| Exam Board | CAIE |
|---|---|
| Module | P2 (Pure Mathematics 2) |
| Year | 2024 |
| Session | March |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Modulus function |
| Type | Sketch y=|linear| then solve equation or inequality (with unknown constants) |
| Difficulty | Moderate -0.3 Part (a) is routine modulus graph sketching requiring finding intercepts and the V-shape vertex. Part (b) requires geometric interpretation of when a line through (4,0) intersects the V-shape twice, which is a standard technique but requires some insight about gradient conditions. Overall slightly easier than average due to being a familiar modulus problem with only 4 marks total. |
| Spec | 1.02l Modulus function: notation, relations, equations and inequalities1.02m Graphs of functions: difference between plotting and sketching1.02s Modulus graphs: sketch graph of |ax+b| |
| Answer | Marks | Guidance |
|---|---|---|
| 2(a) | Draw V-shaped graph with vertex on positive x-axis | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | B1 | Allow if only 7 and 7 shown on relevant axes. |
| Answer | Marks | Guidance |
|---|---|---|
| 2(b) | State or imply that gradient of left-hand part of graph is –3 | B1 |
| State −3k0 | B1 | Using < and not ⩽. |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
Question 2:
--- 2(a) ---
2(a) | Draw V-shaped graph with vertex on positive x-axis | B1
State (7, 0) and (0, 7)
3 | B1 | Allow if only 7 and 7 shown on relevant axes.
3
2
--- 2(b) ---
2(b) | State or imply that gradient of left-hand part of graph is –3 | B1
State −3k0 | B1 | Using < and not ⩽.
2
Question | Answer | Marks | Guidance\begin{enumerate}[label=(\alph*)]
\item Sketch the graph of $y = |3x - 7|$, stating the coordinates of the points where the graph meets the axes. [2]
\item Hence find the set of values of the constant $k$ for which the equation $|3x - 7| = k(x - 4)$ has exactly two real roots. [2]
\end{enumerate}
\hfill \mbox{\textit{CAIE P2 2024 Q2 [4]}}