| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Functions |
| Type | Find intersection of exponential curves |
| Difficulty | Moderate -0.3 This is a straightforward C2 exponential question requiring basic sketching, solving 5^(x-1)=10 using logarithms, and solving 5^(x-1)=2^x (also with logs). All techniques are standard for this module with no novel problem-solving required, making it slightly easier than average but not trivial due to the multi-part structure and calculator work needed. |
| Spec | 1.06a Exponential function: a^x and e^x graphs and properties1.06g Equations with exponentials: solve a^x = b |
\begin{enumerate}
\item (a) Sketch the curve $y = 5 ^ { x - 1 }$, showing the coordinates of any points of intersection with the coordinate axes.\\
(b) Find, to 3 significant figures, the $x$-coordinates of the points where the curve $y = 5 ^ { x - 1 }$ intersects\\
(i) the straight line $y = 10$,\\
(ii) the curve $y = 2 ^ { x }$.
\item As part of a new training programme, Habib decides to do sit-ups every day.
\end{enumerate}
He plans to do 20 per day in the first week, 22 per day in the second week, 24 per day in the third week and so on, increasing the daily number of sit-ups by two at the start of each week.\\
\hfill \mbox{\textit{OCR C2 Q4 [8]}}