SPM Mathematics Trial 2021 (Kelantan), Paper 2 (Question 3 & 4)

Question 3 (4 marks):
Zulaikha is 132₆ years old. Zulaikha’s age is twice the age of her daughter, Zahira. The ratio of Zahira’s age to the age of her younger brother, Ahmad is 7:6. Calculate the total age Zulaikha and her children in base 7.

Solution:
Zulaikha’s age,
132₆ = (1 × 6²) + (3 × 6¹) + (2 × 6⁰)
 = 36 + 18 + 2
 = 56 years old

Zahira’s age = 56 ÷ 2
 = 28 years old

Zahira : Ahmad = 7 : 6
  = (7 × 4) : (6 × 4)
  = 28 : 24
Thus, Ahmad = 24 years old

Total age = 56 + 28 + 24
  = 108 years old

Thus, the total age of Zulaikha and her children in base 7 = 213₇

Question 4 (4 marks):
In a furniture exhibition, there is a piece of round-shaped window decorated with a small circle carving the same size as Diagram 2. The radius of the window is 72 cm. Calculate the area of the uncarved area. (Use π=22/7 )

Diagram 2


Solution:
Radius of small circle = 72 ÷ 3 = 24 cm



$\begin{array}{l}\text{Area of circle}=\pi r^2\\ \text{Area of the uncarved area}\\ \text{= Area of the window }-\text{ Area of 7 small circles}\\ =\left(\frac{\text{22}}{7}\times {72}^2\right)-7\left(\frac{\text{22}}{7}\times {24}^2\right)\\ =\frac{25344}{7}{\text{ cm}}^{\text{2}}\text{ or }3620.57{\text{ cm}}^{\text{2}}\end{array}$