| Exam Board | OCR MEI |
|---|---|
| Module | Paper 2 (Paper 2) |
| Year | 2022 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Functions |
| Type | Sketch exponential graphs |
| Difficulty | Moderate -0.8 This is a straightforward two-part question on exponential functions requiring only basic skills: sketching a standard exponential decay curve (identifying y-intercept and general shape) and solving an exponential equation using logarithms. Both parts are routine textbook exercises with no problem-solving or conceptual challenges, making it easier than average but not trivial since it requires correct application of logarithm laws. |
| Spec | 1.06a Exponential function: a^x and e^x graphs and properties1.06g Equations with exponentials: solve a^x = b |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | (a) | M1 |
| Answer | Marks |
|---|---|
| A1 | 1.1 |
| Answer | Marks |
|---|---|
| 1.1 | decreasing concave up curve in 1st and 2nd quadrants which |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | (b) | log (3×0.4𝑥) = log (0.8) oe |
| Answer | Marks |
|---|---|
| 1.44 cao | M1 |
| Answer | Marks |
|---|---|
| A1 | 3.1a |
| Answer | Marks |
|---|---|
| 1.1 | taking logarithms in any base |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | M1 | M1 |
| Answer | Marks |
|---|---|
| x = 1.44 cao | A1 |
Question 3:
3 | (a) | M1
B1
A1 | 1.1
1.1
1.1 | decreasing concave up curve in 1st and 2nd quadrants which
does not cut the x-axis; mark intent
decreasing curve with intercept (0,3); may be in one quadrant
only
smooth curve from (‒0.5, a) through (2.5, b),
where 4.5 ≤ a ≤ 5 and 0 < b < 0.5
[3]
3 | (b) | log (3×0.4𝑥) = log (0.8) oe
𝑥log0.4 = log0.8−log3 oe
1.44 cao | M1
M1
A1 | 3.1a
1.1
1.1 | taking logarithms in any base
3rd law of logs used correctly
if M0M0 allow SC1 for 1.44 unsupported
Alternatively
0.4𝑥 = 0.8
3
M1
0.8
𝑥 = log ( )
0.4
3 | M1 | M1 | 0.8
may see 𝑥log0.4 = log( ) oe
3
x = 1.44 cao | A1
[3]
Alternatively
0.4𝑥 = 0.8
3\begin{enumerate}[label=(\alph*)]
\item On the axes in the Printed Answer Booklet, sketch the curve with equation $y = 3 \times 0.4^x$. [3]
\item Given that $3 \times 0.4^x = 0.8$, determine the value of $x$ correct to 3 significant figures. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Paper 2 2022 Q3 [6]}}