ECZ 2017 · O-Level Paper 2 · Question 9 — Earth Geometry
W, X, Y and Z are four points on the surface of the earth as shown in the diagram. (Take pi as 3.142 and R = 3437 nm.)
(a(i)) W, X, Y and Z are four points on the surface of the earth as shown in the diagram. Calculate the difference in latitude between W and Y.[2]
Verified working — step 1
W is on latitude 80 degrees N an…(a(ii)(a)) Calculate the distance in nautical miles between X and Z along the longitude 105 degrees E.[2]
Verified working — step 1
X is at 80 degrees N and Z at 30 degrees S on the same meridian, so the difference in latitude is 80 + 30 = 110 degrees.(a(ii)(b)) Calculate the distance in nautical miles between Y and Z along the circle of latitude 30 degrees S.[2]
Verified working — step 1
Y is at 15 degrees W and Z at 105 degrees E, so the difference in longitude is 15 + 105 = 120 degrees.(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
dydx= 6x2 - 6x - 36 = 0(c) Evaluate the integral from -1 to 3 of (3x2 - 2x) dx.[2]
Verified working — step 1
Integral of (3x2 - 2x) dx = 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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