4MA0 Higher June 2012 Paper 4 Q2
2 A group of students take a test.
The group consists of 12 boys and 8 girls.
The mean mark for the boys is 18
The mean mark for the girls is 16.5
Calculate the mean mark for the whole group.
(4)
| Scheme | Marks |
|---|---|
| (12 × 18) + (8 × 16.5) (=348) | M2 |
| “348” ÷ 20 | M1 |
| 17.4 | A1 |
| (Total 4 marks) |
Notes
M2: M1 for 12 × 18 (=216) or 8 × 16.5 (=132)
M1: dep on at least 1 previous M1
A1: 17.4
Alt: Ratio method
| Scheme | Marks |
|---|---|
| 12:8 = 3:2 or 6:4 | M1 |
| 18 × 3 and 16.5 × 2 or 18 × 6 and 16.5 × 4 | M1 |
| (18 × 3 + 16.5 × 2) ÷ 5 or (18 × 6 + 16.5 × 4) ÷ 10 | M1 |
| 17.4 | A1 |
Alt: Proportion method
| Scheme | Marks |
|---|---|
| 60 % boys and 40% girls stated or implied | M1 |
| (0.6 × 18) + (0.4 × 16.5) (= 10.8 + 6.6) | M2 |
| 17.4 | A1 |
Notes
M2: M1 for 0.6 × 18 or 0.4 × 16.5
SC B1 for 17.1 (from {(8 × 18) + (12 × 16.5)}÷20)
Apart from questions 5, 7, 13c, 16b, 20, 21 and 22 (where the mark scheme states otherwise) the correct answer, unless clearly obtained by an incorrect method, should be taken to imply a correct method.