4MA0 Higher June 2012 Paper 4 Q14
14 There are 31 students in a class.
The only languages available for the class to study are French and Spanish.
17 students study French.
15 students study Spanish.
6 students study neither French nor Spanish.
Using a Venn diagram, or otherwise, work out how many students study only one language.
(4)
| Scheme | Marks |
|---|---|
| (2) overlapping circles, 6 outside circles | M1 |
| 10 in F only, 8 in S only, 7 in overlap | M2 |
| 18 | A1 |
| (Total 4 marks) |
Notes
M2: Venn diagram sets have to labelled
if not M2 then M1 for any two values in correct place in union or 7 in overlap
Alt Method
| Scheme | Marks |
|---|---|
| 31 − 6 (=25) or (17+15+6) − 31 (=7) oe | M1 |
| “25”−17 (=8) {Sp} and “25”− 15 (=10) {Fr} or 17 − “7” (=10) {Fr} and 15 − “7” (=8) {Sp} | M1 dep |
| “10” + “8” | M1 dep |
| 18 | A1 |
Notes
M1: Identifies union or intersection
M1 dep: Identifies components to add
or M2 for “25” − “7”
M1 dep: Adds components
A1: (Ans only = M3A1)
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.