Ages 17+ · Grade 11 and beyond

Advanced Maths (Ages 17+)

Advanced maths introduces the tools used in university science, engineering, economics and computing. Calculus is the centrepiece, describing rates of change and accumulated totals, alongside more formal work with functions and statistics.

The lessons here assume solid algebra. They focus on intuition first, then technique, then application.

By the end of this stage

Understand limits intuitively and evaluate simple ones
Differentiate polynomials and composite functions using the chain rule
Integrate polynomials and use definite integrals to find areas
Work with function notation, domain, range and transformations of graphs
Calculate and interpret standard deviation

Lessons for this level

Algebra

Data & Statistics

Standard Deviationσ

Calculus

Money & Finance

Compound Interest%

Try this

The best-shaped box

Take a 20 cm × 20 cm sheet of card and imagine cutting a square of side $x$ from each corner.
Fold up the sides to make an open box. Show that its volume is $V = x(20 - 2x)^2$ .
Differentiate $V$ and set $\tfrac{dV}{dx} = 0$ to find the value of $x$ that gives the largest volume.
Build the box and check your answer against a few other cut sizes.