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).<br /> In each question, a solid of revolution has to be subtracted from or added to the integral. <br /> The curve in one question is described by parametric equations. Another question uses trigonometric functions. <br /> 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: <br /> 1. The coefficient of x is not an even number, which means fractions are needed. <br /> 2. The coefficient of x^2 does not equal 1.<br /> 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.