SPM Mathematics Trial 2021 (Selangor), Paper 2 (Question 14)

Question 14:
(a) Given volume of gas, V varies inversely as the pressure, P. Given V = 2 m³ and P = 500 Nm^-2, express V in terms of P. [2 marks]

(b) Based on the answer in 14(a), complete Table 3 in the answer space. [1 mark]

(c) For this part of the question, use the graph paper provided. You may use a flexible curve rule.
Based on your answers in 14(b) and using a scale of 2 cm to 100 Nm^-2 on the x-axis and 2 cm to 1 m³ on the y-axis, draw the graph for 100 ≤ x ≤ 800. [4 marks]

(d) From the graph in 14(c), find the volume of gas, in m³, if the pressure of gas is 300 Nm^-2. [1 mark]

Answer:

P	100	200	250	400	500	800
V	10	5	4		2	1.25

Table 3


Solution:
(a)

$\begin{array}{l}V\alpha \frac{1}{P}\\ V=\frac{k}{P}\\ k=VP\\ k=\left(2\right)\left(500\right)\\ k=1000\\ \therefore V=\frac{1000}{P}\end{array}$


(b)
$\begin{array}{l}V=\frac{1000}{P}\\ V=\frac{1000}{400}=2.5\end{array}$

P	100	200	250	400	500	800
V	10	5	4	2.5	2	1.25

(c), (d)