4.7 Mathematics Reasoning, SPM Paper 2 (Long Questions)


Question 6:
(a) Complete the following mathematical sentence by writing the symbol > or <.
  (i) 53____ 20 is a false statement.
  (ii) – 3 ____ – 10 is a true statement.

(b) Complete the conclusion in the following argument:
 Premise 1 : If  n 1 2 = n , then  4 1 2 = 4 =2.   Premise 2 :  n 1 2 = n  Conclusion : _____________________
(c) Make a general conclusion by induction for the sequence of numbers 10,
 35, 70, … which follows the following pattern.

10 = 5 (2)2 – 10 
35 = 5 (3)2 – 10
70 = 5 (4)2 – 10
…. = ………..
Solution:
(a)(i) 53   <    20 is a false statement.
(a)(ii)   – 3    >    – 10 is a true statement.

(b)

Conclusion : 4 1 2 = 4 = 2

(c) 5 (n + 1)2 – 10, where n = 1, 2, 3, …


Question 7:
(a)(i) State whether the following compound statement is true or false.
3 + 3 = 9 or   3 × 3 = 9
(a)(ii) Determine whether the following converse is true or false.
If x > 3, then x > 7
(b) Write down Premise 2 to complete the following argument:
Premise 1: If y = mx + 5 is a linear equation, then m is a gradient of the straight line.
Premise 2: _____________________
Conclusion: 2 is the gradient of the straight line.

(c) Angle subtended at the centre of a regular polygon with n sides is 360 o n .
Make one conclusion by deduction for the angle subtended at the centre of a regular polygon with 5 sides.

Solution:
(a)(i) True
(a)(ii) The converse is true

(b) Premise 2: y = 2x + 5 is a linear equation

(c)
Angle subtended at the centre of a regular pentagon = 360 o n = 360 o 5 = 72 o

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