| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Session | Specimen |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Find derivative after algebraic simplification (fractional/mixed powers) |
| Difficulty | Easy -1.3 This is a straightforward C1 differentiation question requiring only direct application of the power rule. All three parts involve routine polynomial differentiation with no problem-solving or conceptual challenges—part (ii) requires expanding brackets first, and part (iii) needs rewriting the square root as x^(1/2), but these are standard textbook exercises testing basic technique recall. |
| Spec | 1.07i Differentiate x^n: for rational n and sums |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(\frac{dy}{dx} = 12x^2\) | M1 A1 | For clear attempt at \(nx^{n-1}\); For completely correct answer |
| 2 | ||
| (ii) \(y = x^4 + 2x^2\). Hence \(\frac{dy}{dx} = 4x^3 + 4x\) | B1 M1 A1 √ | For correct expansion; For correct differentiation of at least one term; For correct differentiation of their 2 terms |
| 3 | ||
| (iii) \(\frac{dy}{dx} = \frac{1}{2}x^{-\frac{1}{2}}\) | M1 A1 | For clear differentiation attempt of \(x^{\frac{1}{2}}\); For correct answer, in any form |
| 2 |
(i) $\frac{dy}{dx} = 12x^2$ | M1 A1 | For clear attempt at $nx^{n-1}$; For completely correct answer
| | 2 |
(ii) $y = x^4 + 2x^2$. Hence $\frac{dy}{dx} = 4x^3 + 4x$ | B1 M1 A1 √ | For correct expansion; For correct differentiation of at least one term; For correct differentiation of their 2 terms
| | 3 |
(iii) $\frac{dy}{dx} = \frac{1}{2}x^{-\frac{1}{2}}$ | M1 A1 | For clear differentiation attempt of $x^{\frac{1}{2}}$; For correct answer, in any form
| | 2 |
---4 Find $\frac { \mathrm { d } y } { \mathrm {~d} x }$ in each of the following cases:\\
(i) $y = 4 x ^ { 3 } - 1$,\\
(ii) $y = x ^ { 2 } \left( x ^ { 2 } + 2 \right)$,\\
(iii) $y = \sqrt { } x$
\hfill \mbox{\textit{OCR C1 Q4 [7]}}