Algebraic methods in real-life applications (Higher GCSE simultaneous & quadratic equations)

Worksheet consists of four longer, exam-style exercises based on real-life applications, covering force, mass and acceleration (two exercises: one about force exerted by a factory drop-hammer, the other about the acceleration and mass of racing cars), manufacturing costs (one exercise: about unit costs and areas of carpet rolls made in a factory) and density, mass and volume (one exercise: finding densities and volumes of two new types of plastics developed in a laboratory). All exercises require simultaneous equations to be constructed by interpretation of the problem. The first exercise leads to a linear equation, the rest to quadratic equations that must be solved by either completing the square or using the Quadratic Formula. A short introduction is given for each set of exercises to give students some insight into the concepts on which they are based. The questions are challenging but are also sort of 'formulaic' in that once you know how to do one the rest become much easier. If you want to work through an example first with your students then check out my free resource entitled "GCSE Higher exam-style quadratic problem", which includes a fully-worked model answer. The latter is a density, mass and volume problem very similar to the one in this resource except that the numbers used are different, thus giving totally different results.

DOCX and PDF worksheets supplied along with fully-worked model answers in JPEG format.