| Exam Board | Edexcel |
|---|---|
| Module | PMT Mocks (PMT Mocks) |
| 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 standard modulus function question requiring sketching a V-shaped graph (straightforward transformation), solving by considering two cases (routine algebraic manipulation), and finding conditions for non-intersection (requires some geometric insight but follows standard methods). The multi-part structure and the non-intersection condition elevate it slightly above average, but all techniques are standard A-level fare. |
| 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 function1.03a Straight lines: equation forms y=mx+c, ax+by+c=0 |
| Answer | Marks | Guidance |
|---|---|---|
| Sketch graph of \(y = 11 - 2 | 2 - x | \) |
| Answer | Marks | Guidance |
|---|---|---|
| Solve \(4x = 11 - 2 | 2 - x | \) |
| Answer | Marks | Guidance |
|---|---|---|
| Find range of possible values of \(k\) where line \(y = kx + 13\) does not meet \(y = 11 - 2 | 2 - x | \) |
**Part (a):**
Sketch graph of $y = 11 - 2|2 - x|$ | (3) | B1 $\Lambda$ shape with intercepts at $(-\frac{7}{2}, 0)$ and $(\frac{15}{2}, 0)$ or marked $-\frac{7}{2}$ and $\frac{15}{2}$ on x-axis; B1 $\Lambda$ shape with intercept at $(0, 7)$ or 7 marked on y-axis; B1 Maximum point at $(2, 11)$ that lies in 1st quadrant
**Part (b):**
Solve $4x = 11 - 2|2 - x|$ | (2) | M1 Attempts to solve $4x = 11 + 2(2 - x) \Rightarrow x = \ldots$ Must reach value for $x$; A1 $x = \frac{5}{2}$
**Part (c):**
Find range of possible values of $k$ where line $y = kx + 13$ does not meet $y = 11 - 2|2 - x|$ | (3) | M1 Attempts to solve $y = kx + 13$ with their $(2, 11)$ to find $k$ or deduces that $k > -1$; A1 Finds that $k = 2$ is critical value; A1 $-1 < k < 2$
---\begin{enumerate}
\item a. Sketch the graph of the function with equation
\end{enumerate}
$$y = 11 - 2 | 2 - x |$$
Stating the coordinates of the maximum point and any points where the graph cuts the $y$-axis.\\
b. Solve the equation
$$4 x = 11 - 2 | 2 - x |$$
A straight line $l$ has equation $y = k x + 13$, where $k$ is a constant.\\
Given that $l$ does not meet or intersect $y = 11 - 2 | 2 - x |$\\
c. find the range of possible value of $k$.\\
\hfill \mbox{\textit{Edexcel PMT Mocks Q11 [8]}}