Course · Mathematics
Mathematics.
Numbers first, then algebra, functions, geometry and trigonometry, each idea built on the one before.
The course, unit by unit
Units
19 units · 75 lessons · about 28 hours
Jump to a unit 19
Number and algebra
4 units · 16 lessons
Unit 1 · 4 lessons
Numbers
The foundations: negative numbers, fractions and decimals, percentages, and the order of operations with powers and roots.
Unit 2 · 4 lessons
Ratio and scale
Comparing amounts by multiplying: ratio and proportion, converting units, scientific notation, and orders of magnitude.
Unit 3 · 4 lessons
Algebraic expressions
Letters that stand for numbers: like terms, expanding brackets and factorising, with every product drawn as a rectangle.
Unit 4 · 4 lessons
Linear equations
Solving an equation step by step, inequalities, rearranging a formula, and two equations in two unknowns.
Lines, curves and shapes
4 units · 17 lessons
Unit 5 · 4 lessons
The linear function
The line y = mx + n up close: slope as rise over run, where it crosses the axes, and slope as a rate of change.
Unit 6 · 4 lessons
The quadratic function
The parabola up close: which way it opens, how to shift it, how many roots it has, and the vertex form.
Unit 7 · 5 lessons
Geometry
Angles and parallel lines, triangles, the areas of polygons and the circle, Pythagoras, similar triangles, and volume.
Unit 8 · 4 lessons
Trigonometry
Sine, cosine and tangent in a right triangle, the unit circle and radians, and vectors and their components.
The plane and its transformations
3 units · 9 lessons
Unit 9 · 3 lessons
Vectors and transformations
A matrix as a map of the plane: turns, stretches, shears and flips, the determinant, and symmetry groups.
Unit 10 · 3 lessons
Complex numbers
The number i and the complex plane: multiplying as turning, Euler’s formula, and a square wave built from sines.
Unit 11 · 3 lessons
Conic sections
Circle, ellipse, parabola and hyperbola as slices of a cone: eccentricity, the foci, and Dandelin spheres.
Growth, change and chance
6 units · 25 lessons
Unit 12 · 4 lessons
Exponents and logarithms
Amounts that grow by multiplying: exponential growth, rates in per cent, logarithms that ask "how many times?", and half-life.
Unit 13 · 4 lessons
Sequences and series
Arithmetic and geometric sequences, their sums, endless sums with a finite total, and Fibonacci in a sunflower.
Unit 14 · 4 lessons
Probability
Counting outcomes with a tree and a table, probability as a fraction, combined events, and why many tosses form a bell.
Unit 15 · 4 lessons
Calculus
How fast something changes, the derivative, and how much it adds up to, the integral, joined by the fundamental theorem.
Unit 16 · 5 lessons
Statistics
Many measurements in a few numbers: averages, spread, histograms, the bell curve, correlation and the line of best fit.
Unit 17 · 4 lessons
Conditional probability
How new information changes a chance: "given that", independent events, probability trees, and Bayes' theorem.
Optional enrichment
2 units · 8 lessons
Unit 18 · 5 lessons
Shapes and spaces
Optional enrichment: the five Platonic solids, a cube in four dimensions, knots, a one-sided loop, and curved triangles.
Unit 19 · 3 lessons
Patterns and chance
Optional enrichment: chaos in a double pendulum, fractals and their dimension, and the prisoner's dilemma.