| Exam Board | AQA |
|---|---|
| Module | Paper 2 (Paper 2) |
| Session | Specimen |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Completing the square and sketching |
| Type | Sketch quadratic curve |
| Difficulty | Moderate -0.8 This is a straightforward question requiring basic quadratic manipulation. Part (a) involves substituting a given root to find k (or using sum/product of roots), which is routine. Part (b) is a standard sketch requiring identification of vertex and y-intercept. Both parts are below-average difficulty, requiring only direct application of well-practiced techniques with no problem-solving insight needed. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions1.02e Complete the square: quadratic polynomials and turning points1.02f Solve quadratic equations: including in a function of unknown1.02n Sketch curves: simple equations including polynomials |
| Answer | Marks |
|---|---|
| 6(a) | Uses either of the given |
| Answer | Marks | Guidance |
|---|---|---|
| (accept product of the roots) | AO1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| Obtains the correct value of k | AO1.1b | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| 6(b) | Sketches a graph with the | |
| correct shape | AO1.2 | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| (must see labels) | AO2.2a | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| of y-axis in fourth quadrant | AO2.2a | B1 |
| Total | 5 | |
| Q | Marking Instructions | AO |
Question 6:
--- 6(a) ---
6(a) | Uses either of the given
coordinates in the given
equation
(accept product of the roots) | AO1.1a | M1 | k 4(2 5)(2 5)2 1
ALT
k 4(2 5)(2 5)2 1
ALT
k (2 5)(2 5) 1
Obtains the correct value of k | AO1.1b | A1
--- 6(b) ---
6(b) | Sketches a graph with the
correct shape | AO1.2 | B1 | –1
Deduces correct relative
positioning of intersections with
axes
(must see labels) | AO2.2a | B1
Deduces minimum lies to right
of y-axis in fourth quadrant | AO2.2a | B1
Total | 5
Q | Marking Instructions | AO | Marks | Typical SolutionA curve $C$ has equation $y = x^2 - 4x + k$, where $k$ is a constant.
It crosses the $x$-axis at the points $(2 + \sqrt{5}, 0)$ and $(2 - \sqrt{5}, 0)$
\begin{enumerate}[label=(\alph*)]
\item Find the value of $k$.
[2 marks]
\item Sketch the curve $C$, labelling the exact values of all intersections with the axes.
[3 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA Paper 2 Q6 [5]}}