ECZ 2018 · O-Level Paper 2 · Question 2 — Sets
At Sambilileni College, 20 students study at least one of the three subjects: Mathematics (M), Chemistry (C) and Physics (P). All those who study Chemistry also study Mathematics. 3 students study all the three subjects. 4 students study Mathematics only, 8 students study Chemistry and 14 students study Mathematics.
(a) Solve the equation 3x2 - x - 5 = 0, giving your answers correct to 2 decimal places.[5]
Verified working — step 1
a = 3, b = -1, c = -5(b(i)) Draw a Venn diagram to illustrate the information about the 20 students.[2]
Verified working — step 1
Every Chemistry student also studies Mathematics, so C is drawn inside M.(b(ii)(a)) How many students study Physics only?[1]
Verified working — step 1
Total studying at least one subject is 20 and Mathematics accounts for 14, so Physics only = 20 - 14 = …(b(ii)(b)) How many students study two subjects only?[1]
Verified working — step 1
Exactly two subjects = (M and C only) + (M and P only) = 5 + 2 = …(b(ii)(c)) How many students study Mathematics and Physics but not Chemistry?[1]
Verified working — step 1
From the Venn diagram, the M and P r…The full step-by-step working and final answer are included with Premium — checked against ECZ marking standards.
Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.
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