Higher January 2020 Paper 2R Q17
17 Some students in a school were asked the following question.
“Do you have a dog (\(D\)), a cat (\(C\)) or a rabbit (\(R\))?”
Of these students
28 have a dog
18 have a cat
20 have a rabbit
8 have both a cat and a rabbit
9 have both a dog and a rabbit
\(x\) have both a dog and a cat
6 have a dog, a cat and a rabbit
5 have not got a dog or a cat or a rabbit
(a) Using this information, complete the Venn diagram to show the number of students in each appropriate subset.
Give the numbers in terms of \(x\) where necessary. (3)
Give the numbers in terms of \(x\) where necessary. (3)
Given that a total of 50 students answered the question,
(b) work out the value of \(x\). (2)
(c) Find \(\;\mathrm{n}(C^{\prime} \cap D^{\prime})\) (1)
| Scheme | Marks |
|---|---|
| Venn diagram with: \(D\) only: \(25 - x\) \(D\) and \(C\) only: \(x - 6\) \(C\) only: \(16 - x\) \(D\) and \(R\) only: 3 \(D\), \(C\) and \(R\): 6 \(C\) and \(R\) only: 2 \(R\) only: 9 outside the circles: 5 | B3 |
| (3) |
Notes
B3: All 8 values inserted correctly
B2 for 4 to 7 correct values
B1 for 2 or 3 correct values
NB: Expressions involving \(x\) do not have to be simplified.
| Scheme | Marks |
|---|---|
| “[\((25 - x) + (x - 6) + (16 - x) + 3 + 6 + 2 + 9 + 5\)]” = 50 | M1ft |
| 10 | A1 |
| (2) |
Notes
M1ft: For sum of all their values = 50 oe
| Scheme | Marks |
|---|---|
| 14 | B1ft |
| (1) | |
| (6 marks) |