Easy -1.8 This is a straightforward three-part question testing basic proportionality, simple algebraic word problems, and exponential decay with explicit percentage given. Part (a) is trivial sketching, part (b) requires setting up one equation with given ratios, and part (c) applies a standard exponential model with all parameters provided. All parts are routine recall and direct application with no problem-solving insight required.
The graph \(G\) shows the relationship between the variables \(y\) and \(x\), where \(y \propto x\). Sketch the graph \(G\). [1]
Mary and Jeff work for a company which pays its employees by hourly rates. Mary's hourly rate is twice Jeff's hourly rate. On a certain day, Jeff worked three times as long as Mary and was paid £120. Calculate Mary's earnings on that day. [3]
Atmospheric pressure, \(P\) units, decreases as the height, \(H\) metres, above sea level increases. The rate of decrease is 12% for every 1000m. At sea level, the pressure \(P\) is 1013 units. Write down the model for \(P\) in terms of \(H\) and find the pressure at the top of Mount Everest, which is 8848m above sea level. [3]
\begin{enumerate}[label=(\alph*)]
\item The graph $G$ shows the relationship between the variables $y$ and $x$, where $y \propto x$. Sketch the graph $G$. [1]
\item Mary and Jeff work for a company which pays its employees by hourly rates. Mary's hourly rate is twice Jeff's hourly rate. On a certain day, Jeff worked three times as long as Mary and was paid £120. Calculate Mary's earnings on that day. [3]
\item Atmospheric pressure, $P$ units, decreases as the height, $H$ metres, above sea level increases. The rate of decrease is 12% for every 1000m. At sea level, the pressure $P$ is 1013 units. Write down the model for $P$ in terms of $H$ and find the pressure at the top of Mount Everest, which is 8848m above sea level. [3]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 1 2022 Q8 [7]}}