Four challenging exam-like questions with fully worked out solutions for A level and IB students who want to test their knowledge of volumes of revolution (C4 Integration). In each question, a solid of revolution has to be subtracted from or added to the integral. The curve in one question is described by parametric equations. Another question uses trigonometric functions. The problem of finding the radius and height of cone/cylinder, is addressed in the solutions.

This is a worksheet for GCSE students who want a challenge. Six parabolas are given with only a bit of extra information, but enough to determine the quadratic equation for each of them. Solutions are included.

This is a worksheet for year 10 and year 11 students who know completing the square, but need more practice on hard cases. The worksheet deals with two difficulties: 1. The coefficient of x is not an even number, which means fractions are needed. 2. The coefficient of x^2 does not equal 1. Solutions are included in the file.

Four questions about the domain and range of a function. It deals with the inverse of a function and its reciprocal. Solutions included.