ECZ 2020 · GCE Paper 2 · Question 3 — Sets
Venn diagram of three courses at a University: Mathematics only = 6, Maths∩Chemistry only = 5 - x, Chemistry only = 7, Maths∩Physics only = 4 - x, Chemistry∩Physics only = 3 - x, all three = x, Physics only = 2.
(a) Solve the equation 2x2 + 3x - 7 = 0, giving your answers correct to 2 decimal places.[5]
Verified working — step 1
Using the quadratic formula on 2x2+3x-7=0:(b(i)) Given that there were 25 students altogether, find the value of x.[2]
Verified working — step 1
Sum all regions and set equal to 25:(b(ii)(a)) How many students studied Mathematics and Chemistry only?[1]
Verified working — step 1
Maths∩Chemistry only = 5 - x = 5 - 1 = …(b(ii)(b)) How many students studied one course only?[1]
Verified working — step 1
Students studying one course only = …(b(ii)(c)) How many students studied Chemistry and Physics but not Mathematics?[1]
Verified working — step 1
Chemistry and Physics but not Maths = Chemistry∩Physics only = 3 - x = 3 - 1 = …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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