| Exam Board | Edexcel |
|---|---|
| Module | P3 (Pure Mathematics 3) |
| Year | 2024 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Modulus function |
| Type | Graph y=a|bx+c|+d given: solve equation or inequality |
| Difficulty | Moderate -0.8 This is a straightforward modulus function question requiring only standard techniques: identifying the vertex from the form y=a|x-h|+k, solving a modulus inequality by considering two cases, and applying function transformations. All parts are routine textbook exercises with no problem-solving insight required, 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|1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \((5, 10)\) | B1 B1 | B1 for one correct coordinate; B1 for both correct. Allow \(x=5\), \(y=10\). Do not allow wrong way round. |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Attempts to solve e.g. \(-2(x-5)+10...6x \Rightarrow x..."\frac{5}{2}"\) | M1 | Attempts to solve a correct equation/inequality with at least one intermediate stage. Modulus signs must be removed. Alternatively may square both sides and solve quadratic. Condone slips in rearrangement; do not be concerned by direction of inequality sign. |
| \(x < \frac{5}{2}\) | A1 | Must be identified as their only inequality (e.g. circling, underlining). Allow \(x \in \left(-\infty, \frac{5}{2}\right)\). Do not accept \(x \leq \frac{5}{2}\). Answers with no working score 0 marks. |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \((7, 30)\) | B1ft, B1ft | B1ft: one correct coordinate; allow \(x=7\) or \(y=30\). Follow through on \(((a)+2, (a)\times 3)\). B1ft: both coordinates correct, allow \(x=7, y=30\); or correct ft \(((a)+2, (a)\times 3)\) — must be evaluated. |
## Question 1:
### Part (a)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $(5, 10)$ | B1 B1 | B1 for one correct coordinate; B1 for both correct. Allow $x=5$, $y=10$. Do not allow wrong way round. |
### Part (b)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Attempts to solve e.g. $-2(x-5)+10...6x \Rightarrow x..."\frac{5}{2}"$ | M1 | Attempts to solve a correct equation/inequality with at least one intermediate stage. Modulus signs must be removed. Alternatively may square both sides and solve quadratic. Condone slips in rearrangement; do not be concerned by direction of inequality sign. |
| $x < \frac{5}{2}$ | A1 | Must be identified as their only inequality (e.g. circling, underlining). Allow $x \in \left(-\infty, \frac{5}{2}\right)$. Do not accept $x \leq \frac{5}{2}$. Answers with no working score 0 marks. |
### Part (c)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $(7, 30)$ | B1ft, B1ft | B1ft: one correct coordinate; allow $x=7$ or $y=30$. Follow through on $((a)+2, (a)\times 3)$. B1ft: both coordinates correct, allow $x=7, y=30$; or correct ft $((a)+2, (a)\times 3)$ — must be evaluated. |
---1.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{5a695b86-1660-4c06-ac96-4cdb07af9a2e-02_520_474_246_797}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
Figure 1 shows a sketch of the graph with equation $y = \mathrm { f } ( x )$ where
$$f ( x ) = 2 | x - 5 | + 10$$
The point $P$, shown in Figure 1, is the vertex of the graph.
\begin{enumerate}[label=(\alph*)]
\item State the coordinates of $P$
\item Use algebra to solve
$$2 | x - 5 | + 10 > 6 x$$
(Solutions relying on calculator technology are not acceptable.)
\item Find the point to which $P$ is mapped, when the graph with equation $y = \mathrm { f } ( x )$ is transformed to the graph with equation $y = 3 \mathrm { f } ( x - 2 )$
\end{enumerate}
\hfill \mbox{\textit{Edexcel P3 2024 Q1 [6]}}