Foundation June 2023 Paper 3 Q24
24 Millie is estimating the value of \(\quad \dfrac{1}{\left(\sqrt[3]{8.34}\right)^2 \times 10.21}\)
She rounds each decimal number to 1 significant figure.
(a) Work out Millie’s estimate.
You must show your working. [2 marks]
(b) Millie says,
“My estimate must be more than the exact value.”
Without working out the exact value, give a reason how she can know this. [1 mark]| Answer | Mark | Comments |
|---|---|---|
| 8 or 10 | M1 | 8 may be implied by \(2^2\) or 4 |
| 8 and 10 and \(\dfrac{1}{40}\) or 0.025 | A1 | 8 may be implied by \(2^2\) or 4 accept 0.03 with \(\dfrac{1}{40}\) or 0.025 seen |
Additional guidance
| Do not allow exact calculations for M1A1 eg \(4.113 = 4\) and \(10.21 = 10\) and \(\dfrac{1}{40}\) | M1A0 |
| \(\dfrac{1}{40}\) or 0.025 with 8 or 10 seen (8 may be implied by \(2^2\) or 4) | M1A0 |
| \(\dfrac{1}{40}\) or 0.025 without 8 or 10 seen (8 may be implied by \(2^2\) or 4) | M0A0 |
| Answer | Mark | Comments |
|---|---|---|
| Valid explanation | B1 | eg both numbers have been rounded down |
Additional guidance
| Ignore irrelevant reasons alongside a correct reason, unless contradictory | |
| Ignore a calculation using exact values alongside a correct reason eg 0.025 is greater than 0.0238… and both numbers rounded down | B1 |
| 0.025 is greater than 0.0238… | B0 |
| The denominator is smaller | B1 |
| The denominator using the exact values is bigger | B1 |
| (Decimals) rounded down | B1 |
| Because 8.34 is more than 8 and 10.21 is more than 10 | B1 |
| One is divided by less (with answer more) | B1 |
| Estimating rounds the numbers down which makes the denominator less | B1 |
| Estimating rounds the numbers down which makes it less | B0 |
| Because it rounds up | B0 |
| Because she rounded each number to one significant figure | B0 |
| The numbers get rounded up so more than the exact value | B0 |
| Rounded up when estimating | B0 |
| Removing the decimals makes the number bigger | B0 |