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Cubic and reciprocal graphs practice questions with answers

Foundation and Higher · Grade 5 · Non-calculator

A second set of cubic and reciprocal graphs 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

On the curve y=x^3, work out the value of y when x=4.

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Answer: 64

  1. Cube 4: 4 × 4 × 4.
  2. Result is 64.
  • Method (1): Cube 4: 4 × 4 × 4.
  • Accuracy (1): Result is 64.

Question 2 Easy

On the curve y=x^3, work out the value of y when x=0.

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Answer: 0

  1. Cube 0: 0 × 0 × 0.
  2. Result is 0.
  • Method (1): Cube 0: 0 × 0 × 0.
  • Accuracy (1): Result is 0.

Question 3 Medium

On the curve y=x^3+1, work out the value of y when x=2.

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Answer: 9

  1. Calculate 2 cubed: 8.
  2. Add 1: 8 + 1 = 9.
  • Method (1): Calculate 2 cubed: 8.
  • Accuracy (1): Add 1: 8 + 1 = 9.

Question 4 Medium

On the curve y=x^3+2, work out the value of y when x=2.

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Answer: 10

  1. Calculate 2 cubed: 8.
  2. Add 2: 8 + 2 = 10.
  • Method (1): Calculate 2 cubed: 8.
  • Accuracy (1): Add 2: 8 + 2 = 10.

Question 5 Hard

On the curve y=12/x, work out the value of y when x=-3.

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Answer: -4

  1. Divide 12 by -3.
  2. 12 / -3 = -4.
  • Method (1): Divide 12 by -3.
  • Accuracy (1): 12 / -3 = -4.

Question 6 Hard

Write down the equation of the vertical asymptote of y=1/x.

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Answer: x=0

  1. Identify the x-value where division by zero occurs.
  2. The vertical asymptote is the line x=0.
  • Method (1): Identify the x-value where division by zero occurs.
  • Accuracy (1): The vertical asymptote is the line x=0.

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

On the curve y=12/x, work out the value of y when x=2.

Show answer

Answer: 6

  1. Substitute x = 2 into y = 12/x.
  2. Divide 12 by 2 to get 6.
  • Method (1): 12 ÷ 2
  • Accuracy (1): 6

Quick checks

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

Check 1

What does cubing a number mean?

  1. Multiplying three copies of the number
  2. Multiplying the number by 3
  3. Squaring and adding 1
Show answer

Multiplying three copies of the number x cubed means x × x × x.

Check 2

On the curve y = x^3, what is y when x = 2?

  1. 8
  2. 6
  3. 4
Show answer

8 2 × 2 × 2 = 8.

Check 3

On the curve y = x^3, what is y when x = 3?

  1. 27
  2. 9
  3. 18
Show answer

27 3 × 3 × 3 = 27.

Check 4

On the curve y = x^3, what is y when x = -2?

  1. -8
  2. 8
  3. -6
Show answer

-8 (-2) × (-2) × (-2) = -8.

Check 5

On the curve y = x^3, what is y when x = -3?

  1. -27
  2. 27
  3. -9
Show answer

-27 (-3) × (-3) × (-3) = -27.

Check 6

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

  1. 9
  2. 8
  3. 7
Show answer

9 2^3 + 1 = 8 + 1 = 9.

Check 7

On the curve y = x^3 + 2, what is y when x = 2?

  1. 10
  2. 8
  3. 12
Show answer

10 2^3 + 2 = 8 + 2 = 10.

Check 8

On the curve y = 12/x, what is y when x = 3?

  1. 4
  2. 36
  3. 9
Show answer

4 12 ÷ 3 = 4.

Check 9

On the curve y = 12/x, what is y when x = 4?

  1. 3
  2. 48
  3. 8
Show answer

3 12 ÷ 4 = 3.

Check 10

On the curve y = 12/x, what is y when x = 6?

  1. 2
  2. 72
  3. 6
Show answer

2 12 ÷ 6 = 2.

Check 11

On the curve y = 12/x, what is y when x = -3?

  1. -4
  2. 4
  3. -36
Show answer

-4 12 ÷ (-3) = -4.

Check 12

What is the vertical asymptote of the reciprocal graph y = 1/x?

  1. x=0
  2. y=0
  3. x=1
Show answer

x=0 Division by zero is undefined at x = 0.

Check 13

What is the horizontal asymptote of y = 1/x?

  1. y=0
  2. x=0
  3. y=1
Show answer

y=0 As x gets very large, y approaches 0.

Check 14

Why does the graph of y = 1/x not touch the y-axis?

  1. Division by zero is undefined
  2. It crosses at (0, 0)
  3. It only exists for positive numbers
Show answer

Division by zero is undefined When x = 0, 1/x has no real value.

Check 15

How does a cubic curve y = x^3 differ from a quadratic y = x^2?

  1. It has rotational symmetry about the origin and takes negative y-values
  2. It is symmetric about the y-axis
  3. It has asymptotes
Show answer

It has rotational symmetry about the origin and takes negative y-values A cubic curve extends across all negative and positive y values.

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