ECZ 2017 · O-Level Paper 2 · Question 9 — Earth Geometry
Question from ECZ 2017 · O-Level Paper 2 · Question 9
(a) W, X, Y and Z are four points on the surface of the earth as shown in the diagram below. (Take π as 3.142 and R = 3437 nm)
(a(i)) Calculate the difference in latitude between W and Y.[2]
Verified working — step 1
W is at 80 N and Y is at 30 S, on opposite sides of the equator.(a(ii)) Calculate the distance in nautical miles between
(a(ii)(a)) X and Z along the longitude 105° E,[2]
Verified working — step 1
X (80 N) and Z (30 S) share meridian 105 E, so measure along the meridian.(a(ii)(b)) Y and Z along the circle of latitude 30° S,[2]
Verified working — step 1
Y (15 W) and Z (105 E) share latitude 30 S, on opposite sides of Greenwich.(b) Find the coordinates of the points on the curve y = 2x3 - 3x2 - 36x - 3 where the gradient is zero.[4]
Verified working — step 1
Zero gradient means dydx = 0.(c) Evaluate ∫3-1 (3x2 - 2x) dx.[2]
Verified working — step 1
Antiderivative: x3 - x2.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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