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Direct & inverse proportion (algebraic) practice questions with answers

Higher · Grade 7 · Calculator

A second set of direct & inverse proportion (algebraic) questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.

More questions

Question 1 Easy

y is proportional to the square of x. y = 32 when x = 4. Find y when x = 2.

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Answer: 8

  1. k = 32/16 = 2.
  2. y = 2 × 4 = 8.
  • Method (1): k = 32/16 = 2.
  • Accuracy (1): y = 2 × 4 = 8.

Question 2 Easy

y is proportional to the square of x. y = 27 when x = 3. Find the constant k.

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Answer: 3

  1. k = 27 / 3².
  2. k = 27 / 9 = 3.
  • Method (1): k = 27 / 3².
  • Accuracy (1): k = 27 / 9 = 3.

Question 3 Medium

y is inversely proportional to x squared. y = 48 when x = 1. Find y when x = 2.

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Answer: 12

  1. k = 48 × 1 = 48.
  2. y = 48 / 4 = 12.
  • Method (1): k = 48 × 1 = 48.
  • Accuracy (1): y = 48 / 4 = 12.

Question 4 Medium

y is inversely proportional to x squared. y = 12 when x = 2. Find the constant k.

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Answer: 48

  1. k = 12 × 2².
  2. k = 12 × 4 = 48.
  • Method (1): k = 12 × 2².
  • Accuracy (1): k = 12 × 4 = 48.

Question 5 Hard

y is inversely proportional to x squared. y = 4 when x = 3. Find y when x = 6.

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Answer: 1

  1. k = 4 × 9 = 36.
  2. y = 36 / 36 = 1.
  • Method (1): k = 4 × 9 = 36.
  • Accuracy (1): y = 36 / 36 = 1.

Question 6 Hard

y is inversely proportional to x squared. y = 12 when x = 2. Find y when x = 1.

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Answer: 48

  1. k = 12 × 4 = 48.
  2. y = 48 / 1 = 48.
  • Method (1): k = 12 × 4 = 48.
  • Accuracy (1): y = 48 / 1 = 48.

Exam-style question

A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.

Exam-style question 14 marks

y is inversely proportional to x squared. y = 3 when x = 4. Find y when x = 2.

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Answer: 12

  1. Write equation: y = k / x².
  2. Substitute known values: 3 = k / (4²) = k / 16.
  3. Find constant k: k = 3 × 16 = 48.
  4. Calculate y when x = 2: y = 48 / (2²) = 48 / 4.
  5. Simplify: y = 12.
  • Method (1): Form model y = k / x²
  • Method (1): Find k = 48 from 3 = k / 16
  • Method (1): Substitute x = 2: y = 48 / 4
  • Accuracy (1): State y = 12

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

Write y proportional to the square of x with a constant.

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Equation is y = kx². Equation is y = kx².

Check 2

How do you find k from y = 18 and x = 3 in a square law?

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Divide y by x squared: 18 / 9 = 2. Divide y by x squared: 18 / 9 = 2.

Check 3

If k = 2 and x = 5 in y = kx², what is y?

  1. 50
  2. 100
  3. 5
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50 2 × 5² = 2 × 25 = 50.

Check 4

Write y inversely proportional to x squared.

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Equation is y = k/x². Equation is y = k/x².

Check 5

How do you find k for an inverse square?

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Multiply y by x squared: k = yx². Multiply y by x squared: k = yx².

Check 6

y = 12 when x = 2, inverse square. What is k?

  1. 2
  2. 11
  3. 48
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48 k = 12 × 2² = 48.

Check 7

With that k, what is y when x = 4?

  1. 2
  2. 3
  3. 6
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3 y = 48 / 4² = 48 / 16 = 3.

Check 8

Why is the graph not a straight line?

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The non-linear power curves the graph. The non-linear power curves the graph.

Check 9

From y = 2x², how do you find a positive x?

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Divide y by 2, then take the square root. Divide y by 2, then take the square root.

Check 10

y = 8 at x = 2, square law. What is y at x = 4?

  1. 2
  2. 8
  3. 32
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32 k = 2, so y = 2 × 16 = 32.

Check 11

y = 12 at x = 2, square law. What is y at x = 5?

  1. 75
  2. 76
  3. 2
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75 k = 3, so y = 3 × 25 = 75.

Check 12

Inverse square, y = 48 at x = 1. What is y at x = 2?

  1. 1
  2. 12
  3. 24
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12 k = 48, so y = 48 / 4 = 12.

Check 13

What is k if y = 50 and x = 5 in a square law?

  1. 2
  2. 1
  3. 5
Show answer

2 50 / 25 = 2.

Check 14

A student finds k by dividing y by x. What did they miss?

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x must be squared first before dividing. x must be squared first before dividing.

Check 15

Inverse square from x = 2 to x = 4 multiplies x by 2. What happens to y?

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Doubling x divides y by 2² = 4. Doubling x divides y by 2² = 4.

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