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Year 11
Higher

Abstract inverse proportion

I can identify, write and solve inverse proportion questions involving algebra.

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New
New
Year 11
Higher

Abstract inverse proportion

I can identify, write and solve inverse proportion questions involving algebra.

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Lesson details

Key learning points

  1. Inverse proportion equations are of the form y = k ÷ x^n
  2. k is the constant of proportionality.
  3. To find k, you can use a pair of values.

Keywords

  • Inversely proportional - Two variables are inversely proportional if there is a constant multiplicative relationship between one variable and the reciprocal of the other.

Common misconception

For all direct and inverse proportions, the multiplicative relationship is with x and y.

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.


To help you plan your year 11 maths lesson on: Abstract inverse proportion, download all teaching resources for free and adapt to suit your pupils' needs...

Staff attendance is important in business. Allow pupils to be "the boss" in a business which takes x number of staff to complete a product in n number of hours. There is a full quota of staff working for 3 days, then 3 fewer staff for 6 days. How many more hours are needed to complete the product?
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Lesson video

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6 Questions

Q1.
Two variables are proportional if there is a constant multiplicative relationship between one variable and the reciprocal of the other.
jointly
directly
Correct answer: inversely
promisingly
uncommonly
Q2.
Pair up the reciprocals with the following numbers.
Correct Answer:3,$$\frac{1}{3}$$
tick

$$\frac{1}{3}$$

Correct Answer:5,$$\frac{1}{5}$$
tick

$$\frac{1}{5}$$

Correct Answer:$$\frac{3}{2}$$,$$\frac{2}{3}$$
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$$\frac{2}{3}$$

Correct Answer:2,$$\frac{1}{2}$$
tick

$$\frac{1}{2}$$

Correct Answer:12,$$\frac{1}{12}$$
tick

$$\frac{1}{12}$$

Correct Answer:$$\frac{5}{9}$$,$$\frac{9}{5}$$
tick

$$\frac{9}{5}$$

Q3.
What is the single multiplier that connects 9 to 54?
Correct Answer: 6, six
Q4.
What is the single multiplier that connects 15 to 10?
$$\frac{3}{2}$$
Correct answer: $$\frac{2}{3}$$
$$\frac{9}{5}$$
$$\frac{15}{10}$$
Q5.
What is the single multiplier that connects 24 to 9.6?
$$\frac{24}{9.6}$$
$$\frac{9.6}{24}$$
$$\frac{5}{2}$$
Correct answer: $$\frac{2}{5}$$
$$\frac{2}{3}$$
Q6.
$$y\propto \sqrt{x}$$, when $$x=64, y=6$$. Work out the value of $$y$$ when $$x=400$$.
Correct Answer: 15

6 Questions

Q1.
Match the equations with the correct proportions.
Correct Answer:$$y\propto\frac{1}{x^2}$$ ,$$y=\frac{3}{x^2}$$
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$$y=\frac{3}{x^2}$$

Correct Answer:$$y\propto\frac{1}{\sqrt{x}}$$ ,$$y=\frac{10}{\sqrt{x}}$$
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$$y=\frac{10}{\sqrt{x}}$$

Correct Answer:$$y\propto\frac{1}{\sqrt[3]{x}}$$ ,$$y=\frac{3}{4\sqrt[3]{x}}$$
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$$y=\frac{3}{4\sqrt[3]{x}}$$

Correct Answer:$$y\propto\frac{1}{x}$$ ,$$y=\frac{\sqrt{2}}{x}$$
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$$y=\frac{\sqrt{2}}{x}$$

Correct Answer:$$y\propto x^2$$ ,$$y= 9x^2$$
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$$y= 9x^2$$

Correct Answer:$$y\propto \sqrt{x}$$ ,$$y= 5\sqrt{x}$$
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$$y= 5\sqrt{x}$$

Q2.
Which of the following are examples of inverse proportion?
Converting euros to dollars or vice versa
The hours you work and the salary received
Correct answer: The taps to fill a water bucket and the time it takes to fill the bucket
Correct answer: The number of robots to complete a job and the time to complete the job
Q3.
$$p\propto \frac{1}{q}$$, match the correct values for A, B and C.
An image in a quiz
Correct Answer:A,20
tick

20

Correct Answer:B,1000
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1000

Correct Answer:C,62.5
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62.5

Q4.
It takes 10 workers 6 hours to build a wall. They all work at the same rate. Firstly, all workers build for 2 hours, then 6 workers leave. How many hours will it take the 4 workers to finish the wall?
Correct Answer: 10, ten, 10 hours, 10 hrs
Q5.
$$y\propto \frac{1}{\sqrt{x}}$$, when $$x=25, y=16$$. Work out the value of $$y$$ when $$x=400$$.
Correct Answer: 4, four
Q6.
$$y\propto \frac{1}{\sqrt[3]{x}}$$, when $$x=125, y=0.15$$. Work out the value of $$y$$ when $$x=0.008$$.
Correct Answer: 3.75