ECZ 2020 · O-Level Paper 2 · Question 8 — Earth Geometry
Question from ECZ 2020 · O-Level Paper 2 · Question 8
(a) P, Q, R and T are points on the surface of the earth as shown in the diagram below. (Take π as 3.142 and R = 3437 nm)
(a(i)) Find the difference in longitude between points Q and R.[2]
Verified working — step 1
Q (41 E) and R (21 W) sit on opposi…(a(ii)) Calculate the distance, in nautical miles, of
(a(ii)(a)) PQ,[2]
Verified working — step 1
P (80 N) and Q (60 S) share meridian 41 E, on opposite sides of the equator.(a(ii)(b)) RT.[2]
Verified working — step 1
R (21 W) and T (71 W) share latitude 60 S, both west of Greenwich.(b) A curve has gradient x2 - 4x + 3. Find the equation of this curve if it passes through the point (3, -1).[3]
Verified working — step 1
Integrate the gradient to recover the curve:(c) Find the equation of the normal to the curve y = x3 - 2x2 - 4x + 1 at the point (-1, 2).[3]
Verified working — step 1
dydx = 3x2 - 4x - 4; at x = -1 the tangent gradient is 3 + 4 - 4 = 3.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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