Mathematics I  Old Questions
1. In class of 100 students 40 students failed in Mathematics, 70 failed in English and 20 failed in both subjects. Find
a) How many students passed in both subjects?
b) How many students passed in Mathematics only?
c) How many students failed in mathematics only?
5 marks

Asked in 2019
Let M and E be the set of students who failed in Mathematics and English respectively.
Then,
n(U) = 100
n(M) = 40
n(E) = 70
n(M∩E) = 20
i) We have,
Therefore, number of students passed in both subjects = 10.
ii)
Number of students passed in Mathematics only =
iii)
Number of students failed in mathematics only = n(M)  n(M∩E) = 40  20 = 20