| Exam Board | Edexcel |
|---|---|
| Module | PMT Mocks (PMT Mocks) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Modulus function |
| Type | Sketch y=|linear| and y=linear with unknown constants, then solve |
| Difficulty | Standard +0.3 This is a straightforward modulus question requiring a standard sketch and solving a linear modulus inequality by considering two cases. The algebra is routine and the techniques are well-practiced at A-level, making it slightly 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 |
|---|---|
| Part a. | (2 marks) |
| B1 | V shape with vertex on x-axis but not at the origin |
| B1 | Correct V shape with (0,a) or just a and (\(\frac{a}{2}\),0) or just \(\frac{a}{2}\) marked in the correct places. Left branch must cross or touch the y-axis. |
| Answer | Marks |
|---|---|
| Part b. | (3 marks) |
| M1 | Attempts to solve \(a - 2x = x + 2a\) \(\Rightarrow x = \cdots\) or \(-a + 2x = x + 2a\) \(\Rightarrow x = \cdots\) |
| Answer | Marks |
|---|---|
| M1 | Attempts to solve \(a - 2x = x + 2a\) \(\Rightarrow x = \cdots\) and \(-a + 2x = x + 2a\) \(\Rightarrow x = \cdots\) |
| A1 | Chooses outside region giving correct answer only. \(x < -\frac{a}{3}\) or \(x > 3a\) |
**Part a.** | (2 marks)
**B1** | V shape with vertex on x-axis but not at the origin
**B1** | Correct V shape with (0,a) or just a and ($\frac{a}{2}$,0) or just $\frac{a}{2}$ marked in the correct places. Left branch must cross or touch the y-axis.
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**Part b.** | (3 marks)
**M1** | Attempts to solve $a - 2x = x + 2a$ $\Rightarrow x = \cdots$ or $-a + 2x = x + 2a$ $\Rightarrow x = \cdots$
Example: $a - 2x = x + 2a$ $\Rightarrow -3x = a$ $\Rightarrow x = -\frac{a}{3}$ or $-a + 2x = x + 2a$ $\Rightarrow 2x - x = 2a + a$ $\Rightarrow x = 3a$
**M1** | Attempts to solve $a - 2x = x + 2a$ $\Rightarrow x = \cdots$ and $-a + 2x = x + 2a$ $\Rightarrow x = \cdots$
**A1** | Chooses outside region giving correct answer only. $x < -\frac{a}{3}$ or $x > 3a$
Allow alternative e.g. $x < -\frac{a}{3}$ $\cup$ $x > 3a$
---\begin{enumerate}
\item Given that $a$ is a positive constant,\\
a. Sketch the graph with equation
\end{enumerate}
$$y = | a - 2 x |$$
Show on your sketch the coordinates of each point at which the graph crosses the $x$-axis and $y$-axis.\\
b. Solve the inequality $| a - 2 x | > x + 2 a$\\
\hfill \mbox{\textit{Edexcel PMT Mocks Q1 [5]}}