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Ratio as a fraction or linear function practice questions with answers

Foundation and Higher · Grade 5 · Non-calculator

A second set of ratio as a fraction or linear function 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 = 5x + 4. When x = 1, find y.

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Answer: 9

  1. Substitute x = 1: y = 5(1) + 4.
  2. Calculate: 5 + 4 = 9.
  • Method (1): Substitute x = 1: y = 5(1) + 4.
  • Accuracy (1): Calculate: 5 + 4 = 9.

Question 2 Easy

y = 2x + 7. When x = 6, find y.

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Answer: 19

  1. Substitute x = 6: y = 2(6) + 7.
  2. Calculate: 12 + 7 = 19.
  • Method (1): Substitute x = 6: y = 2(6) + 7.
  • Accuracy (1): Calculate: 12 + 7 = 19.

Question 3 Medium

y = (4/3)x when x = 9, find y.

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Answer: 12

  1. Divide by denominator: 9 / 3 = 3.
  2. Multiply by numerator: 4 × 3 = 12.
  • Method (1): Divide by denominator: 9 / 3 = 3.
  • Accuracy (1): Multiply by numerator: 4 × 3 = 12.

Question 4 Medium

y = (5/2)x when x = 4, find y.

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Answer: 10

  1. Divide by denominator: 4 / 2 = 2.
  2. Multiply by numerator: 5 × 2 = 10.
  • Method (1): Divide by denominator: 4 / 2 = 2.
  • Accuracy (1): Multiply by numerator: 5 × 2 = 10.

Question 5 Hard

y = 3x + 1. When y = 10, what is x?

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Answer: 3

  1. Subtract 1 from both sides: 3x = 9.
  2. Divide by 3: x = 9 / 3 = 3.
  • Method (1): Subtract 1 from both sides: 3x = 9.
  • Accuracy (1): Divide by 3: x = 9 / 3 = 3.

Question 6 Hard

y = 4x - 2. When y = 10, what is x?

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Answer: 3

  1. Add 2 to both sides: 4x = 12.
  2. Divide by 4: x = 12 / 4 = 3.
  • Method (1): Add 2 to both sides: 4x = 12.
  • Accuracy (1): Divide by 4: x = 12 / 4 = 3.

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 12 marks

y = 5x + 5. Work out the value of x when y = 35.

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Answer: 6

  1. Subtract 5 from both sides: 5x = 30.
  2. Divide by 5: x = 30 / 5 = 6.
  • Method (1): 35 − 5 = 30, or 5x = 30
  • Accuracy (1): 6

Quick checks

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

Check 1

To substitute into y = mx + c, which operation comes first?

  1. Multiply by the gradient m
  2. Add the constant c
  3. Divide by the input x
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Multiply by the gradient m Multiply x by the gradient before adding the constant.

Check 2

On y = 2x + 3, what is the value when x = 4?

  1. 11
  2. 14
  3. 9
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11 2 × 4 + 3 = 11.

Check 3

On y = 3x + 1, what is the value when x = 2?

  1. 7
  2. 6
  3. 9
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7 3 × 2 + 1 = 7.

Check 4

What is three quarters of 8, written y = (3/4)x when x = 8?

  1. 6
  2. 2
  3. 24
Show answer

6 8 ÷ 4 = 2, and 2 × 3 = 6.

Check 5

What is two fifths of 10, written y = (2/5)x when x = 10?

  1. 4
  2. 5
  3. 20
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4 10 ÷ 5 = 2, and 2 × 2 = 4.

Check 6

A machine multiplies by 2 and then adds 3. What is the output for input 4?

  1. 11
  2. 14
  3. 10
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11 4 × 2 = 8, then 8 + 3 = 11.

Check 7

A machine multiplies by 3 and then adds 1. What is the output for input 5?

  1. 16
  2. 18
  3. 15
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16 5 × 3 = 15, then 15 + 1 = 16.

Check 8

To undo y = 2x + 3 when y = 11, what is x?

  1. 4
  2. 7
  3. 14
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4 11 − 3 = 8, and 8 ÷ 2 = 4.

Check 9

To undo y = 3x + 1 when y = 10, what is x?

  1. 3
  2. 4
  3. 9
Show answer

3 10 − 1 = 9, and 9 ÷ 3 = 3.

Check 10

In the expression 2x + 3, what must you do before adding 3?

  1. Multiply x by 2
  2. Subtract 3
  3. Divide by 2
Show answer

Multiply x by 2 Multiplication has priority over addition.

Check 11

To solve y = mx + c for x, which step is first?

  1. Subtract the intercept c
  2. Divide by the gradient m
  3. Add the intercept c
Show answer

Subtract the intercept c Undo the addition of c before dividing by m.

Check 12

What does a fraction (a/b) in front of x represent?

  1. A multiplier of a/b
  2. Adding a then dividing by b
  3. A power of x
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A multiplier of a/b A coefficient fraction multiplies the variable x.

Check 13

What is four thirds of 9?

  1. 12
  2. 9
  3. 27
Show answer

12 9 ÷ 3 = 3, and 3 × 4 = 12.

Check 14

What is five halves of 4?

  1. 10
  2. 8
  3. 20
Show answer

10 4 ÷ 2 = 2, and 2 × 5 = 10.

Check 15

What is the input of a function machine?

  1. The starting number fed in
  2. The final output value
  3. The operations inside
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The starting number fed in The input is the value fed into the machine first.

Keep going with Ratio as a fraction or linear function

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