- Product lawResult
- Quotient lawResult
- Power lawResult
- logarithmDefine
- Write 2 log 3 + log 4 as a single logarithm.Check
- State how to straighten an exponential or power modelRecall
- log(x + y) is the same as log x + log y.Spot the error
Algebra and functionsThe rewrites and the wordings the first half of every pure paper runs on.8 cards
- DiscriminantResult
- State what completing the square hands youRecall
- State the factor theoremRecall
- State how to prove a line and a curve never meetRecall
- State which graph transformations go the way you do not expectRecall
- State what an inverse function does to the domain and the rangeRecall
- State the partial fraction form to write downRecall
- fg(x) means apply f first, then g.Spot the error
Coordinate geometry and vectorsLines, circles and vectors, and the facts a diagram question expects you to already have.6 cards
- Perpendicular gradient (m ≠ 0)Result
- Circle from the expanded formResult
- State the three circle facts a coordinate question leans onRecall
- State how to turn parametric equations into a cartesian oneRecall
- Magnitude and unit vectorResult
- If A and B have position vectors a and b, the vector from A to B is a + b.Spot the error
Trigonometry: identities and equationsThe identities you must produce unprompted, and the interval trap that eats marks.7 cards
- The other two Pythagorean identitiesResult
- cos 2θ, all three formsResult
- Small angle approximations, θ in radians onlyResult
- State how to find R and α in the harmonic formRecall
- State what to do with the interval when the equation contains 2xRecall
- The sine rule gives sin B = 0.6, so B = 36.9° and the triangle is settled.Spot the error
- sin 2θ is 2 sin θ.Spot the error
Sequences and seriesThe nth terms to write from memory, and the condition that decides whether a series converges.5 cards
Proof and numerical methodsThe wordings a proof question marks you on, and what an approximation is actually worth.5 cards
Key definitionsWording that earns marks, term by term.7 cards
Spot the errorThe favourite wrong turns, and why each one fails.6 cards
- √(a² + b²) simplifies to a + b.Spot the error
- (x + 3)² = x² + 9.Spot the error
- In (x² + 5x)/x², the x² terms cancel to leave 1 + 5x.Spot the error
- If sin x = 0.5 then x = 30° is the complete answer.Spot the error
- Dividing both sides of x² = 4x by x gives x = 4, done.Spot the error
- ln(a)/ln(b) simplifies to ln(a/b).Spot the error
Statistics essentialsThe formulas the booklet keeps to itself, and the wording that earns marks.16 cards
- HistogramsResult
- Variance from sumsResult
- Outlier fencesResult
- Addition ruleResult
- Conditional probabilityResult
- The sample mean's distributionResult
- independent eventsDefine
- StandardisingResult
- actual significance levelDefine
- State the effect of coding on the mean and the standard deviationRecall
- A firm has 900 full-time and 300 part-time staff. How many of each go into a stratified sample of 60?Check
- X ~ B(20, 0.15). Write P(X ≥ 5) in calculator-ready cumulative form.Check
- One fair die is rolled; X is the score. Name the distribution of X. Does the total of two dice have the same one?Check
- In a histogram, the tallest bar holds the most values.Spot the error
- A strong correlation shows that one variable causes the other.Spot the error
- Once you have the regression line you can predict y for any x you like.Spot the error
Mechanics essentialsForces, friction, moments and the projectile split, ready to quote.15 cards
- WeightResult
- MomentsResult
- The friction lawResult
- Projectile componentsResult
- Weight on a slopeResult
- Variable accelerationResult
- State what each modelling word removesRecall
- limiting equilibriumDefine
- uniform beamDefine
- A 5 kg crate is pulled by 30 N against 10 N of resistance. Find its acceleration.Check
- Masses of 7 kg and 3 kg hang over a smooth pulley. Write the two equations of motion.Check
- At the top of its flight, a projectile's acceleration is zero.Spot the error
- A moving object must have a force pushing it along.Spot the error
- State the method for a particle in equilibriumRecall
- A block resting on a rough slope has friction of size μR.Spot the error
Further Maths: core resultsThe results a Core Pure paper expects on demand, from De Moivre to the auxiliary equation.19 cards
- State how to divide by a complex numberRecall
- State which matrix acts first in a productRecall
- De Moivre's theoremResult
- Multiplying complex numbersResult
- State the conjugate root theorem and what it is forRecall
- State where the nth roots of a non-zero complex number sitRecall
- 2 × 2 determinant and inverseResult
- State what the determinant of a transformation matrix tells youRecall
- Cubic root relationsResult
- State how to sum a series that does not start at r = 1Recall
- State the two ways to get a Maclaurin seriesRecall
- Volume of revolutionResult
- cosh in terms of eResult
- Hyperbolic identityResult
- Logarithmic formResult
- Polar areaResult
- Integrating factorResult
- Second order equationsResult
- State which particular integral to tryRecall
Further Maths: definitions and slipsThe wordings that earn marks and the traps that lose them.11 cards
- principal argumentDefine
- invariant lineDefine
- improper integralDefine
- State the three ways to write a plane, and how to move between themRecall
- Evaluate (1 + i)⁴ without expanding four brackets.Check
- Find the distance from the origin to the plane 2x + 2y + z = 9.Check
- Find the mean value of f(x) = x³ on [0, 2].Check
- Differentiating cosh introduces a minus sign, just as cos does.Spot the error
- Polar area is the integral of r dθ, by analogy with area under a graph.Spot the error
- Once the inductive step is proved, the statement holds for all n.Spot the error
- State the trick for an induction divisibility proofRecall
Further Pure 1: results and formsThe option paper's own toolkit: t-formulae, conic constants, cross products and difference formulae.12 cards
