| Exam Board | CAIE |
|---|---|
| Module | P2 (Pure Mathematics 2) |
| Year | 2020 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Modulus function |
| Type | Sketch modulus of linear and non-modulus linear, find intersection |
| Difficulty | Moderate -0.8 This is a straightforward modulus question requiring a standard sketch of a V-shaped graph and a linear function, followed by solving a routine inequality by considering two cases (2x-3 ≥ 0 and 2x-3 < 0). The techniques are well-practiced and require no novel insight, making it easier than average but not trivial since it involves multiple steps and careful case analysis. |
| 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 | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Draw V-shaped graph with vertex on positive \(x\)-axis | B1 | |
| Draw (more or less) correct graph of \(y = 3x + 5\) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| State equation \(3x + 5 = -(2x - 3)\) or corresponding inequality | B1 | |
| Attempt solution of linear equation/inequality where signs of \(3x\) and \(2x\) are different | M1 | |
| State answer \(x < -\frac{2}{5}\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Square both sides of equation/inequality and attempt solution of 3-term quadratic equation/inequality | M1 | |
| Obtain (eventually) only \(-\frac{2}{5}\) | A1 | |
| State answer \(x < -\frac{2}{5}\) | A1 |
## Question 5(a):
| Answer | Mark | Guidance |
|--------|------|----------|
| Draw V-shaped graph with vertex on positive $x$-axis | B1 | |
| Draw (more or less) correct graph of $y = 3x + 5$ | B1 | |
## Question 5(b):
| Answer | Mark | Guidance |
|--------|------|----------|
| State equation $3x + 5 = -(2x - 3)$ or corresponding inequality | B1 | |
| Attempt solution of linear equation/inequality where signs of $3x$ and $2x$ are different | M1 | |
| State answer $x < -\frac{2}{5}$ | A1 | |
**Alternative method:**
| Answer | Mark | Guidance |
|--------|------|----------|
| Square both sides of equation/inequality and attempt solution of 3-term quadratic equation/inequality | M1 | |
| Obtain (eventually) only $-\frac{2}{5}$ | A1 | |
| State answer $x < -\frac{2}{5}$ | A1 | |
---5
\begin{enumerate}[label=(\alph*)]
\item Sketch, on the same diagram, the graphs of $y = | 2 x - 3 |$ and $y = 3 x + 5$.
\item Solve the inequality $3 x + 5 < | 2 x - 3 |$.
\end{enumerate}
\hfill \mbox{\textit{CAIE P2 2020 Q5 [5]}}