SPM Mathematics Trial 2021 (Kelantan), Paper 2 (Question 9 & 10)

Question 9 (4 marks):
Mr Khairil has a medical insurance policy with Quddus Insurans with a deductible provision of RM 800 and a co – insurance percentage participation clause of 80/20 in his policy. Calculate the cost incurred by Quddus Insurans and Encik Khairil himself if the medical costs covered by his policy amount to RM 22 500.


Solution:
Medical costs after deductible provision
= RM22 500 – RM800
= RM21 700

$\begin{array}{l}\text{Cost incurred by Quddus Insurans}\\ =\frac{\text{80}}{\text{100}}\times \text{RM21 700}\\ =\text{RM}17\text{ 36}0\\ \\ \text{Cost incurred by Encik Khairil}\\ =\frac{\text{20}}{\text{100}}\times \text{RM21 700}+\text{RM800}\leftarrow \boxed{\text{Deductible provision}}\\ =\text{RM5 14}0\end{array}$

Question 10 (4 marks):
Figure 4 shows two right angled-triangles, ACE and DBE. BCE is a straight line and AE = DE = 8 cm. Calculate the value of x.

Figure 4

Solution:

$\begin{array}{l}\sin \angle A=\frac{CE}{AE}\\ \sin {45}^o=\frac{CE}{8}\\ CE=\sin {45}^o\times 8\\ =\frac{1}{\sqrt{2}}\times 8\\ =5.657\text{ cm}\\ \\ cos\angle E=\frac{BE}{DE}\\ cos{30}^o=\frac{BC+CE}{8}\\ 8\times cos{30}^o=x+5.657\\ x=8\times cos{30}^o-5.657\\ x=1.27\text{ cm}\end{array}$