O-LevelAdditional MathematicsPermutations and combinations4037/21 · May/June 2017 · Q76 Marks
On each of the Venn diagrams below shade the region which represents the given set. [Figure 7.1]
- (a)On each of the Venn diagrams below shade the region which represents the given set. [Figure 7.1][2]
- (b)(i)In a group of students, each student studies at most two of art, music and design. No student studies both music and design. A denotes the set of students who study art, M denotes the set of students who study music, D denotes the set of students who study design. Write the following using set notation. No student studies both music and design.[1]
- (b)(ii)There are 100 students in the group. 39 students study art, 45 study music and 36 study design. 12 students study both art and music. 25 students study both art and design. Complete the Venn diagram below to represent this information and hence find the number of students in the group who do not study any of these subjects. [Figure 7.2][3]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.
- [B2] B1 for each
- [B1] n(M ∩ D) = 0 or M ∩ D = Ø No additional brackets e.g. M ∩ D = {Ø} is B0
- [B3] B1 correct intersection of circles with 12 and 25 correct
- [B1] 33, 2, 11 correctly placed
- [B1FT] 17; must be on the Venn diagram and identified as the required answer FT on 100- (sum of their 5 correctly positioned values)
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