| Exam Board | Edexcel |
|---|---|
| Module | Paper 2 (Paper 2) |
| Year | 2020 |
| Session | October |
| Marks | 7 |
| 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: (a) identifying the vertex by inspection, (b) solving a linear-modulus equation by cases (standard technique), and (c) finding tangent gradients using basic calculus or geometry. All parts use routine methods with no novel insight 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 function |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Mark | Guidance |
| \(x=-4\) or \(y=-5\) | B1 | 1.1b - One correct coordinate |
| \(P(-4,-5)\) | B1 | 2.2a - Deduces correct point |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Mark | Guidance |
| \(3x+40=-2(x+4)-5 \Rightarrow x=...\) | M1 | 1.1b - Attempts to solve, must reach value for \(x\) |
| \(x=-10.6\) | A1 | 2.1 |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Mark | Guidance |
| \(a>2\) | B1 | 2.2a - Deduces \(a>2\) |
| \(y=ax \Rightarrow -5=-4a \Rightarrow a=\frac{5}{4}\) | M1 | 3.1a - Attempts to find value of \(a\) using \(P(-4,-5)\) |
| \(\{a: a\leqslant 1.25\} \cup \{a: a>2\}\) | A1 | 2.5 - Correct range in acceptable set notation |
# Question 11:
## Part (a):
| Working | Mark | Guidance |
|---------|------|----------|
| $x=-4$ **or** $y=-5$ | B1 | 1.1b - One correct coordinate |
| $P(-4,-5)$ | B1 | 2.2a - Deduces correct point |
## Part (b):
| Working | Mark | Guidance |
|---------|------|----------|
| $3x+40=-2(x+4)-5 \Rightarrow x=...$ | M1 | 1.1b - Attempts to solve, must reach value for $x$ |
| $x=-10.6$ | A1 | 2.1 |
## Part (c):
| Working | Mark | Guidance |
|---------|------|----------|
| $a>2$ | B1 | 2.2a - Deduces $a>2$ |
| $y=ax \Rightarrow -5=-4a \Rightarrow a=\frac{5}{4}$ | M1 | 3.1a - Attempts to find value of $a$ using $P(-4,-5)$ |
| $\{a: a\leqslant 1.25\} \cup \{a: a>2\}$ | A1 | 2.5 - Correct range in acceptable set notation |
---11.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{e28350e9-5090-4079-97da-e669ef9a5a7a-30_677_817_251_621}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{center}
\end{figure}
Figure 2 shows a sketch of the graph with equation
$$y = 2 | x + 4 | - 5$$
The vertex of the graph is at the point $P$, shown in Figure 2.
\begin{enumerate}[label=(\alph*)]
\item Find the coordinates of $P$.
\item Solve the equation
$$3 x + 40 = 2 | x + 4 | - 5$$
A line $l$ has equation $y = a x$, where $a$ is a constant.\\
Given that $l$ intersects $y = 2 | x + 4 | - 5$ at least once,
\item find the range of possible values of $a$, writing your answer in set notation.
\end{enumerate}
\hfill \mbox{\textit{Edexcel Paper 2 2020 Q11 [7]}}