# SPM Additional Mathematics 2018, Paper 1 (Question 8 – 10)

Question 8 (3 marks):
Diagram 3 shows vectors drawn on a square grid.

Diagram 3

Solution:
(a)
$\stackrel{\to }{OM}=\underset{˜}{p}+2\underset{˜}{q}$

(b)

Question 9 (4 marks):

Solution:

(a)

(b)

Question 10 (3 marks):
The following information refers to the equation of two straight lines, AB and CD.

Given the straight lines AB and CD are perpendicular to each other, express h in terms of k.

Solution:
$\begin{array}{l}AB:y-2kx-3=0\\ y=2kx+3\\ {m}_{AB}=2k\\ \\ CD:\frac{x}{3h}+\frac{y}{4}=1\\ {m}_{CD}=-\frac{4}{3h}\\ \\ {m}_{AB}×{m}_{CD}=-1\\ 2k×\left(-\frac{4}{3h}\right)=-1\\ -8k=-3h\\ h=\frac{8}{3}k\end{array}$