ECZ 2020 · O-Level Paper 2 · Question 8 — Earth Geometry
P, Q, R and T are points on the surface of the earth as shown in the diagram. (Take pi as 3.142 and R = 3437 nm.)
(a(i)) P, Q, R and T are points on the surface of the earth as shown in the diagram. Find the difference in longitude between points Q and R.[2]
Verified working — step 1
Q lies on longitude 41 degrees E an…(a(ii)(a)) Calculate the distance PQ in nautical miles.[2]
Verified working — step 1
P (80 degrees N) and Q (60 degrees S) both lie on longitude 41 degrees E, so PQ runs along a great circle.(a(ii)(b)) Calculate the distance RT in nautical miles.[2]
Verified working — step 1
R (21 degrees W) and T (71 degrees W) both lie on latitude 60 degrees S, so RT runs along a circle of latitude.(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
y = integral of (x2 - 4x + 3) dx = x3/3 - 2x2 + 3x + c(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 - 4The 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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