# 4.7.1 Mathematics Reasoning, SPM Paper 2 (Long Questions)

Question 1:
(a) State if each of the following statements is true or false.
(i)
(ii) 17 is a prime number or an even number.

(b) Complete the statement, in the answer space, to form a true statement by
using the quantifier ‘all’ or ‘some’.

(c) Write down two implications based on the following statement:

 A number is a prime number if and only if it is only divisible by 1 and itself.
Solution:
(a)(i) False
(a)(ii) True

(b)   Some   multiples of 3 are multiples of 6.

(c) Implication 1: If a number is a prime number, then it is only divisible by 1 and itself.
Implication 2: If a number is only divisible by 1 and itself, then it is a prime
number.

Question 2:
(a) State if each of the following statements is true or false.
(i)  2 × 3 = 6 or 2 + 3 = 6
(ii) 2 is a prime number and 5 is an even number.

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

Hence, state whether the converse is true or false.

 If x is a multiple of 12, then x is a multiple of 3.
(c) Complete the premise in the following argument:

 Premise 1: All hexagons have six sides Premise 2: _____________________ Conclusion: ABCDEF has six sides.
Solution:
(a)(i) True
(a)(ii) False

(b) Converse: If x is a multiple of 3, then x is a multiple of 12.
The converse is false.

(c) Premise 2: ABCDEF is a hexagon.

Question 3:
(a) Complete each of the following statements with the quantifier ‘all’ or ‘some’ so that it will become a true statement.
(i) ___________ of the prime numbers are odd numbers.
(ii) ___________ pentagons have five sides.

(b) Write down two implications based on the following statement:

 A ∩ B = B if and only if A υ B = A.
(c) Complete the premise in the following argument:

 Premise 1: If a number is a factor of 24, then it is a factor of 48. Premise 2: 12 is a factor of 24. Conclusion: _____________________

Solution:
(a)(i)    Some  of the prime numbers are odd numbers.
(a)(ii)  All pentagons have five sides.

(b) Implication 1: If AB = B, then A υ B = A.
Implication 2: If A υ B = A, then AB = B.

(c)
Conclusion: 12 is a factor of 48.