SPM Mathematics 2017, Paper 2 (Questions 1 & 2)

Question 1 (3 marks):
The Venn diagram in the answer space shows set P, set Q and set R such that the universal set ξ = P U Q U R.
On the diagram in the answer space, shade the set
(a) P’,
(b) (P ∩ Q) U R

Answer:



Solution:
(a)



(b)

Question 2 (3 marks):
Diagram 1 shows a right prism with a rectangular base EFGH on a horizontal plane. Triangle FGS is the uniform cross section of the prism. GS and HR are vertical edges.

Diagram 1

(a) Name the angle between the plane EFSR and the plane EFGH.
(b) Hence, calculate the angle between the plane EFSR and the plane EFGH.


Solution:
(a)
Angle between the plane EFSR and the plane EFGH
= ∠REH or ∠SFG

(b)
$\begin{array}{l}cos\angle SFG=\frac{1.5\text{ cm}}{4.5\text{ cm}}\\ cos\angle SFG=\frac{1}{3}\\ \angle SFG={70.53}^o\end{array}$