| Exam Board | AQA |
|---|---|
| Module | Further Paper 1 (Further Paper 1) |
| Session | Specimen |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Modulus transformation only |
| Difficulty | Standard +0.3 This is a standard Further Maths rational function sketching question requiring identification of asymptotes (vertical at x=-1, horizontal at y=-4), intercepts, and reflection for the modulus part. While it involves multiple features, these are routine techniques for Further Maths students with no novel problem-solving required. |
| Spec | 1.02l Modulus function: notation, relations, equations and inequalities1.02m Graphs of functions: difference between plotting and sketching1.02n Sketch curves: simple equations including polynomials |
| Answer | Marks |
|---|---|
| 8(a) | Indicates correct |
| Answer | Marks | Guidance |
|---|---|---|
| on x and y axes | AO1.1b | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| asymptote | AO1.1b | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| shape of curve | AO1.2 | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| asymptotes marked | AO1.1b | B1 |
| (b) | Draws sketch fully |
| Answer | Marks | Guidance |
|---|---|---|
| marked | AO1.1b | B1 |
| Total | 5 | |
| Q | Marking Instructions | AO |
Question 8:
--- 8(a) ---
8(a) | Indicates correct
coordinate or intercept
on x and y axes | AO1.1b | B1 | x=0 y =0
⇒ y=5 ⇒5−4x =0
⇒(0, 5) 5
⇒ x =
4
5
⇒( ,0)
4
x =−1
As x→∞, y→−4
y = −4
Indicates correct
vertical or horizontal
asymptote | AO1.1b | B1
Sketches correct
shape of curve | AO1.2 | B1
Draws fully correct
sketch including
intercepts and both
asymptotes marked | AO1.1b | B1
(b) | Draws sketch fully
correct including
shape at x-intercept
both asymptotes
marked | AO1.1b | B1
Total | 5
Q | Marking Instructions | AO | Marks | Typical SolutionA curve has equation $$y = \frac{5 - 4x}{1 + x}$$
\begin{enumerate}[label=(\alph*)]
\item Sketch the curve.
[4 marks]
\item Hence sketch the graph of $y = \left|\frac{5 - 4x}{1 + x}\right|$.
[1 mark]
\end{enumerate}
\hfill \mbox{\textit{AQA Further Paper 1 Q8 [5]}}