2.5 SPM Practice (Long Questions)

Question 6:
(a) Complete the table in the answer space for the equation $y=\frac{36}{x}$   by writing down the values of y when x = 3 and x = 8.

(b) For this part of the question, use graph paper. You may use a flexible curve rule.
By using a scale of 1 cm to 1 unit on the x-axis and 1 cm to 1 unit on the y-axis, draw the graph of $y=\frac{36}{x}$  for 2 ≤ x ≤ 14.

(c) From your graph, find
(i) the value of y when x = 2.6,
(ii) the value of x when y = 4.

(d) Draw a suitable straight line on your graph to find the values of x which satisfy the equation $\frac{36}{x}+x-14=0$  for 2 ≤ x ≤ 14.

Answer:

x	2	2.4	3	4	6	8	10	12	14
y	18	15		9	6		3.6	3	2.6

Solution:
(a)
$\begin{array}{l}y=\frac{36}{x}\\ \text{when }x=3\\ y=\frac{36}{3}=12\\ \\ \text{when }x=8\\ y=\frac{36}{8}=4.5\end{array}$

(b)


(c)
(i) From the graph, when x = 2.6, y = 13.6
(ii) From the graph, when y = 4, x = 9

(d)
$\begin{array}{l}y=\frac{36}{x}\mathrm{...........}\left(1\right)\\ 0=\frac{36}{x}+x-14\mathrm{...........}\left(2\right)\\ \left(1\right)-\left(2\right):\\ y=-x+14\end{array}$

The suitable straight line is y = –x + 14.

x	2	12
y = –x + 14	12	2

From the graph, x = 3.4, 10.6.