| Exam Board | Edexcel |
|---|---|
| Module | P3 (Pure Mathematics 3) |
| Year | 2020 |
| Session | October |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Modulus function |
| Type | Graph y=a|bx+c|+d given: solve equation or inequality |
| Difficulty | Standard +0.3 This is a straightforward modulus function question requiring standard techniques: evaluating a function, solving a linear equation with modulus (splitting into cases), identifying the range for two roots from a graph, and applying transformations to find constants. All parts are routine applications of A-level methods with no novel problem-solving required, making it slightly easier than average. |
| 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 function1.02w Graph transformations: simple transformations of f(x) |
(a) $ff(6) = f(13) = -1$ M1 A1
(2 marks)
(b) Attempts $21 + 2(2-x) = 5x \Rightarrow x = \ldots$ or $21 - 2(x-2) = 5x \Rightarrow x = \ldots$ M1
$x = \frac{25}{7}$ only A1
(2 marks)
(c) Either $k < 21$ or $k \geq 17$ M1
$17 \leq k < 21$ A1
(2 marks)
(d) $a = \frac{1}{7}$ B1
$b = 4$ B1
(2 marks)
(8 marks)4.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{96948fd3-5438-4e95-b41b-2f649ca8dfac-10_780_839_123_557}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{center}
\end{figure}
Figure 2 shows a sketch of part of the graph with equation $y = \mathrm { f } ( x )$ where
$$\mathrm { f } ( x ) = 21 - 2 | 2 - x | \quad x \geqslant 0$$
\begin{enumerate}[label=(\alph*)]
\item Find ff(6)
\item Solve the equation $\mathrm { f } ( x ) = 5 x$
Given that the equation $\mathrm { f } ( x ) = k$, where $k$ is a constant, has exactly two roots,
\item state the set of possible values of $k$.
The graph with equation $y = \mathrm { f } ( x )$ is transformed onto the graph with equation $y = a \mathrm { f } ( x - b )$ The vertex of the graph with equation $y = a \mathrm { f } ( x - b )$ is (6, 3).
Given that $a$ and $b$ are constants,
\item find the value of $a$ and the value of $b$.
\includegraphics[max width=\textwidth, alt={}, center]{96948fd3-5438-4e95-b41b-2f649ca8dfac-11_2255_50_314_34}
\end{enumerate}
\hfill \mbox{\textit{Edexcel P3 2020 Q4 [8]}}