Mathematics Reasoning Long Questions (Question 1 – 3)


Question 1:
(a) State if each of the following statements is true or false.
 (i) 2 4 = 16 and 12 ÷ 27 3 = 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.
(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:


AB = 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.

Leave a Reply

Your email address will not be published. Required fields are marked *