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

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:

(c) It is given that the interior angle of a regular polygon of n sides
is   $\left(1-\frac{2}{n}\right)×{180}^{\circ }$ .
Make one conclusion by deduction on the size of the interior angle of a
regular hexagon.

Solution:

(a)(i) True
(a)(ii) False

(b)

(c)
$\begin{array}{l}\text{Size of an interior angle of a regular hexagon}\\ =\left(1-\frac{2}{6}\right)×{180}^{\circ }\\ =\frac{2}{3}×{180}^{\circ }\\ ={120}^{\circ }\end{array}$