ECZ 2016 · GCE Paper 2 · Question 10 — Graphs of Functions
Question from ECZ 2016 · GCE Paper 2 · Question 10
(a) Answer the whole of this question on a sheet of graph paper. The variables x and y are connected by the equation y = x2/5 + 2x. Some corresponding values of x and y correct to 1 decimal place, where necessary, are given in the table below. x0.30.611.523456y6.73.42.21.81.82.53.75.4q
(a(i)) Calculate the value of q, giving your answer correct to 1 decimal place.[1]
Verified working — step 1
q is the y-value at x = 6 on y = x2/5 + 2x.(a(ii)) Taking 2 cm to represent 1 unit on each axis, draw the x and y axes for 0 ≤ x ≤ 6 and 0 ≤ y ≤ 8. Draw the graph of y = x2/5 + 2x.[3]
Verified working — step 1
Scale: 2 cm to 1 unit on each axis, x from 0 to 6 and y from 0 to 8.(a(iii)) Use your graph to solve the equation x2/5 + 2x = 3.[2]
Verified working — step 1
The solutions are where the curve meets the line y = 3.(a(iv)(a)) On the same axes, draw the graph of y = x + 72.[1]
Verified working — step 1
y = x + 72 is a straight line, so two points are enough.(a(iv)(b)) Hence or otherwise, solve the equation x2/5 + 2x = x + 72.[2]
Verified working — step 1
The solutions are where the line y = x + 72 crosses the curve.(b) K480.00 is invested in an account which pays 10% per year compound interest. Find the total interest earned if money is left in the account for 3 years.[3]
Verified working — step 1
Compound interest: A = P1 + r100n = 480(1.1)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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