| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/2 (Pre-U Mathematics Paper 2) |
| Year | 2015 |
| Session | June |
| Marks | 4 |
| Topic | Modulus function |
| Type | Sketch y=|f(x)| for non-linear f(x) |
| Difficulty | Easy -1.2 This is a straightforward modulus function question requiring a basic V-shaped sketch and recognition that the graph fails the horizontal line test. Both parts involve standard textbook procedures with no problem-solving or novel insight required, making it easier than average. |
| Spec | 1.02l Modulus function: notation, relations, equations and inequalities1.02m Graphs of functions: difference between plotting and sketching |
| Answer | Marks | Guidance |
|---|---|---|
| Notes: Referring to just 'multiple' or 'many' \(x\)-values is B0. Must be using correct \(f(x)\), so not just \( | x-2 | \). B0 if additional incorrect statement, such as 'many to one'. |
**Question 3:**
**(i)**
- **M1**: Sketch V-shape graph, vertex in any quadrant
- **A1**: Vertex at $(2,3)$, $y$-intercept at 5
- **A1**: Fully correct graph for at least $-5 \leq x \leq 5$
**Total for (i): [3]**
**(ii)** Two $x$-values correspond to the same $y$-value
- **B1**: Or give numerical example such as $f(1)=4=f(3)$
Notes: Referring to just 'multiple' or 'many' $x$-values is B0. Must be using correct $f(x)$, so not just $|x-2|$. B0 if additional incorrect statement, such as 'many to one'.
**Total for (ii): [1]**3 The function f is given by $\mathrm { f } ( x ) = | x - 2 | + 3$ for $- 5 \leqslant x \leqslant 5$.\\
(i) Sketch the graph of $y = \mathrm { f } ( x )$.\\
(ii) Explain why f is not one-one.
\hfill \mbox{\textit{Pre-U Pre-U 9794/2 2015 Q3 [4]}}