| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Year | 2016 |
| Session | Specimen |
| Marks | 6 |
| 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 |
**Question 2(i)**
- Attempt differentiation of at least one term — M1
- Obtain $3x^2 - 4x - 4$ — A1
**Question 2(ii)**
- 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: 6 marks**2 The equation of a curve is $y = x ^ { 3 } - 2 x ^ { 2 } - 4 x + 3$.\\
(i) Find $\frac { \mathrm { d } y } { \mathrm {~d} x }$.\\
(ii) Hence find the coordinates of the stationary points on the curve.
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2016 Q2 [6]}}