| Exam Board | AQA |
|---|---|
| Module | Further Paper 1 (Further Paper 1) |
| Year | 2021 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Multiple separate transformations (sketch-based, modulus involved) |
| Difficulty | Standard +0.3 This is a standard graph transformations question testing three common transformations: |f(x)|, 1/f(x), and f(|x|). While it requires understanding of multiple transformation types and careful attention to asymptotes and intercepts, these are well-practiced techniques in Further Maths. The transformations are systematic rather than requiring novel insight, making it slightly easier than average for a Further Maths paper. |
| Spec | 1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks |
|---|---|
| 7(a) | Reflects the part of the graph |
| Answer | Marks | Guidance |
|---|---|---|
| Condone any continuous curve | 3.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| including all the intercepts | 1.1b | A1 |
| Total | 2 | |
| Q | Marking Instructions | AO |
| Answer | Marks | Guidance |
|---|---|---|
| 7(b) | Shows correct asymptotes | 2.2a |
| Answer | Marks | Guidance |
|---|---|---|
| Condone one wrong asymptote | 3.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| Condone one wrong asymptote | 1.1b | A1F |
| Total | 3 | |
| Q | Marking Instructions | AO |
| Answer | Marks |
|---|---|
| 7(c) | Sketches and reflects the part of |
| Answer | Marks | Guidance |
|---|---|---|
| about the y-axis | 1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| intercepts on their sketch | 1.1b | A1 |
| Total | 2 | |
| Question total | 7 | |
| Q | Marking Instructions | AO |
Question 7:
--- 7(a) ---
7(a) | Reflects the part of the graph
which lies below the x-axis in
the x-axis
Condone any continuous curve | 3.1a | M1
Obtains the correct graph
including all the intercepts | 1.1b | A1
Total | 2
Q | Marking Instructions | AO | Marks | Typical solution
--- 7(b) ---
7(b) | Shows correct asymptotes | 2.2a | B1
Draws graph of correct shape:
1) Curve above the x-axis to left
of x = 1 and an increasing
function
2) Curve below x-axis between
x = 1 and x = 3, with a local
maximum
3) Curve above the x-axis to
right of x = 3 and a decreasing
function
Condone one wrong asymptote | 3.1a | M1
Obtains correct graph including
intercept (ignore other details
such as the y-values for
minimum and maximum values
of x)
Condone one wrong asymptote | 1.1b | A1F
Total | 3
Q | Marking Instructions | AO | Marks | Typical solution
--- 7(c) ---
7(c) | Sketches and reflects the part of
the graph which lies to the right
of the y-axis in the y-axis
Condone reasonable attempt at
the graph being symmetric
about the y-axis | 1.1a | M1
Correctly shows all the
intercepts on their sketch | 1.1b | A1
Total | 2
Question total | 7
Q | Marking Instructions | AO | Marks | Typical solutionThe diagram below shows the graph of $y = \mathrm{f}(x)$ ($-4 \leq x \leq 4$)
The graph meets the $x$-axis at $x = 1$ and $x = 3$
The graph meets the $y$-axis at $y = 2$
\includegraphics{figure_7}
\begin{enumerate}[label=(\alph*)]
\item Sketch the graph of $y = |\mathrm{f}(x)|$ on the axes below.
Show any axis intercepts.
[2 marks]
\includegraphics{figure_7a}
\item Sketch the graph of $y = \frac{1}{\mathrm{f}(x)}$ on the axes below.
Show any axis intercepts and asymptotes.
[3 marks]
\includegraphics{figure_7b}
\item Sketch the graph of $y = \mathrm{f}(|x|)$ on the axes below.
Show any axis intercepts.
[2 marks]
\includegraphics{figure_7c}
\end{enumerate}
\hfill \mbox{\textit{AQA Further Paper 1 2021 Q7 [7]}}