ECZ 2015 · O-Level Paper 2 · Question 7 — Quadratic Functions

Question from ECZ 2015 · O-Level Paper 2 · Question 7

(a) The variables x and y are connected by the equation y = x2 - 2x + 1. Some of the corresponding values of x and y correct to 1 decimal place are given in the table below. x-1.5-1-0.500.511.522.53yp42.310.300.312.34

(a(i)) Calculate the value of p,[1]

Verified working — step 1

p is the y-value at x = -1.5 on y = x2 - 2x + 1.

(a(ii)) Using a scale of 2 cm to represent 1 unit on both axes, draw the graph of y = x2 - 2x + 1 for -2 ≤ x ≤ 3 and 0 ≤ y ≤ 10.[3]

Verified working — step 1

Scale: 2 cm to 1 unit on both axes, x from -2 to 3 and y from 0 to 10.

(a(iii)) Calculate an estimate of the gradient of the curve at the point (0, 1).[2]

Verified working — step 1

Draw the tangent to the curve at (0, 1).

(a(iv)) Showing your method clearly, use your graph to solve the equation x2 - 2x + 1 = 1.5.[3]

Verified working — step 1

Draw the horizontal line y = 1.5 on the same axes.

(b) Given that Kachinja uses K46.90 to buy $7,

(b(i)) calculate the cost of buying $1,[1]

Verified working — step 1

K46.90 buys $7.

(b(ii)) how much Kwacha will be required to buy $3?[2]

Verified working — step 1

Use the unit rate from part (i).

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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