Foundation June 2022 Paper 2 Q22
22 A school play takes place each day from Monday to Friday.
Here are the attendances on four of the days.
| Monday | Tuesday | Wednesday | Thursday |
|---|---|---|---|
| 72 | 83 | 88 | 97 |
For all five days, the mean attendance is 90
Work out the attendance on Friday. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(90 \times 5\) or 450 or \(\dfrac{72 + 83 + 88 + 97 + x}{5}\) or \(\dfrac{340 + x}{5}\) | M1 | oe any letter or symbol |
| \(90 \times 5 - 72 - 83 - 88 - 97\) or \(90 \times 5 - 340\) or \(72 + 83 + 88 + 97 + x = 90 \times 5\) or \(340 + x = 90 \times 5\) | M1dep | oe any letter or symbol equations must have fraction eliminated |
| 110 | A1 | |
| Alternative method 2 | ||
| Trial of any value with mean correctly evaluated | M1 | also allow if given to the next or previous integer eg1 trial of 100 \(\dfrac{72 + 83 + 88 + 97 + 100}{5} = 88\) eg2 trial of 78 \(\dfrac{340 + 78}{5} = 83\) (or 84 or 83.6) ignore trials with mean not evaluated or incorrectly evaluated |
| Trial of 110 with mean evaluated to 90 | M1dep | eg \(\dfrac{72 + 83 + 88 + 97 + 110}{5} = 90\) this mark implies M1M1 |
| 110 | A1 | |
| Alternative method 3 | ||
| \(\dfrac{72 + 83 + 88 + 97}{4}\) or \(\dfrac{340}{4}\) or 85 | M1 | oe |
| their \(85 + 5 \times (90 -\) their 85) or their \(85 + 5 \times 5\) or their \(85 + 25\) | M1dep | oe \(90 + 4 \times (90 -\) their 85) |
| 110 | A1 | |
| Alternative method 4 | ||
| \(\dfrac{72 + 83 + 88 + 97}{5}\) or \(\dfrac{340}{5}\) or 68 | M1 | oe |
| \(5 \times (90 -\) their 68) or \(5 \times 22\) | M1dep | oe |
| 110 | A1 | |
| Alternative method 5 | ||
| \((90 - 72) + (90 - 83) + (90 - 88) + (90 - 97)\) or \(18 + 7 + 2 - 7\) or 20 | M1 | oe eg \((72 - 90) + (83 - 90) + (88 - 90) + (97 - 90)\) or \(90 \times 4 - 72 - 83 - 88 - 97\) or \(-18 - 7 - 2 + 7\) or \(-20\) |
| \(90 +\) their 20 | M1dep | oe eg \(90 -\) their \(-20\) |
| 110 | A1 | |
Additional guidance
| M1 may be awarded for correct work with no, or incorrect answer, even if this is seen amongst multiple attempts | |
| Embedded 110 scores M1M1A0 using Alt 2 (even if a different answer is given) | |
| Condone eg Alt 3 \(72 + 83 + 88 + 97 \div 4\) No further marks unless recovered | M1 |
| Alt 5 1st M1 Subtractions must be consistent | |
| Condone 110% for 110 |