| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Year | 2019 |
| Session | Specimen |
| Marks | 2 |
| Topic | Tangents, normals and gradients |
| Type | Find stationary points |
| Difficulty | Moderate -0.8 This is a straightforward calculus question requiring basic differentiation of a polynomial and solving a quadratic equation to find stationary points. Both parts are standard textbook exercises with no problem-solving insight needed, making it easier than average but not trivial since it requires correct execution of multiple steps. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.07n Stationary points: find maxima, minima using derivatives |
(a) Attempt differentiation of at least one term — **M1**
Obtain $3x^2 - 4x - 4$ — **A1**
**Total: 2**
(b) State derivative equal to $0$ — **B1**
Attempt to solve quadratic — **M1**
Obtain $x = -\frac{2}{3}$ and $2$ — **A1**
Obtain $y = 4.48$ and $-5$ — **A1**
**Total: 4**2 The equation of a curve is $y = x ^ { 3 } - 2 x ^ { 2 } - 4 x + 3$.
\begin{enumerate}[label=(\alph*)]
\item Find $\frac { \mathrm { d } y } { \mathrm {~d} x }$.
\item Hence find the coordinates of the stationary points on the curve.
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2019 Q2 [2]}}