| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2006 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Find derivative of simple polynomial (integer powers) |
| Difficulty | Easy -1.2 This is a straightforward C1 question testing basic differentiation and gradient of a line segment. Part (i) requires only the formula (y₂-y₁)/(x₂-x₁), and part (ii) requires differentiating a simple polynomial and substituting x=3. Both are routine recall with minimal problem-solving, making this easier than average. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.07i Differentiate x^n: for rational n and sums |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{21-3}{4-1} = \frac{18}{3} = 6\) | M1, A1 | Uses \(\frac{y_2 - y_1}{x_2 - x_1}\) |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{dy}{dx} = 2x+1\) | B1 | |
| \(2 \times 3 + 1 = 7\) | B1 | 2 marks total |
## (i)
$\frac{21-3}{4-1} = \frac{18}{3} = 6$ | M1, A1 | Uses $\frac{y_2 - y_1}{x_2 - x_1}$
## (ii)
$\frac{dy}{dx} = 2x+1$ | B1 |
$2 \times 3 + 1 = 7$ | B1 | 2 marks total
---The points $A(1, 3)$ and $B(4, 21)$ lie on the curve $y = x^2 + x + 1$.
\begin{enumerate}[label=(\roman*)]
\item Find the gradient of the line $AB$. [2]
\item Find the gradient of the curve $y = x^2 + x + 1$ at the point where $x = 3$. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR C1 2006 Q1 [4]}}