O Level Mathematics (4024) Notes

Every chapter of the mathematics syllabus for Cambridge O Level 4024, in the order the book takes them. 32 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 Cambridge O Level, CAIE O Level.

01

Number

▸Real NumbersHow the number system is built, and what a radical really is · 20 min · 8 questions→▸Sets and FunctionsCollections, the operations on them, and the rule that turns one set into another · 22 min · 8 questions→▸Indices, Roots and Standard FormThe laws of powers, and a way to write numbers too big to say · 20 min · 8 questions→▸Fractions, Decimals and PercentagesThree ways of writing the same thing, and the reverse percentage everybody gets wrong · 20 min · 8 questions→▸Estimation and Limits of AccuracyRounding on purpose, and knowing how wrong an answer might be · 18 min · 8 questions→▸Ratio, Proportion and RatesComparing quantities, and knowing whether more means more or less · 20 min · 8 questions→▸Money, Time and GrowthWages, currency, timetables, and quantities that grow by a percentage each period · 18 min · 8 questions→

02

Algebra and graphs

▸Introduction to AlgebraLetters standing for numbers, and the rules that do not change because of it · 18 min · 8 questions→▸Factorization and Algebraic ManipulationTurning a sum back into a product, and the identities worth knowing by heart · 22 min · 8 questions→▸Algebraic FractionsCancelling safely, and never forgetting what you are not allowed to divide by · 20 min · 8 questions→▸Linear Equations and InequalitiesSolving for one unknown, and what changes when the equals sign becomes a less-than · 20 min · 8 questions→▸Quadratic EquationsStandard form, the three methods of solution, and the discriminant · 20 min · 6 questions→▸Sequences and SeriesPatterns with a rule, and what happens when you add them all up · 22 min · 8 questions→▸Graphs in Practical SituationsWhat the gradient means, what the area means, and when neither means anything · 18 min · 8 questions→▸Graphs of FunctionsPlotting a curve, and reading answers off it · 20 min · 8 questions→▸Functions and GraphsDomain, range, and the shapes you should recognise before plotting a point · 20 min · 8 questions→

03

Coordinate geometry

▸Coordinate GeometryDistance, midpoint, gradient — all three from one right-angled triangle · 20 min · 8 questions→

04

Geometry

▸Angles and PolygonsThe angle facts that generate every other one, and the polygon formulas that follow · 20 min · 8 questions→▸Loci and ConstructionWhere a point can be, drawn with a straight edge and a pair of compasses · 18 min · 8 questions→▸Similar FiguresSame shape, different size — and what that does to areas and volumes · 20 min · 8 questions→▸Transformations and SymmetryMoving a shape, and describing exactly what you did · 20 min · 8 questions→▸Tangent and Angles of a CircleSix theorems that turn a diagram into a one-line calculation · 22 min · 8 questions→▸Chords and Arcs of a CircleWhat the centre knows about every chord drawn in the circle · 20 min · 8 questions→

05

Mensuration

▸Area, Perimeter and UnitsMeasuring flat shapes, and the unit conversions that trip everyone up · 20 min · 8 questions→▸Surface Area and VolumeSolids, and the difference between covering one and filling it · 20 min · 8 questions→

06

Trigonometry

▸TrigonometryOne circle explains every wave you will ever meet · 18 min · 6 questions→

07

Transformations and vectors

▸Transformations and SymmetryMoving a shape, and describing exactly what you did · 20 min · 8 questions→▸Vectors in a PlaneQuantities that carry a direction, and the algebra that handles them · 20 min · 8 questions→

08

Probability

▸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→

09

Statistics

▸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→