| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Functions |
| Type | Tangent to exponential curve |
| Difficulty | Moderate -0.8 This is a straightforward question testing basic understanding of gradients and tangents. Part (i) requires drawing a tangent by eye and reading off the gradient—a simple graphical skill. Part (ii) uses the chord gradient formula with given x-values, requiring only substitution into 2^x and basic arithmetic. Both parts are routine procedures with no problem-solving or conceptual depth required. |
| Spec | 1.06a Exponential function: a^x and e^x graphs and properties1.07a Derivative as gradient: of tangent to curve |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{1}{2}x^{-\frac{1}{2}} - 3x^{-2}\) oe; isw | B3 | need not be simplified; B2 for one term correct; ignore \(+ c\); if B0 allow M1 for either \(x^{1/2}\) or \(x^{-1}\) seen before differentiation; deduct one mark for extra term in \(x\) |
## Question 6:
$\frac{1}{2}x^{-\frac{1}{2}} - 3x^{-2}$ oe; isw | B3 | need not be simplified; B2 for one term correct; ignore $+ c$; if B0 allow M1 for either $x^{1/2}$ or $x^{-1}$ seen before differentiation; deduct one mark for extra term in $x$
---(i) On the copy of Fig. 5, draw by eye a tangent to the curve at the point where $x = 2$. Hence find an estimate of the gradient of $y = 2 ^ { x }$ when $x = 2$.\\
(ii) Calculate the $y$-values on the curve when $x = 1.8$ and $x = 2.2$. Hence calculate another approximation to the gradient of $y = 2 ^ { x }$ when $x = 2$.
\hfill \mbox{\textit{OCR MEI C2 Q6 [5]}}