ECZ 2022 · O-Level Paper 2 · Question 2 — Vectors In Two Dimensions

Question from ECZ 2022 · O-Level Paper 2 · Question 2

(a) Solve the equation 3x² - 5x - 7 = 0, giving your answers correct to 2 decimal places.[5]

Verified working — step 1

Use the formula with a = 3, b = -5, c = -7.

(b) In the parallelogram OABC, OA = 4a, OC = 6c, AP = (23)AC and M is the midpoint of BC.

(b(i)) Find in terms of a and/or c

(b(i)(a)) AC,[1]

Verified working — step 1

Head minus tail: AC = …

(b(i)(b)) OP,[1]

Verified working — step 1

AP = (23)AC, so OP = OA + (23)AC.

(b(i)(c)) OM.[1]

Verified working — step 1

OABC is a parallelogram, so OB = OA + OC = 4a + 6c.

(b(ii)) Hence or otherwise, show that the points O, P and M are collinear.[2]

Verified working — step 1

OP = (43)a + 4c and OM = 2a + 6c.

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.

Have a different question?

Search it — if it is from a past paper or a school mock, chances are we have it worked out, or one that uses the same method.