**Question 6**:

**(a)**Complete the following mathematical sentence by writing the symbol > or <.

**(i)**5

^{3}____ 20 is a false statement.

**(ii)**– 3 ____ – 10 is a true statement.

**(b)**Complete the conclusion in the following argument:

$$\overline{)\begin{array}{l}\text{Premise1:If}{n}^{\frac{1}{2}}=\sqrt{n},\text{then}{4}^{\frac{1}{2}}=\sqrt{4}=2.\text{}\\ \text{Premise2:}{n}^{\frac{1}{2}}=\sqrt{n}\\ \text{Conclusion:\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}\end{array}}$$

**(c)**Make a general conclusion by induction for the sequence of numbers 10,

35, 70, … which follows the following pattern.

10 = 5 (2)

^{2}– 1035 = 5 (3)

^{2}– 1070 = 5 (4)

^{2}– 10…. = ………..

*Solution:***(a)(i)**

**5**

^{3}__<__20 is a false statement.**(a)(ii)**

**– 3**

__>__– 10 is a true statement.**(b)**

$\text{Conclusion :}{4}^{\frac{1}{2}}=\sqrt{4}=2$

**(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 $\frac{{360}^{o}}{n}.$

Make one conclusion by deduction for the angle subtended at the centre of a regular polygon with 5 sides.

Solution:

Solution:

**(a)(i)**True

**(a)(ii)**The converse is true

**(b)**Premise 2:

*y =*2

*x*+ 5 is a linear equation

**(c)**

$\begin{array}{l}\text{Anglesubtendedatthecentreofaregularpentagon}\\ =\frac{{360}^{o}}{n}\\ =\frac{{360}^{o}}{5}\\ ={72}^{o}\end{array}$