| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/2 (Pre-U Mathematics Paper 2) |
| Year | 2016 |
| 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 e^(-kt) = 1/3 or 1/5), sketching standard exponential curves, and adding concentrations from two injections. All techniques are routine A-level material with no novel insight required, making it slightly easier than average. |
| Spec | 1.06a Exponential function: a^x and e^x graphs and properties1.06i Exponential growth/decay: in modelling context |
(i) 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]
(ii) Two *decaying* exponentials in the first quadrant [B1]
Correct intercepts on the $c$-axis [B1]
Crossing over at a value of $t < 23$ [B1]
(iii) Assume additive nature of the concentrations [M1]
$5e^{-0.07\times 30} + 5e^{-0.07\times 10} = 3.10$ [A1]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.\\
(i) Show that Coldcure becomes ineffective before Antiflu.\\
(ii) Sketch, on the same diagram, the graphs of concentration against time for each drug.\\
(iii) 20 hours after the first injection, Diane is given a second injection. Determine the concentration of Coldcure 10 hours later.
\hfill \mbox{\textit{Pre-U Pre-U 9794/2 2016 Q6 [8]}}