ECZ 2014 · O-Level Paper 2 · Question 10 — Graphs of Functions
Question from ECZ 2014 · O-Level Paper 2 · Question 10
(a) The graphs of y = 7 - 3x - x2 and y = x + 4 are shown in the diagram below.
(a(i)) Use the graph above to solve the following equations;
(a(i)(a)) 9 - 3x - x2 = 0,[3]
Verified working — step 1
Rewrite so the left matches the drawn curve y = 7 - 3x - x2.(a(i)(b)) 7 - 3x - x2 = x + 4.[2]
Verified working — step 1
The solutions are where the curve meets the line y = x + 4.(a(ii)) Estimate the area bounded by the curve, x = -3, x = -1 and y = x + 4.[3]
Verified working — step 1
Measure the vertical gap between curve and line at each x.(a(iii)) Find the maximum value of y = 7 - 3x - x2.[1]
Verified working — step 1
For y = 7 - 3x - x2 the vertex is at x = -b2a with a = -1, b = -3.(b) In a certain school, the ratio of boys to girls is 3 : 5. Given that there are 600 girls, calculate the total number of pupils in the school.[3]
Verified working — step 1
5 parts represent 600 girls, so 1 part = 120.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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