Direct and Inverse Proportion GCSE revision and worksheets

Direct and inverse proportion require a good understanding of algebra. If you are revising for your GCSE Maths exams and you are looking to practice proportionality questions then the direct and inverse proportion questions and worksheets below will help. From rearranging formula to substitution of numbers in to those formulae, proportionality is a challenge topic for many GCSE Maths students.

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What you need to know

What you need to know:

If two quantities, A, B, are directly proportional, then as you increase one the other also increases by a specific amount determined by a fixed number called the constant of proportionality. To denote this, we write A \propto B (said “A is proportional to B”), from which you should be able to write down the equation A = kB, where k is the aforementioned constant of proportionality.

If two quantities, C, D, are inversely proportional, then this is equivalent to saying that C is proportional to \frac{1}{D} (so as one increases, the other decreases). We write C \propto \frac{1}{D} from which you should be able to obtain the equation C = \frac{k}{D}, again where k is the (not necessarily the same as previously) constant of proportionality.

You should fully understand these definitions, firstly. You are also expected to know how to:

  • Determine the constant of proportionality between two quantities, and then use your information to calculate new values of the quantities in question;
  • Interpret (and in the higher course, also form them yourself) equations which involve both direct and inverse proportionality;
  • Understand and relate the proportionality equations to their graphs (there are only two shapes of graph concerned here, all that changes is how steep they are).

Are you looking for proportionality worksheets? Do you want locate more direct and inverse proportion questions? If you are a GCSE Maths tutor or a Maths teacher in secondary school then these proportionality resources should be useful to you either way. With worksheets which can be used as homework and revision tests which are a great way to either introduce the topic or refresh it, Maths Made Easy has everything you need in order to effectively teach proportionality. See our GCSE Maths revision page for more resources.

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