Year 11 - Maths
Checking and securing understanding of inverse proportion graphs
Direct and inverse proportion
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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 inverse proportion graphs from their features and can use the graph to create an equation to algebraically model this relationship.
Key Notes
- Inverse proportion can be recognised graphically.
- An inverse proportion graph is always a curve that does not touch either axis.
- The equation is of the form y = k/x
- k is the constant of proportionality.
Vocabulary To Learn
- Inverse proportion: 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
- Assuming the the graph will eventually intercept the axes.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Inverse proportion can be recognised graphically. An inverse proportion graph is always a curve that does not touch either axis.
2. Use this key word in a maths sentence and explain it clearly. 'Inverse proportion'
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: Assuming the the graph will eventually intercept the axes. Correction: Pupils can experiment with very large numbers. Here a spreadsheet is useful to generate numbers very quickly and show that although it gets very close to zero it never actually gets there.
More Lessons In This Unit
- Abstract direct proportion Study Guide
- Abstract inverse proportion Study Guide
- Checking and securing understanding of direct 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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