High School (11–12) Mathematics

Beyond the textbook: the locus of a moving point, the bisectors of the angles between two lines, and the reflection of a point or ray in a line. Then the centres of a triangle and pairs of lines, the straight-line problems that JEE and A-Level Further Maths ask most, with a full timed paper.

The series that JEE, A-Level Further Maths and IB Higher Level ask most: sums of n, n squared and n cubed, arithmetico-geometric series, telescoping sums and the method of differences, with a full timed paper.

The counting problems that JEE, A-Level Further Maths and maths olympiads set most: circular arrangements, distributing objects into groups, the gaps method, and counting by complements and cases, with a full timed paper.

Beyond the textbook: the polar form, multiplication as a rotation, the cube roots of unity, and loci on the Argand plane, the parts that JEE, A-Level Further Maths and IB Higher Level ask about most, with a full timed paper.

What the exams add to this chapter: solving trigonometric equations, the greatest and least values of an expression, and identities in a triangle, each with worked examples, and a full timed paper.

Can you find a function when you know only how it behaves? If f(x + y) = f(x) + f(y) for all x and y, what can f be? In this course we read three ideas that the main chapter only touches: equations whose unknown is a function, the number of solutions of an equation read from a graph (with the fixed points of a function), and the counting of onto functions. Then we solve harder problems at the level of JEE Advanced, A-Level Further Maths and IB Higher Level, and take an advanced timed test.