SPM 2023 Add Maths Paper 2, Question 2Vectors

Solved on video in English and Bahasa Melayu · Form 4, Vectors · 4:23 video

The question

(a)(i)

Diagram 1 shows quadrilateral BCDE and right-angled triangle ABC (right angle at B). It is given that AB = 2x, AC = 3y, AB = (2/3)AE and CD = (1/3)x + y (all symbols denote vectors).

(a)(i) Express BC in terms of x and y.

(a)(ii)

It is given that AB = 2x, AC = 3y, AB = (2/3)AE and CD = (1/3)x + y.

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

(b)

Diagram 1 shows quadrilateral BCDE and right-angled triangle ABC. It is given that AB = 2x, AC = 3y, AB = (2/3)AE and CD = (1/3)x + y.

(b) Show that ED and BC are parallel.

SPM 2023 Add Maths Paper 2, Question 2: the question as drawn in Eduly's video4:23

Part (a)(i)

Step 1

Apply the triangle law in triangle ABC: BC = BA + AC.

Why this step

We aren't given BC, but we know AB and AC. So we go the long way round: B to A, then A to C.

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

Final answer

BC = −2x + 3y

Where students lose marks

Watch out: BA is the opposite of AB, so BA = −2x, not +2x. Check the direction of every arrow.

Part (a)(ii)

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

Final answer

ED = −(8/3)x + 4y

Where students lose marks

Watch out: keep the (1/3)x from CD. Chain EA + AC + CD fully, or you end up with the wrong −3x + 4y.

Part (b)

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

Final answer

Shown: ED = (4/3)BC, so they are parallel

Where students lose marks

Watch out: use the same multiple for both x and y, then write the conclusion that ED and BC are parallel.

Watch every step of this question solved on video (4:23), with the reason behind each step and a box that checks your own answer.

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