SPM 2020 Add Maths Paper 2, Question 4Vectors

Solved on video in English and Bahasa Melayu · 7 marks · Form 4, Vectors · 5:18 video

The question

(a)(i)

Diagram 1 shows a triangle AOB with point P on AB. It is given that OA = 2x, OB = 3y, AP = (1/3)AB and AQ = kOB, where k is a constant (x and y are vectors). (a) Express in terms of x and y: (i) AB.

(a)(ii)

(a)(ii) Express OP in terms of x and y.

[3 marks]

(b)

(b) State OQ in terms of k, x and y. Hence, find the value of k if the points O, P and Q are collinear.

[4 marks]

SPM 2020 Add Maths Paper 2, Question 4: the question as drawn in Eduly's video

5:18

Part (a)(i)

Step 1

Using the triangle law: AB = AO + OB.

Why this step

Examiners want the triangle law written. Any side equals the sum of the other two laid tail to head, so A to B goes through O.

2 more steps, each with the reason for it, in the full solution

Final answer

AB = −2x + 3y

Where students lose marks

Watch out: write down the triangle law you use, and keep AB and BA apart. AO is −OA, so the sign flips.

Part (a)(ii)

4 more steps, each with the reason for it, in the full solution

Final answer

OP = (4/3)x + y

Where students lose marks

Watch out: write the triangle law OP = OA + AP, and apply the 1/3 to AB (not BA or another vector).

Part (b)

6 more steps, each with the reason for it, in the full solution

Final answer

OQ = 2x + 3ky; k = 1/2

Where students lose marks

Watch out: use OQ to satisfy 'hence' (OP = λOQ). x and y are general vectors, so never write them as column vectors.

Watch every step of this question solved on video (5:18), with the reason behind each step and a box that checks your own answer.

Start 7 days free Already a member? Watch it now

No card. Every past-year question on video, in English and BM.

All questions in SPM 2020 Paper 2

Vectors: lessons and every past-year question

Baca dalam Bahasa Melayu

SPM 2020 Add Maths Paper 2, Question 4Vectors

The question

Part (a)(i)

Part (a)(ii)

Part (b)

More Vectors questions