4.6 SPM Practice (Long Questions)

Question 11 (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 12 (5 marks):
(a) State whether the following statement is true or false.


(b) Write down the converse of the following implication:
 

(c) Write down Premise 2 to complete the following argument:
Premise 1   :  If x is an odd number, then x is not divisible by 2.
Premise 2   : ………………………………………………………
Conclusion : 24 is not an odd number.

(d) Based on the information below, make one conclusion by deduction for the surface area of sphere with radius 9 cm.



Solution:
(a)
True

(b)
If an angle is an acute angle, then the angle lies between 0^o and 90^o.

(c)
24 is divisible by 2.

(d)
4π(9)² = 324π
Surface area of the sphere is 324π.