High School (11–12) Mathematics

Beyond the textbook. Find the plane through a line and a point, the plane through two lines, and the plane in a whole family. Reflect a point in a plane or a line, find a shortest path that bounces off a mirror, and bisect the angle between two planes. It is at the level of JEE Advanced, A-Level Further Maths and IB Higher Level, with a full timed paper.

Beyond the textbook. Turn an equation that is not standard into one that is, by a substitution. Solve Bernoulli equations, exact equations and equations of the form $\dfrac{dy}{dx} = f(ax + by + c)$

Beyond the textbook. Build reduction formulas that bring a hard integral down to an easy one, use the symmetry properties on harder integrals, and turn limits of sums into integrals. Then compare integrals without evaluating them, and differentiate an integral whose limits depend on $x$. It is at the level of JEE Advanced, A-Level Further Maths and IB Higher Level, with a full timed paper.

Beyond the textbook. Find where absolute-value, greatest-integer and piecewise functions fail to be differentiable. See what a functional equation such as f(x + y) = f(x) + f(y) forces when f is continuous at one point. Then find patterns in the n-th derivative with Leibniz's rule. It is at the level of JEE Advanced, A-Level Further Maths and IB Higher Level, with a full timed paper.

Beyond the textbook: the greatest term and the greatest coefficient, and the coefficient of a power in a product of expansions. Then sums of series with binomial coefficients, the problems that JEE and A-Level Further Maths ask most, with a full timed paper.

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.