4.6 SPM Practice (Long Questions)

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 $\frac{{360}^o}{n}.$
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)
$\begin{array}{l}\text{Angle subtended at the centre of a regular pentagon}\\ =\frac{{360}^o}{n}\\ =\frac{{360}^o}{5}\\ ={72}^o\end{array}$

Question 8:
(a) State whether the following sentence is a statement or not a statement.

x + 7 = 9

(b) Complete the following compound statement by writing the word ‘or’ or ‘and’ to form a true statement.
2³ = 6 …… 5 × 0 = 0

(c) Write down Premise 2 to complete the following argument:
Premise 1: All isosceles triangles have two equal sides.
Premise 2: _____________________
Conclusion: ABC has two equal sides.

(d) Make a general conclusion by induction for the sequence of numbers 1, 7, 17, 31, … which follows the following pattern.
1 = (2 × 1) – 1
7 = (2 × 4) – 1
17 = (2 × 9) – 1
31 = (2 × 16) – 1

Solution:
(a) Not a statement

(b) 2³ = 6 …or… 5 × 0 = 0

(c) ABC is an isosceles triangle.

(d)
1 = (2 × 1) – 1 =  (2 × 1²) – 1
7 = (2 × 4) – 1 =  (2 × 2²) – 1
17 = (2 × 9) – 1 =  (2 × 3²) – 1
31 = (2 × 16) – 1 =  (2 × 4²) – 1
  =  2n² – 1, n = 1, 2, 3, …