Year 11 - Maths
Problem solving with direct and 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 use your knowledge of direct and inverse proportion to solve problems.
Key Notes
- Algebraic manipulation is needed to solve proportion problems.
- Proportional relationships can be modelled graphically and algebraically.
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.
- Direct proportion: Two variables are in direct proportion if they have a constant multiplicative relationship.
Common Mistakes To Avoid
- Directly proportional graphs all start from (0,0) and are above the y axis.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Algebraic manipulation is needed to solve proportion problems. Proportional relationships can be modelled graphically and algebraically.
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: Directly proportional graphs all start from (0,0) and are above the y axis. Correction: Directly proportional means there is a multiplier between y and x. This graph is always y=kx and is linear passing through (0,0). A proportionality graphs show the multiplicative relationship between y and x^n and can be linear and non linear.
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
- 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
- Proportion modelled algebraically Study Guide
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