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 ⅓ = 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 b x + a y = a b .
(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 b x + a y = a b . _ Implication 2: If b x + a y = a b , then x a + y b = 1. _
(c)
Size of an interior angle of a regular hexagon = ( 1 2 6 ) × 180 = 2 3 × 180 = 120

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