Squares, cubes & roots
AQA GCSE Maths revision on Squares, cubes & roots. Aligned to the AQA GCSE Mathematics 8300 specification. This bank has 16 practice questions on this topic.
Sample questions (3 of 16)
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Question 1
A student claims that since 4 squared is 16, then 8 squared must be 32. Which mathematical concept has the student misunderstood?
- A) Linear scaling
- B) Inverse proportionality
- C) Exponential growth
- D) Commutative property
Show answer
Answer: Linear scaling
Squaring is a non-linear operation, meaning the output does not increase at the same rate as the input. Doubling the base number actually quadruples the result because (2x)^2 = 4x^2. The student applied a linear relationship to a quadratic function.
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Question 2
Why is the square root of a negative number not defined within the set of real numbers?
- A) Because a negative times a negative is always positive
- B) Because roots only apply to positive integers
- C) Because negative numbers do not have prime factors
- D) Because the square root of a negative is always zero
Show answer
Answer: Because a negative times a negative is always positive
By definition, a square is the product of a number and itself. Since the product of two positive numbers is positive, and the product of two negative numbers is also positive, there is no real number that can result in a negative product when squared.
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Question 3
If the side length of a cube is multiplied by a factor of 3, by what factor does the volume increase?
- A) 3
- B) 6
- C) 9
- D) 27
Show answer
Answer: 27
The volume of a cube is calculated by s cubed. If you replace s with 3s, the new volume becomes (3s)^3, which equals 27s^3. This demonstrates the cubic relationship between linear dimensions and volume.
Want to test yourself on the remaining cards for this topic?
13 more questions on Squares, cubes & roots — plus mistakes tracking and spaced repetition across the whole Maths spec.