A Level Mathematics (9709) Notes

Every chapter of the mathematics syllabus for Cambridge A Level 9709, in the order the book takes them. 38 chapters have a finished lesson — notes, worked examples, a graph you can move, flashcards and a quiz. The rest are mapped and being written.

Also called AS Level, Cambridge A Level, CAIE A Level.

01

Pure Mathematics 1

▸Quadratic EquationsStandard form, the three methods of solution, and the discriminant · 20 min · 6 questions→▸Functions and GraphsDomain, range, and the shapes you should recognise before plotting a point · 20 min · 8 questions→▸Introduction to Analytic GeometryLines as equations, and the standard distances worth memorising · 20 min · 8 questions→▸Circular MeasureThe angle unit that makes arc length and sector area almost trivial · 22 min · 8 questions→▸TrigonometryOne circle explains every wave you will ever meet · 18 min · 6 questions→▸Sequences and SeriesPatterns with a rule, and what happens when you add them all up · 22 min · 8 questions→▸CalculusRates of change, and areas under curves · 22 min · 6 questions→▸IntegrationAdding up infinitely many infinitely thin slices · 22 min · 6 questions→

02

Pure Mathematics 2

▸The Modulus FunctionSize without sign, and the two cases that always come with it · 20 min · 8 questions→▸Division of PolynomialsLong division, and the two theorems that make most of it unnecessary · 18 min · 8 questions→▸LogarithmsThe exponent, written the other way round · 20 min · 8 questions→▸Trigonometric Identities and EquationsSix functions, a handful of identities, and how to pick the right one · 26 min · 8 questions→▸CalculusRates of change, and areas under curves · 22 min · 6 questions→▸IntegrationAdding up infinitely many infinitely thin slices · 22 min · 6 questions→▸Numerical Solution of EquationsFinding a root when there is no formula to rearrange · 22 min · 8 questions→

03

Pure Mathematics 3

▸The Modulus FunctionSize without sign, and the two cases that always come with it · 20 min · 8 questions→▸Division of PolynomialsLong division, and the two theorems that make most of it unnecessary · 18 min · 8 questions→▸Partial FractionsTaking a single fraction apart again, because the pieces are easier to work with · 18 min · 8 questions→▸Mathematical Induction and the Binomial TheoremProving infinitely many statements at once, and expanding a bracket without multiplying it out · 22 min · 8 questions→▸LogarithmsThe exponent, written the other way round · 20 min · 8 questions→▸Trigonometric Identities and EquationsSix functions, a handful of identities, and how to pick the right one · 26 min · 8 questions→▸CalculusRates of change, and areas under curves · 22 min · 6 questions→▸IntegrationAdding up infinitely many infinitely thin slices · 22 min · 6 questions→▸Numerical Solution of EquationsFinding a root when there is no formula to rearrange · 22 min · 8 questions→▸Vectors in SpaceThree dimensions, and the two ways of multiplying vectors · 22 min · 8 questions→▸Differential EquationsTurning a sentence about a rate of change into a function of time · 24 min · 8 questions→▸Complex NumbersWhat happens when you stop refusing to take the square root of −1 · 20 min · 8 questions→▸Complex Numbers in Polar FormModulus and argument, and why multiplying becomes rotating · 20 min · 8 questions→

04

Mechanics

▸Vectors & EquilibriumAdding quantities that point somewhere · 18 min · 6 questions→▸Friction, Slopes and Connected ParticlesWhat holds a block still, and what happens when two are tied together · 26 min · 8 questions→▸KinematicsDescribing motion: displacement, velocity, acceleration and the graphs · 28 min · 12 questions→▸MomentumThe quantity that survives every collision, and why it makes cars safer · 20 min · 8 questions→▸MechanicsMotion, forces and energy · 24 min · 6 questions→▸Work, Energy & PowerThe bookkeeping that never fails to balance · 18 min · 6 questions→

05

Probability & Statistics 1

▸Information HandlingFrequency tables, the three averages, and how far the data spreads · 20 min · 8 questions→▸Information Handling (Grouped Data)Histograms, cumulative frequency, and the quartiles read off an ogive · 20 min · 8 questions→▸Scatter Diagrams and CorrelationLooking for a relationship between two things, and not overclaiming when you find one · 18 min · 8 questions→▸Permutations and CombinationsCounting arrangements and selections without listing them · 20 min · 8 questions→▸ProbabilityMeasuring how likely something is, on a scale from 0 to 1 · 20 min · 8 questions→▸Probability of Combined EventsAdding, multiplying, and knowing which of the two the question wants · 20 min · 8 questions→▸Discrete Random VariablesA list of outcomes with probabilities attached, and the two numbers that summarise it · 24 min · 8 questions→▸The Normal DistributionOne curve, one table, and the trick of relabelling the axis · 26 min · 8 questions→

06

Probability & Statistics 2

▸The Poisson DistributionCounting rare events when there is no fixed number of trials · 22 min · 8 questions→▸Linear Combinations of Random VariablesWhat happens to the mean and the variance when variables are scaled and added · 20 min · 8 questions→▸Continuous Random VariablesWhen the sum becomes an integral · 22 min · 8 questions→▸Sampling and EstimationWhat a sample can tell you about a population it came from · 24 min · 8 questions→▸Hypothesis TestingDeciding whether the evidence is strong enough to abandon an assumption · 26 min · 8 questions→