| Exam Board | Edexcel |
|---|---|
| Module | P3 (Pure Mathematics 3) |
| Year | 2018 |
| Session | Specimen |
| Marks | 5 |
| 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 students to (a) solve a linear equation with modulus by considering cases, and (b) identify the range of k-values from the graph where a horizontal line intersects twice. Both parts are routine applications of standard techniques with no novel insight required, making it easier than average. |
| Spec | 1.02l Modulus function: notation, relations, equations and inequalities1.02t Solve modulus equations: graphically with modulus function |
| VIIIV SIHI NI JIIIM ION OC | VIIV SIHI NI JAHAM ION OO | VI4V SIHIL NI JIIIM ION OC |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(-2(3-x) + 5 = \frac{1}{2}x + 30\) | M1 | Deduces solution found by solving this equation |
| Multiplies out bracket, collects terms: \(\frac{3}{2}x = 31\) | M1 | Correct method to solve |
| \(x = \frac{62}{3}\) only | A1 | Do not allow 20.6 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Two intersections required; implied by either endpoint \(k > 5\) or \(k \leqslant 11\) | M1 | Deduces two distinct roots when \(y=k\) intersects \(y=f(x)\) twice |
| \(5 < k \leqslant 11\) | A1 | Correct solution only \(\{k : k \in \mathbb{R}, 5 < k \leqslant 11\}\) |
## Question 3:
### Part (a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $-2(3-x) + 5 = \frac{1}{2}x + 30$ | M1 | Deduces solution found by solving this equation |
| Multiplies out bracket, collects terms: $\frac{3}{2}x = 31$ | M1 | Correct method to solve |
| $x = \frac{62}{3}$ only | A1 | Do not allow 20.6 |
### Part (b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Two intersections required; implied by either endpoint $k > 5$ or $k \leqslant 11$ | M1 | Deduces two distinct roots when $y=k$ intersects $y=f(x)$ twice |
| $5 < k \leqslant 11$ | A1 | Correct solution only $\{k : k \in \mathbb{R}, 5 < k \leqslant 11\}$ |
---3.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{d8e25332-3a45-43ca-a5b8-0a16f47f13b9-08_542_540_269_696}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
Figure 1 shows a sketch of part of the graph $y = \mathrm { f } ( x )$ where
$$\mathrm { f } ( x ) = 2 | 3 - x | + 5 \quad x \geqslant 0$$
\begin{enumerate}[label=(\alph*)]
\item Solve the equation
$$f ( x ) = \frac { 1 } { 2 } x + 30$$
Given that the equation $\mathrm { f } ( x ) = k$, where $k$ is a constant, has two distinct roots,
\item state the set of possible values for $k$.\\
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
VIIIV SIHI NI JIIIM ION OC & VIIV SIHI NI JAHAM ION OO & VI4V SIHIL NI JIIIM ION OC \\
\hline
\end{tabular}
\end{center}
\end{enumerate}
\hfill \mbox{\textit{Edexcel P3 2018 Q3 [5]}}