The mass, $y$ mg, of a radioactive substance decreases with time, $x$ hours, after the start of

Question

The mass, $y$ mg, of a radioactive substance decreases with time, $x$ hours, after the start of the experiment. The research analyst claims that the data can be modelled by an equation of the form $x^2 y = a + bx^2$, where $a$ and $b$ are constants. Values of $y$ for different values of $x$ have been collected. Explain how a straight line graph can be drawn to represent the formula, and state how the values of $a$ and $b$ could be obtained from the line.[4] The table shows experimental values of two variables $R$ and $t$. $t$$10$$20$$30$$40$$50$ $R$$2.32$$2.79$$3.31$$4.74$$4.90$ It is known that $R$ and $t$ are related by the equation $R = R_0(3^{-kt})$, where $R_0$ and $k$ are constants. An error was made in recording one of the values of $R$. Plot $\ln R$ against $t$ and draw a straight line graph to illustrate the information.[2] From your straight line graph, identify the incorrect reading and suggest a corrected value for R.[2] Use your graph to estimate the values of $R_0$ and $k$[3]

Accepted Answer

(i) $\frac{1}{\cosec x-\cot x}-\frac{1}{\sin x}=\cot x$ (ii) $x=\tan^{-1}\left(\frac{1}{2}\right),\ \pi+\tan^{-1}\left(\frac{1}{2}\right),\ \frac{3\pi}{4},\ \frac{7\pi}{4}$

2025 SST PRELIMS P1 Q7

2025 SST PRELIMS P1 Q7

Solution:

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