| Exam Board | AQA |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2006 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Find tangent at given point (polynomial/algebraic) |
| Difficulty | Moderate -0.8 This is a straightforward C1 differentiation question requiring only basic power rule application, substitution to find gradient, and using y-mx+c for the tangent. All steps are routine with no problem-solving or conceptual challenges beyond standard textbook exercises. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.07m Tangents and normals: gradient and equations1.07o Increasing/decreasing: functions using sign of dy/dx |
3 A curve has equation $y = 7 - 2 x ^ { 5 }$.
\begin{enumerate}[label=(\alph*)]
\item Find $\frac { \mathrm { d } y } { \mathrm {~d} x }$.
\item Find an equation for the tangent to the curve at the point where $x = 1$.
\item Determine whether $y$ is increasing or decreasing when $x = - 2$.
\end{enumerate}
\hfill \mbox{\textit{AQA C1 2006 Q3 [7]}}