2.5 SPM Practice (Long Questions)

Question 13 (12 marks):
(a) Complete Table 2 in the answer space, for the equation $y=\frac{30}{x}$  by writing down the values of y when x = 2 and x = 5.

(b) For this part of the question, use the graph paper. You may use a flexible curve ruler.
Using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis, draw the graph of $y=\frac{30}{x}\text{ for }0\le x\le 7.$  

(c) From the graph in 12(b), find
(i) the value of y when x = 2.6,
(ii) the value of x when y = 17.5.

(d) Draw a suitable straight line on the graph in 12(b) to find the values of x which satisfy the equation $\frac{30}{x}=-5x+30\text{ for }0\le x\le 7.$
State the values of x.

Answer:
Table 2


Solution:
(a)



(b)



(c) From the graph
(i) When x = 2.6; y = 11.5
(ii) When y = 17.5; x = 1.7

(d)
$\begin{array}{l}\text{Given,}\frac{30}{x}=-5x+30\\ y=-5x+30\\ \text{From the graph; }x=1.25\text{ and }4.75\end{array}$