Unit 6
5 marks · Normal6. In a group of 40 students, 25 study Mathematics, 22 study Biology, and 15 study both. Let M be the set of students studying Mathematics and B the set studying Biology.
Represent this information on a Venn diagram by clearly showing all regions and the number of students in each.
How many students do not study either subject?
Using algebra, let x be the number who study only Mathematics and y the number who study only Biology. Set up and solve equations to find x and y.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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(a) Venn diagram with 10 only M, 7 only B, 15 both, 8 neither. · must show Correct numbers in all regions
(b) 8
(c) x=10,y=7
Must show: Intersection, Correct calculations
Common mistakes: Not subtracting intersection; Wrong total count
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Lay out Venn diagram with correct sets and overlap.
A1 (a) · 1 mark · Correctly places numbers for only M, only B, both. (follow-through)
B1 (b) · 1 mark · Calculates neither (8).
M2 (c) · 1 mark · Sets up and solves correct equations for x and y.
A2 (c) · 1 mark · Finds x=10, y=7. (follow-through)
Worked solution
a) Both M and B: 15. Only M: 25-15=10. Only B: 22-15=7. Outside both: 40-(10+7+15)=8. Diagram should show these four regions.
b) Neither: 8 as above.
c) x+15+y+8=40, x+y=17, from (a). x=10, y=7.