| Exam Board | AQA |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Year | 2019 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Sketch with inequalities or regions |
| Difficulty | Moderate -0.8 This is a straightforward AS-level question requiring routine skills: expanding or analyzing a factored cubic to identify roots (x=-2, x=1 with multiplicity 2), sketching the curve with correct shape and intercepts, then reading off where the curve is below the x-axis. The factored form makes finding roots trivial, and the inequality solution follows directly from the sketch with no additional problem-solving required. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable1.02n Sketch curves: simple equations including polynomials |
| Answer | Marks | Guidance |
|---|---|---|
| 5(a) | Draws a correctly orientated cubic | |
| graph with a max and a min | 1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| axi–s | 1.1b | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| x-axis at 1 | 2.2a | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| 5(b) | States correct lower region | 2.5 |
| Answer | Marks | Guidance |
|---|---|---|
| solves the inequality | 2.2a | B1 |
| Total | 5 | |
| Q | Marking Instructions | AO |
Question 5:
--- 5(a) ---
5(a) | Draws a correctly orientated cubic
graph with a max and a min | 1.1a | M1 | g(x) = 0 at - and 1 (twice)
2
Shows that the curve meets x-axis
at 2 and 1
Ignore an additional cutting of the
axi–s | 1.1b | A1
Deduces the graph touches the
x-axis at 1 | 2.2a | B1
--- 5(b) ---
5(b) | States correct lower region | 2.5 | B1 | x ≤ 2
x = –1
Deduces that point value x = 1
solves the inequality | 2.2a | B1
Total | 5
Q | Marking Instructions | AO | Marks | Typical Solution\begin{enumerate}[label=(\alph*)]
\item Sketch the curve $y = g(x)$ where
$$g(x) = (x + 2)(x - 1)^2$$
[3 marks]
\item Hence, solve $g(x) \leq 0$
[2 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA AS Paper 1 2019 Q5 [5]}}