| Exam Board | AQA |
|---|---|
| Module | Paper 2 (Paper 2) |
| Year | 2021 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Modulus function |
| Type | Sketch y=|linear| and y=linear, solve inequality: numeric coefficients |
| Difficulty | Moderate -0.8 This is a straightforward modulus function question requiring sketching a V-shaped graph by reflecting the negative portion, then solving linear equations in different regions to find intersections. The techniques are standard and mechanical with no conceptual challenges beyond basic modulus definition, making it easier than average but not trivial due to the multi-step nature and need for case-by-case analysis. |
| Spec | 1.02l Modulus function: notation, relations, equations and inequalities1.02s Modulus graphs: sketch graph of |ax+b|1.02t Solve modulus equations: graphically with modulus function |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| V-shaped graph with apex on positive \(x\)-axis | M1 (1.1a) | Any V shaped graph with apex on positive \(x\) axis |
| Roughly symmetrical V-shape touching positive \(x\)-axis, intersecting \(y= | 2x | \) twice in first quadrant |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \( | 3x-6 | = |
| \(x=6\) | A1 (1.1b) | |
| \(x=1.2\) | A1 (1.1b) | OE |
| \(y=12\) and \(y=2.4\) | A1 (1.1b) |
## Question 4(a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| V-shaped graph with apex on positive $x$-axis | M1 (1.1a) | Any V shaped graph with apex on positive $x$ axis |
| Roughly symmetrical V-shape touching positive $x$-axis, intersecting $y=|2x|$ twice in first quadrant | A1 (1.1b) | Condone missing or incorrect labels on axes |
## Question 4(b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $|3x-6|=|2x|$ | M1 (3.1a) | Forms equation and selects appropriate method to remove modulus signs e.g. squares both sides to obtain $9x^2-36x+36=4x^2$, or considers $3x-6=2x$ or $3x-6=-2x$ |
| $x=6$ | A1 (1.1b) | |
| $x=1.2$ | A1 (1.1b) | OE |
| $y=12$ and $y=2.4$ | A1 (1.1b) | |4
\begin{enumerate}[label=(\alph*)]
\item On Figure 1 add a sketch of the graph of
$$y = | 3 x - 6 |$$
4
\item Find the coordinates of the points of intersection of the two graphs.\\
Fully justify your answer.\\
\includegraphics[max width=\textwidth, alt={}, center]{b7df05bf-f3fc-4705-a13c-6b562896fa9f-05_2488_1716_219_153}
\end{enumerate}
\hfill \mbox{\textit{AQA Paper 2 2021 Q4 [6]}}