AQA C1 2006 June — Question 3 7 marks

Exam BoardAQA
ModuleC1 (Core Mathematics 1)
Year2006
SessionJune
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicTangents, normals and gradients
TypeFind tangent at given point (polynomial/algebraic)
DifficultyModerate -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.
Spec1.07i 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 \(y = 7 - 2 x ^ { 5 }\).
  1. Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\).
  2. Find an equation for the tangent to the curve at the point where \(x = 1\).
  3. Determine whether \(y\) is increasing or decreasing when \(x = - 2\).

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]}}