The time taken, $t$ in minutes, to download a particular gaming software is related to internet sp

Question

The time taken, $t$ in minutes, to download a particular gaming software is related to internet speed, $x\text{ Mbps}$. The variables $x$ and $t$ are related by the formula $t = \frac{a}{b + x}$, where $a$ and $b$ are positive constants. The data below shows some measured values of $x$ and $t$. $x\text{ (Mbps)}$$50$$100$$200$$500$$1000$ $t\text{ (minutes)}$$23$$13$$7.3$$3.2$$1.6$ Plot $\frac{1}{t}$ against $x$ and draw a straight line graph.[2] Use the graph to estimate the value of $a$ and of $b$, correct to $2$ significant figures.[4] Use the graph to estimate the time taken for John to download the gaming software if the speed of his internet is $240\text{ Mbps}$.[2] Suggest an alternative set of variables to be plotted on each axis to draw a straight line to represent the formula.[1] The diagram shows part of a straight line graph drawn to represent the equation $y = px^q$. Given that the line passes through the point $(2.5, 8.1)$ and has a gradient of $3$, find the value of $p$ correct to the nearest integer. [3]

Accepted Answer

(a)(i) Straight line of best fit for $1/t$ against $x$. (ii) $a\approx1.6\times10^3,\ b\approx23$ (2 s.f.; graph-dependent). (iii) $t\approx6.23\text{ min}$ (graph-dependent). (iv) $xt$ against $t$. (b) $p=4$

2025 PHS P2 Q4

2025 PHS P2 Q4

Solution:

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