SPM 2024 Add Maths Paper 1, Question 3Vectors

Solved on video in English and Bahasa Melayu · Form 4, Vectors · 5:47 video

The question

(a)(i)

Diagram 3 shows vector a and vector CD on a square grid. (i) Express vector CD in terms of a.

(a)(ii)

(ii) Draw −4a on Diagram 3.

(b)

Solutions by scale drawing and / or vector are not accepted. Diagram 4 shows the straight line AB with A(5, 8) and B(−1, −1). Given that point C lies on AB such that AC : CB = 2 : 1, find the coordinates of C.

(c)

Solutions by scale drawing are not accepted. It is given that P(4, 5) and Q(2, 1) lie on a Cartesian plane. Find the equation of the straight line which is perpendicular to the straight line PQ and passing through point P.

Part (a)(i)

Step 1

Observe that CD is parallel to vector a and in the same direction.

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

Final answer

CD = (5/2)a

Where students lose marks

Watch out: don't leave the answer as 2a + (1/2)a. Combine it into one simplified multiple, (5/2)a.

Part (a)(ii)

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

Final answer

Drawing (see video)

Where students lose marks

Watch out: the direction must be opposite to a and the length exactly 4 times a. Count the grid squares carefully.

Part (b)

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

Final answer

C = (1, 2)

Where students lose marks

Watch out: don't swap m and n. n multiplies A's coordinates and m multiplies B's; swapping gives the wrong point (3, 5).

Part (c)

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

Final answer

y = −(1/2)x + 7

Where students lose marks

Watch out: the line must pass through P(4, 5), not Q(2, 1). Using Q gives the wrong equation y = −(1/2)x + 2.

Watch every step of this question solved on video (5:47), with the reason behind each step and a box that checks your own answer.

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