The full Cambridge International AS & A Level Mathematics course: Pure Mathematics 1, 2 and 3, Mechanics, and Probability & Statistics 1 and 2. Every topic is explained in plain language with fully worked examples.
Lesson 1 is free to try. The other 194 lessons in Mathematics and its exam practice are for schools on RudimentaryLabs.
Complete the square, use the discriminant and solve quadratic equations, inequalities and simultaneous equations.
Domain, range, composite and inverse functions, and how transformations move and stretch graphs.
Straight lines, circles and where lines and curves meet.
Radians, arcs and sectors, trigonometric graphs, exact values, identities and equations.
Binomial expansions and arithmetic and geometric progressions, including sums to infinity.
Gradients of curves, the chain rule, tangents and normals, rates of change and stationary points.
Integration as reverse differentiation, definite integrals, areas and volumes of revolution.
The modulus function, polynomial division, the factor theorem, partial fractions and binomial expansions for any rational power.
Laws of logarithms, the exponential function and natural logarithm, exponential equations and turning curves into straight lines.
Secant, cosecant and cotangent, compound and double angle formulae, and combining sine and cosine into a single wave.
Derivatives of exponential, logarithmic and trigonometric functions, the product and quotient rules, and parametric and implicit differentiation.
Integrating exponentials, reciprocals and trigonometric functions, and estimating integrals with the trapezium rule.
Partial fractions, the f'(x) over f(x) pattern, integration by parts and integration by substitution.
Locating roots by sign change and finding them to any accuracy with iteration.
Vectors in two and three dimensions, lines in vector form, and the scalar product.
Forming and solving first order differential equations by separating the variables, and interpreting the solutions.
Complex arithmetic, the Argand diagram, polar and exponential forms, roots of polynomials and loci.
Force diagrams, resolving forces, equilibrium, friction and Newton's third law.
Displacement, velocity and acceleration, motion graphs, constant acceleration formulae and calculus.
Linear momentum and its conservation in collisions.
Using F = ma for particles moving vertically, on slopes and connected by strings or rods.
Work done by forces, kinetic and potential energy, conservation of energy and power.
Choosing and drawing data displays, and calculating and comparing averages and spread.
Counting arrangements and selections, with repeated items and restrictions.
Calculating probabilities by counting, combining events, independence and conditional probability.
Probability distributions, expectation and variance, and the binomial and geometric distributions.
Modelling with the normal distribution, standardising, and approximating the binomial.
Modelling random events with the Poisson distribution and using it and the normal as approximations.
Expectation and variance of scaled and combined random variables, including normal and Poisson sums.
Probability density functions and how to find probabilities, means, variances and medians from them.
Random samples, the distribution of the sample mean, unbiased estimates and confidence intervals.
Setting up and carrying out hypothesis tests for binomial, Poisson and normal situations, and the errors they can make.