| Exam Board | AQA |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2018 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Completing the square and sketching |
| Type | Discriminant for real roots condition |
| Difficulty | Moderate -0.8 Part (a) is a routine completing the square exercise with straightforward algebraic manipulation. Part (b) requires understanding that 'no intersection' means the discriminant of 2x² - 5x + (k-3) = 0 must be negative, which is a standard application tested frequently at AS level. Both parts are textbook exercises requiring no novel insight. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points1.02g Inequalities: linear and quadratic in single variable |
\begin{enumerate}[label=(\alph*)]
\item Express $2x^2 - 5x + k$ in the form $a(x - b)^2 + c$ [3 marks]
\item Find the values of $k$ for which the curve $y = 2x^2 - 5x + k$ does not intersect the line $y = 3$ [3 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA AS Paper 2 2018 Q7 [6]}}