- t-formulaResult
- t-formulaResult
- Weierstrass substitutionResult
- State how to build a series solution to a differential equationRecall
- ParabolaResult
- Ellipse against hyperbola: which way round?Result
- State how to get the tangent to a conic at a parametric pointRecall
- Vector productResult
- Scalar triple productResult
- State the condition Simpson's rule needsRecall
- L'Hospital's ruleDefine
- To solve x/(x − 2) < 3, multiply both sides by x − 2 and solve the result.Spot the error
Further Statistics 1: distributions and testsMeans, variances and test machinery for the distributions the option paper adds.14 cards
- Discrete varianceResult
- Linear transformationResult
- PoissonResult
- GeometricResult
- Negative binomialResult
- State what the Central Limit Theorem buys youRecall
- State how a Poisson hypothesis test differs from a binomial oneRecall
- Goodness of fitResult
- Contingency tableResult
- Generating functionResult
- Variance from a PGFResult
- power of a testDefine
- A test at the 5% level is wrong 5% of the time.Spot the error
- A goodness-of-fit test has 6 classes after pooling, with one parameter estimated from the data. State the degrees of freedom.Check
Further Pure 2: groups, matrices and number theoryAxioms, eigen-machinery, Argand transformations and the modular arithmetic the second pure option adds.15 cards
- groupDefine
- Lagrange's theoremDefine
- Reduction formulaResult
- Arc lengthResult
- Surface of revolutionResult
- EigenvaluesResult
- DiagonalisationResult
- Cayley-Hamilton theoremDefine
- Apollonius locusDefine
- InversionResult
- Fermat's little theoremResult
- Bezout's identityDefine
- Recurrence relationsResult
- The letters of BANANA can be arranged in 6! ways.Spot the error
- A group has order 8. Explain why it cannot contain an element of order 3.Check
Further Statistics 2: regression, densities and testsLeast squares, continuous distributions, and the intervals and tests that follow once the variance is unknown.15 cards
- Least squaresResult
- residualDefine
- Density and distributionResult
- Continuous mean and varianceResult
- positive skewDefine
- Continuous uniformResult
- Correlation coefficients (Spearman assumes no tied ranks)Result
- State the rules for the correlation testRecall
- Combining independent normalsResult
- Standard error and interval, σ knownResult
- Difference of two meansResult
- Testing a varianceResult
- Pooled varianceResult
- A 95% confidence interval has a 95% chance of containing the population mean.Spot the error
- Samples of sizes 13 and 9 give variances 24.5 and 8.2. State the F statistic and its degrees of freedom for the alternative that the first population is the more variable.Check
Further Mechanics 1: impulse, energy and collisionsMomentum, Hooke's law and the restitution machinery the first mechanics option runs on.13 cards
- ImpulseResult
- conservation of momentumDefine
- State how impulse works in two dimensionsRecall
- Work and power, θ between force and displacementResult
- work-energy principleDefine
- Hooke's lawResult
- Elastic energyResult
- Newton's law of restitutionResult
- State what happens to momentum and kinetic energy in an impactRecall
- Bouncing ball, dropped from height hResult
- State the rule for oblique impact on a smooth surfaceRecall
- A ball that bounces back off a wall at the speed it arrived has received no impulse.Spot the error
- Why is momentum not conserved when a ball bounces off the floor?Check
Further Mechanics 2: circles, balance and oscillationRadial acceleration, centres of mass, and the simple harmonic condition that ties the second mechanics option together.13 cards
- Circular motionResult
- Banked trackResult
- State the condition for completing a vertical circleRecall
- Centre of massResult
- Explain how a lamina and a framework differRecall
- Centre of mass by integrationResult
- Block of width 2a and height 2h on a slopeResult
- State how to choose the form of accelerationRecall
- Simple harmonic motionResult
- Speed in simple harmonic motionResult
- Spring oscillationResult
- A particle going round a circle at constant speed has no acceleration.Spot the error
- A lamina is suspended freely from a corner. Where does its centre of mass end up?Check
Decision Mathematics 1: algorithms and networksThe definitions and stopping conditions the first decision paper turns on.15 cards
- order of an algorithmDefine
- State the bin packing lower boundRecall
- Eulerian and semi-EulerianDefine
- minimum spanning treeDefine
- Explain how Prim and Kruskal differRecall
- State Dijkstra's ruleRecall
- Route inspectionResult
- State the travelling salesman lower boundRecall
- critical activityDefine
- Total floatResult
- Lower bound on workersResult
- slack, surplus and artificialDefine
- State the Simplex rulesRecall
- The nearest neighbour algorithm gives the shortest tour.Spot the error
- Why must the number of odd nodes in any graph be even?Check
Decision Mathematics 2: allocation, flow and gamesMoving goods, assigning jobs, pushing flow and choosing under uncertainty.19 cards
- north-west corner methodDefine
- State the m + n − 1 rule for a transportation problemRecall
- Improvement indexResult
- Explain the stepping-stone loopRecall
- Hungarian reductionDefine
- State the minimum lines test and what to do when it failsRecall
- Explain how to maximise an allocationRecall
- capacity of a cutDefine
- Max-flow min-cut theoremResult
- flow-augmenting pathDefine
- Bellman's principle of optimalityDefine
- Explain play safe and stable solutionsRecall
- dominanceDefine
- Explain how to solve a mixed gameRecall
- expected monetary valueDefine
- State how to work back through a decision treeRecall
- The entering cell is the unused cell with the lowest cost in the table.Spot the error
- Once every route from source to sink contains a full arc, the flow is maximal.Spot the error
- Why might a firm reject the option with the highest expected monetary value?Check