| Exam Board | OCR MEI |
|---|---|
| Module | Paper 3 (Paper 3) |
| Year | 2023 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Modulus function |
| Type | Solve |linear| < constant with sketch or follow-up application |
| Difficulty | Moderate -0.8 This is a straightforward modulus question requiring a basic sketch of reflecting negative values and solving a standard |linear| < constant inequality using the definition -3 < 5-2x < 3. Both parts are routine textbook exercises with no problem-solving insight needed, making it easier than average. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable1.02l Modulus function: notation, relations, equations and inequalities1.02s Modulus graphs: sketch graph of |ax+b| |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| [Graph: V-shape going over given line above x-axis, to left of y-axis, then going up from x-axis at same angle] | B1 | Going over the given line above the x-axis and to the left of the y-axis and then going up from the x-axis at the same angle (by eye). Condone right hand line segment dotted/dashed |
| [1] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(-3 < 5 - 2x < 3\) | M1 | Could be treated as two separate inequalities (at least one correct) in \(x\) not \( |
| \(2 < 2x < 8\) | A1 if only one inequality correct; OR for \(1 \leq x \leq 4\); OR for \(1 < x\), \(x < 4\); OR for '\(1 < x\) or \(x < 4\)' | |
| \(1 < x < 4\) oe e.g. '\(1 < x\) and \(x < 4\)' | A2 | |
| [3] |
## Question 2(a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| [Graph: V-shape going over given line above x-axis, to left of y-axis, then going up from x-axis at same angle] | B1 | Going over the given line above the x-axis and to the left of the y-axis and then going up from the x-axis at the same angle (by eye). Condone right hand line segment dotted/dashed |
| **[1]** | | |
---
## Question 2(b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $-3 < 5 - 2x < 3$ | M1 | Could be treated as two separate inequalities (at least one correct) in $x$ not $|x|$; OR $(5-2x)^2 < 9$; If only one linear inequality in $x$ stated scores **M0 A0 A0**; OR $4x^2 - 20x + 16 < 0$ or $x^2 - 5x + 4 < 0$; OR $(x-1)(x-4) < 0$; Allow **M1** if treated as equations in $x$ not $|x|$ |
| $2 < 2x < 8$ | | **A1** if only one inequality correct; OR for $1 \leq x \leq 4$; OR for $1 < x$, $x < 4$; OR for '$1 < x$ or $x < 4$' |
| $1 < x < 4$ oe e.g. '$1 < x$ and $x < 4$' | A2 | |
| **[3]** | | |2 The straight line $y = 5 - 2 x$ is shown in the diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{20639e13-01cc-4d96-b694-fb3cf1828f4d-04_705_773_881_239}
\begin{enumerate}[label=(\alph*)]
\item On the copy of the diagram in the Printed Answer Booklet, sketch the graph of $y = | 5 - 2 x |$.
\item Solve the inequality $| 5 - 2 x | < 3$.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Paper 3 2023 Q2 [4]}}