SPM 2023 Add Maths Paper 1, Question 5Vectors

Solved on video in English and Bahasa Melayu · Form 4, Vectors · 4:32 video

The question

(a)

Diagram 4 shows three points on a Cartesian plane: P(−1, 5), S(1, 2) and Q. (a) State vector SP.

(b)(i)

Using the same points as part (a), it is given that PQ = 5i + mj. (b)(i) If SP + 3PQ = 13i + 15j, find the value of m by using vector's arithmetic operations.

(b)(ii)

Hence, using PQ = 5i + 4j from part (b)(i), determine the unit vector in the direction of PQ.

SPM 2023 Add Maths Paper 1, Question 5: the question as drawn in Eduly's video4:32

Part (a)

Step 1

SP = SO + OP = −OS + OP.

Why this step

We only know position vectors from O, so we travel S → O → P. Going S to O is backwards, so it is −OS, not OS.

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

Final answer

SP = −2i + 3j

Where students lose marks

Watch out: SP = −OS + OP, not OS + OP. That wrong sign gives 7j instead of −2i + 3j.

Part (b)(i)

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

Final answer

m = 4

Where students lose marks

Watch out: use the correct SP from (a). Using SP = 7j gives m = 8/3, which is wrong.

Part (b)(ii)

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

Final answer

(5√41/41)i + (4√41/41)j

Where students lose marks

Watch out: use PQ = 5i + 4j from (b)(i). A wrong PQ gives a wrong magnitude and unit vector.

Watch every step of this question solved on video (4:32), with the reason behind each step and a box that checks your own answer.

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