SPM Mathematics 2016, Paper 2 (Questions 3 & 4)

Question 3 (4 marks):
Calculate the value of x and of y that satisfy the following simultaneous linear equations:
2x + y = 8
–x + 4y = 5

Solution:
$\begin{array}{l}2x+y=8\mathrm{\dots \dots \dots \dots \dots }\left(1\right)\\ -x+4y=5\mathrm{\dots \dots \dots \dots \dots }\left(2\right)\\ \left(2\right)\times 2:-2x+8y=10\mathrm{\dots \dots \dots ..}\left(3\right)\\ \\ \left(1\right)+\left(3\right):\\ y+8y=8+10\\ 9y=18\\ y=\frac{18}{9}\\ y=2\\ \\ \text{From }\left(1\right):\\ 2x+2=8\\ 2x=8-2\\ 2x=6\\ x=\frac{6}{2}\\ x=3\\ \\ \therefore x=3,y=2\end{array}$

Question 4 (4 marks):
Diagram 4 shows a signboard placed by a cleaner in front of a toilet.

Diagram 4

It is given that SP = SU = RQ = RT = 90 cm and the peak of the signboard, SR, is 40 cm vertically above the horizontal floor.
(a) Name the angle between the plane PQRS and the plane UTRS.
(b) Hence, calculate the angle.


Solution:
(a)
Angle between the plane PQRS and the plane UTRS is ∠QRT.

(b)

$\begin{array}{l}\text{cos }x=\frac{40}{90}\\ x={63}^{o}37‘\\ \angle QRT={63}^{o}37‘+{63}^{o}37‘\\ ={127}^{o}14‘\end{array}$