Mathematics Reasoning Long Questions (Question 4 & 5)


Question 4:
(a) Combine the following two statements to form one true statement.
      Statement 1: (– 3)² = 9
      Statement 2: –3 (3) = 19

(b) Complete the premise in the following argument:

Premise 1: _____________________
Premise 2: x is a multiple of 25.
Conclusion: x is a divisible of 5.

(c) Make a general conclusion by induction for the sequence of numbers 7, 14, 
      27, … which follows the following pattern.

7 = 3 (2)1 + 1
14 = 3 (2)2 + 2
27 = 3 (2)3 + 3
…. = ………..

Solution:
(a) (– 3)² = 9 or –3 (3) = 19.

(b) Premise 1: All multiples of 25 is divisible by 5.

(c) 3 (2)n + n, where n = 1, 2, 3, …



Question 5:
(a) State if each of the following statements is true or false.
     (i)                23 = 8 or  = 1.33.
     (ii)             – 6 > – 8 and 6 > 8.

(b) Write down two implications based on the following statement:
x a + y b =1 if and only if bx+ay=ab.
(c) It is given that the interior angle of a regular polygon of n sides
      is   ( 1 2 n )× 180 .
      Make one conclusion by deduction on the size of the interior angle of a
      regular hexagon.

Solution:
(a)(i) True
(a)(ii) False

(b) 
Implication 1:   If   x a + y b =1, then bx+ay=ab. _ Implication 2:   If  bx+ay=ab, then  x a + y b =1. _
(c)
Size of an interior angle of a regular hexagon =( 1 2 6 )× 180 = 2 3 × 180 = 120