ECZ 2012 · O-Level Paper 2 · Question 10 — Graphs of Functions

Question from ECZ 2012 · O-Level Paper 2 · Question 10

(a) The variables x and y are connected by the equation y = 42 - x - x2. The table below shows some corresponding values of x and y. x-8-6-4-2-1035yq12304042423012

(a(i)) Calculate the value of q.[1]

Verified working — step 1

q is the y-value at x = -8 on y = 42 - x - x2.

(a(ii)) Using a scale of 1 cm to represent 1 unit on the x-axis for -8 ≤ x ≤ 6 and a scale of 2 cm to represent 10 units on the y-axis for -20 ≤ y ≤ 50, draw the graph of y = 42 - x - x2.[3]

Verified working — step 1

Scale: x-axis 1 cm to 1 unit (-8 to 6), y-axis 2 cm to 10 units (-20 to 50).

(a(iii)) By drawing the line 7y - 20x = 140 on the same graph, solve the equation 42 - x - x2 = 20x7 + 20.[3]

Verified working — step 1

Rearranging 7y - 20x = 140 gives y = 20x7 + 20, so draw that line.

(a(iv)) Estimate the area under the curve between x = 0, y = 0 and x = 4.[2]

Verified working — step 1

Ordinates at x = 0, 1, 2, 3, 4 are 42, 40, 36, 30, 22.

(b) Given that x = 2 and y = -3, find the value of x2 - 6xy + 3y - 3x.[3]

Verified working — step 1

Substitute x = 2 and y = -3 into each term.

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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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