Year 11 - Maths
Proportion modelled algebraically
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 and solve proportion questions involving algebra.
Key Notes
- The question does not always state the type of proportion.
- The context of the question can be used to determine the type of proportion.
- If more than one pair of values is given, this can determine the type of proportion.
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
- The constant of proportionality shows the gradient for inversely proportional graphs.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The question does not always state the type of proportion. The context of the question can be used to determine the type of proportion.
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: The constant of proportionality shows the gradient for inversely proportional graphs. Correction: The constant of proportionality shows the gradient for directly proportional graphs only. The constant for a reciprocal graph in the form k/x^n, shows the distance of the reciprocal from the origin.
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
- Problem solving with direct and inverse proportion Study Guide
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