SPM Mathematics 2017, Paper 2 (Questions 5 & 6)

Question 5 (5 marks):
(a) State whether the following compound statement is true or false.
2 > 3 and (–2)³ = –8

(b) Write down two implications based on the following statement:
a > b if and only if a – b > 0

(c) Table 1 shows the number of sides and the number of axes of symmetry for some regular polygons.

Table 1

Make a conclusion by induction by completing the statement in the answer space:
The number of axes of symmetry for a regular polygon with n sides is __________.


Solution:
(a)
Palsu. Nilai bagi 2 adalah kurang daripada 3, 2 < 3.

(b)
Implication 1: Jika a > b, maka a – b > 0
Implication 2: Jika a – b > 0, maka a – b > 0

(c)
The number of axes of symmetry for a regular polygon with n sides is
Number of sides of regular polygon = Number of axes of symmetry of regular polygon

Question 6 (4 marks):
An aquarium has the length of (x + 7) cm, the width of x cm and the height of 60 cm.
The total volume of the aquarium is 48000 cm³. The aquarium will be filled fully with water.
Calculate the value of x.

Solution:


$\begin{array}{l}\text{Volume of aquarium}=48000{\text{ cm}}^3\\ \text{So,}\\ \left(x\right)\left(x+7\right)\left(60\right){\text{ cm}}^3=48000{\text{ cm}}^3\\ \left(x\right)\left(x+7\right)=\frac{48000}{60}\\ x^2+7x=800\\ x^2+7x-800=0\\ \left(x-25\right)\left(x+32\right)=0\\ x-25=0\text{ or }x+32=0\\ x=25\text{ or }x=-32\left(\text{not accepted}\right)\\ \\ \text{So the value of }x=25\text{ cm}\end{array}$