ECZ 2010 · O-Level Paper 2 · Question 9 — Graphs of Functions

The variables x and y are connected by the equation y = (15)x(10 - x²). The table below shows some corresponding values of x and y. The values of y are given correct to one decimal place where necessary. x-101233.54y-1.801.82.40.6-1.6p

(a) Calculate the value of p.[1]

Verified working — step 1

p is the y-value at x = 4 on y = (15)x(10 - x²).

(b) Using a scale of 2 cm to represent 1 unit on both axes for -1 ≤ x ≤ 5 and -5 ≤ y ≤ 3, draw the graph of y = (15)x(10 - x²).[3]

Verified working — step 1

Scale: 2 cm to 1 unit on both axes, x from -1 to 5 and y from -5 to 3.

(c) By drawing a tangent to the curve, estimate the gradient of the curve at the point (1, 1.8).[2]

Verified working — step 1

Draw a tangent touching the curve at (1, 1.8) and take its rise over run.

(d) On the same graph, draw the line whose equation is 5y + 4x = 4.[2]

Verified working — step 1

Rearrange into y = form: 5y = 4 - 4x, so y = 4 - 4x5.

(e) Use your graphs to find the solutions of (15)x(10 - x²) = -(45)x + 45.[2]

Verified working — step 1

The solutions are where the curve meets the line.

(f) Estimate the area under the curve between x = 1, x = 3 and the line y = 0.[2]

Verified working — step 1

Ordinates at x = 1, 2, 3 are 1.8, 2.4 and 0.6.

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Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.

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