ECZ 2015 · GCE Paper 2 · Question 8 — Graphs of Functions
Answer the whole of this question on graph paper.
(a) The variables x and y are connected by the equation y = x2/6 + 12x - 6. The table below shows some corresponding values of x and y. The values of y are given correct to one decimal place. x11.5234566.5y6.22.40.7-0.5-0.30.62.0p
(a(i)) Calculate the value of p, correct to 1 decimal place.[1]
Verified working — step 1
p is the y-value at x = 6.5 on y = x2/6 + 12x - 6.(a(ii)) Using a scale of 2 cm to represent 1 unit on each axis, draw the graph of y = x2/6 + 12x - 6.[3]
Verified working — step 1
Scale: 2 cm to 1 unit on each axis.(a(iii)) By drawing a tangent, find the gradient of the curve at the point (6, 2).[2]
Verified working — step 1
Draw a tangent touching the curve at (6, 2) and take its rise over run.(a(iv)) On the same axes, draw the graph of the straight line y = x4, hence solve the equation x2/6 + 12x - 6 = x4.[3]
Verified working — step 1
Draw the line y = x4 through (0, 0) and (4, 1).(b) Mofu, Kopa and Nora are partners in business. Mofu owns 50% of the shares while Kopa and Nora own the remaining shares equally. Given that Mofu's shares are valued at K1 800.00,
(b(i)) calculate the sum of all the shares,[1]
Verified working — step 1
Mofu's 50% share is worth K1 800.00.(b(ii)) express the shares of Mofu, Kopa and Nora as a ratio in its simplest form.[2]
Verified working — step 1
Mofu has 50%; Kopa and Nora share the remaining 50% equally, so 25% each.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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