SPM 2017 Add Maths Paper 2, Question 8Vectors
Solved on video in English and Bahasa Melayu · 10 marks · Form 4, Vectors · 5:58 video
The question
Diagram 5 shows a triangle PQR. The straight line PT intersects with the straight line QR at point S. Point V lies on the straight line PT. It is given that vector QS = (1/3) vector QR, vector PR = 6x and vector PQ = 9y. (a) Express in terms of x and/or y: (i) vector QR, (ii) vector PS. (b) It is given that vector PV = m·(vector PS) and vector QV = n(x - 9y), where m and n are constants. Find the value of m and of n. (c) Given vector PT = hx + 9y, where h is a constant, find the value of h.
[10 marks]
5:58Step 1
QR = QP + PR = -9y + 6x = 6x - 9y
Why this step
QP runs the opposite way to PQ, so QP = −PQ. Missing that minus sign is the classic slip, and it would give +9y instead of −9y.
11 more steps, each with the reason for it, in the full solution
Final answer
QR = 6x − 9y; PS = 2x + 6y; m = 3/8, n = 3/4; h = 3
Where students lose marks
Watch out: QP = −PQ, so mind the sign in QR, and simplify the vector equation fully before comparing coefficients in (b).
Watch every step of this question solved on video (5:58), with the reason behind each step and a box that checks your own answer.
No card. Every past-year question on video, in English and BM.
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