This worksheet is aimed at the new Higher maths specification from 2017 onwards. It consists of three challenging, longer, exam-style exercises based on real-life applications, using formula for cylinders and spheres. The first sheet lists the formula students will need to use. Diagrams, created with Word drawing objects, are used to illustrate all three exercises. Each exercise has multiple parts. To solve the problems the 1st exercise requires additional skills with ratios; the 2nd both simultaneous and quadratic equations (this is hinted at in the question by saying 'Using an algebraic method..'); and the 3rd requiring creation of an equation that links the relative volumes of a cylinder and a hemisphere. Calculation of the surface area of the machine part (see cover image) in Exercise 3 is more complex and challenging than normal, though it is entirely logical. It is not too difficult as long as a methodical approach is taken. This exercise concludes by using density and volume to calculate the mass of zinc required to galvanise a production run of the machine part. There are also various measurement conversions required such as converting cubic millimeters to cubic centimetres and litres, and grams to kilograms.
DOCX and PDF worksheets supplied along with 9 pages of fully-worked model answers in JPEG format.