| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/2 (Pre-U Mathematics Paper 2) |
| Year | 2019 |
| Session | Specimen |
| Marks | 8 |
| Topic | Exponential Functions |
| Type | Sketch exponential graphs |
| Difficulty | Moderate -0.3 This is a straightforward applied exponential decay question requiring basic manipulation of exponential functions (solving ae^{-kt} = 1), sketching standard exponential curves, and adding concentrations. The context is accessible, all steps are routine A-level techniques with no novel insight required, making it slightly easier than average. |
| Spec | 1.02n Sketch curves: simple equations including polynomials1.06a Exponential function: a^x and e^x graphs and properties1.06g Equations with exponentials: solve a^x = b |
**(a)**
Attempt to solve $c = 1$ for at least one drug, and obtain a solution — **M1**
Obtain 54.9 (hours) for Antiflu — **A1**
Obtain 23.0 (hours) for Coldcure — **A1** [3]
**(b)**
Two *decaying* exponentials in the first quadrant — **B1**
Correct intercepts on the $c$-axis — **B1**
Crossing over at a value of $t < 23$ — **B1** [3]
**(c)**
Assume additive nature of the concentrations — **M1**
$5e^{-0.07\times 30} + 5e^{-0.07\times 10} = 3.10$ — **A1** [2]6 Diane is given an injection that combines two drugs, Antiflu and Coldcure. At time $t$ hours after the injection, the concentration of Antiflu in Diane's bloodstream is $3 \mathrm { e } ^ { - 0.02 t }$ units and the concentration of Coldcure is $5 \mathrm { e } ^ { - 0.07 t }$ units. Each drug becomes ineffective when its concentration falls below 1 unit.
\begin{enumerate}[label=(\alph*)]
\item Show that Coldcure becomes ineffective before Antiflu.
\item Sketch, on the same diagram, the graphs of concentration against time for each drug.
\item 20 hours after the first injection, Diane is given a second injection. Determine the concentration of Coldcure 10 hours later.
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9794/2 2019 Q6 [8]}}