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
(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.

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:

Volume of aquarium=48000 cm3So,(x)(x+7)(60) cm3=48000 cm3(x)(x+7)=4800060x2+7x=800x2+7x−800=0(x−25)(x+32)=0x−25=0 or x+32=0x=25 or x=−32(not accepted)So the value of x=25 cm
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:

Volume of aquarium=48000 cm3So,(x)(x+7)(60) cm3=48000 cm3(x)(x+7)=4800060x2+7x=800x2+7x−800=0(x−25)(x+32)=0x−25=0 or x+32=0x=25 or x=−32(not accepted)So the value of x=25 cm