4.6 SPM Practice (Long Questions)

Question 1:
(a) State if each of the following statements is true or false.
 (i) $(\text{i})2^4=16\text{ and }12÷\sqrt[3]{27}=3.$
 (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.

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.