ECZ 2018 · GCE Paper 2 · Question 7 — Earth Geometry
A and B are points on latitude 60°N, C and D are points on latitude 60°S; A and D lie on longitude 60°W, B and C on longitude 60°E [π = 3.142, R = 3437 nm]. Also: the curve y = 2x2 - 3x - 2.
(a(i)) Calculate the distance BC along the longitude 60°E in nautical miles.[2]
Verified working — step 1
BC lies along a meridian (longitude 60°E), so the arc from 60°N to 60°S subtends an angle at the centre of 60°+60° = 120°.(a(ii)) A ship sails from C to D in 12 hours. Find its speed in knots.[4]
Verified working — step 1
C and D lie on latitude 60°S, and the longitude difference between 60°E and 60°W is 120°.(b(i)) Determine the equation of the normal to the curve y = 2x2 - 3x - 2 that passes through the point (3, 7).[3]
Verified working — step 1
y = 2x² - 3x - 2(b(ii)) Evaluate the integral from 0 to 1 of (x2 - 2x - 3) dx.[3]
Verified working — step 1
∫₀¹ (x² - 2x - 3) dxThe 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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