Year 11 - Maths
Abstract inverse proportion
Direct and inverse proportion
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Study Guides
This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit, pupils learn how to represent direct and inverse proportion algebraically as an extension of work done in the linear graphs unit.
Lesson Summary
You will learn to identify, write and solve inverse proportion questions involving algebra.
Key Notes
- Inverse proportion equations are of the form y = k ÷ x^n
- k is the constant of proportionality.
- To find k, you can use a pair of values.
Vocabulary To Learn
- Inversely proportional: Two variables are inversely proportional if there is a constant multiplicative relationship between one variable and the reciprocal of the other.
Common Mistakes To Avoid
- For all direct and inverse proportions, the multiplicative relationship is with x and y.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Inverse proportion equations are of the form y = k ÷ x^n. k is the constant of proportionality.
2. Use this key word in a maths sentence and explain it clearly. 'Inversely proportional'
Two variables are inversely proportional if there is a constant multiplicative relationship between one variable and the reciprocal of the other. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: For all direct and inverse proportions, the multiplicative relationship is with x and y. Correction: The multiplicative relationship whether direct or inverse can be shown as y and x^n. Show a ratio table of y and 1/x^2 and a table of y and 1/x. The inverse multiplicative relationship is seen with y and 1/x^2 and not with 1/x.
More Lessons In This Unit
- Abstract direct proportion Study Guide
- Checking and securing understanding of direct proportion graphs Study Guide
- Checking and securing understanding of inverse proportion graphs Study Guide
- Finding the constant of proportionality for direct proportion Study Guide
- Finding the constant of proportionality for directly proportional relationships Study Guide
- Finding the constant of proportionality for inverse proportion Study Guide
- Problem solving with direct and inverse proportion Study Guide
- Proportion modelled algebraically Study Guide
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