Higher November 2020 Paper 2 Q10
10 Alex and Bev sat six tests, each with 50 marks.
The table shows their mean percentages after five tests.
| Alex | 60% |
| Bev | 52% |
After all six tests, their mean percentages were equal.
In the sixth test, Alex scored 24 out of 50
Work out Bev’s score, out of 50, in the sixth test. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 Total % for A after 6 tests \(-\) total % for B after 5 tests | ||
| \(60 \times 5\) or 300 or \(52 \times 5\) or 260 | M1 | oe |
| \(\dfrac{24}{50} \times 100\) or \(0.48 \times 100\) or 48 | M1 | oe 348 implies M1M1 |
| \(60 \times 5 + \dfrac{24}{50} \times 100 - 52 \times 5\) or \(300 + 48 - 260\) or 88 | M1dep | oe eg \(348 - 260\) dep on M1M1 |
| 44 | A1 | allow \(\dfrac{44}{50}\) |
| Alternative method 2 Total score for A after 6 tests \(-\) total score for B after 5 tests | ||
| \(\dfrac{60}{100} \times 50\) or 30 | M1 | oe allow \(\dfrac{30}{50}\) implied by 150 or 174 |
| \(\dfrac{52}{100} \times 50\) or 26 | M1 | oe allow \(\dfrac{26}{50}\) implied by 130 |
| \(\dfrac{60}{100} \times 50 \times 5 + 24 - \dfrac{52}{100} \times 50 \times 5\) or \(150 + 24 - 130\) | M1dep | oe eg \(174 - 130\) dep on M1M1 |
| 44 | A1 | allow \(\dfrac{44}{50}\) |
| Alternative method 3 Total score for A after 6 tests \(-\) total score for B after 5 tests | ||
| \(50 \times 5\) or 250 | M1 | oe implied by 150 or 130 or 174 |
| \(\dfrac{60}{100} \times 50 \times 5\) or 150 and \(\dfrac{52}{100} \times 50 \times 5\) or 130 | M1dep | oe allow \(\dfrac{150}{250}\) and \(\dfrac{130}{250}\) |
| \(\dfrac{60}{100} \times 50 \times 5 + 24 - \dfrac{52}{100} \times 50 \times 5\) or \(150 + 24 - 130\) | M1dep | oe eg \(174 - 130\) |
| 44 | A1 | allow \(\dfrac{44}{50}\) |
| Alternative method 4 Difference in scores after 5 tests \(+\) 6th score for A | ||
| \(60 - 52\) or 8 | M1 | oe |
| \(\dfrac{60 - 52}{100} \times 50\) or 4 | M1dep | oe eg \(\dfrac{60}{100} \times 50 - \dfrac{52}{100} \times 50\) or \(30 - 26\) allow \(\dfrac{4}{50}\) |
| \(\dfrac{60 - 52}{100} \times 50 \times 5 + 24\) or \(4 \times 5 + 24\) or \(20 + 24\) | M1dep | oe |
| 44 | A1 | allow \(\dfrac{44}{50}\) |
Additional guidance
To award the 3rd M a calculation or a value (not an equation) must be seen
Select the scheme that favours the student for the first 2 M marks even if not subsequently used
Alt 1 Do not award 1st M for 300 if incorrect method seen
eg \(6 \times 50 = 300\) does not score the 1st M
Alt 1 Do not award 2nd M for 48 if incorrect method seen
eg \(100 - 52 = 48\) does not score the 2nd M
Alt 2 Do not award 2nd M for 26 if incorrect method seen
eg \(50 - 24 = 26\) does not score the 2nd M