Foundation June 2025 Paper 3 Q9
9
(a) The square of a whole number is a two-digit number.
Work out
the smallest number that could have been squared
and
the largest number that could have been squared. [3 marks]
(b) Which has the larger value \(\quad 0.8^2 \quad\) or \(\quad 0.8^3\) ?
Tick a box.
- \(0.8^2\)
- \(0.8^3\)
Give a reason for your answer. [1 mark]
| Answer | Mark | Comments |
|---|---|---|
| 4 and 9 in correct positions | B3 | B2 9 in smallest position and 4 in largest position or only 4 in correct position or only 9 in correct position or \(4^2\) in smallest position and \(9^2\) in largest position or 16 or \(\sqrt{16}\) in smallest position and 81 or \(\sqrt{81}\) in largest position B1 \(4^2\) or 16 or \(\sqrt{16}\) or \(9^2\) or 81 or \(\sqrt{81}\) |
Additional guidance
| \(4^2 = 16\) in smallest position and \(9^2 = 81\) in largest position | B2 |
| 16, 4 in smallest position and 81, 9 in largest position | B2 |
| \(2^2 = 4\) in smallest position is not 4 in smallest position \(3^2 = 9\) in largest position is not 9 in largest position |
| Answer | Mark | Comments |
|---|---|---|
| \(0.8^2\) ticked with either 0.64 and 0.512 or \(\dfrac{64}{100}\) and \(\dfrac{64}{125}\) or \(0.8 \lt 1\) or suitable worded reason | B1 | oe in comparable form fractions must have same numerator or same denominator eg multiplying by decimals below 1 makes numbers smaller |
Additional guidance
| Ignore further work after correct values in comparable form | |
| Condone 0.51 for 0.512 | |
| \(\dfrac{16}{25}\) and \(\dfrac{64}{125}\) (fractions do not have same numerator or denominator) | B0 |
| \(0.8^2\) ticked and squaring makes numbers bigger | B0 |