Higher June 2023 Paper 2 Q24
24 \(a = 65\) to the nearest integer
\(b = 30\) to 1 significant figure
Work out the upper bound for \(\quad 2a^2 - b^2\)
You must show your working. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| 64.5 or 65.5 or 25 or 35 | M1 | allow \(65.4\dot{9}\) or \(34.\dot{9}\) implied by 4160.25 or 4290.25 or 8320.5 or 8580.5 or 625 or 1225 |
| \(2 \times\) their \(65.5^2 -\) their \(25^2\) or \(2 \times 4290.25 - 625\) or \(8580.5 - 625\) | M1 | their 65.5 must be (65, 66] their 25 must be [20, 30) |
| 65.5 and 25 and 7955.5 | A1 |
Additional guidance
| Up to M2 may be awarded for correct work with no answer or incorrect answer, even if this is seen amongst multiple attempts | |
| If multiple attempts are seen and one is fully correct, the correct one must be unambiguously selected (eg ticked or circled) to award A1 if the answer line is blank | |
| Note that M0M1A0 is possible eg \(2 \times 66^2 - 21^2\) | M0M1A0 |
| Condone eg 65.50 for 65.5 |