| Exam Board | CAIE |
|---|---|
| Module | P3 (Pure Mathematics 3) |
| Year | 2021 |
| Session | November |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Modulus function |
| Type | Sketch y=|linear| and y=linear, solve inequality: numeric coefficients |
| Difficulty | Moderate -0.8 Part (a) is a routine sketch of a single modulus function requiring only knowledge of the V-shape transformation (critical point at x=3/2). Part (b) is a standard modulus inequality solved by considering two cases, which is a well-practiced technique at this level. Both parts are textbook exercises with no novel problem-solving required. |
| Spec | 1.02l Modulus function: notation, relations, equations and inequalities1.02s Modulus graphs: sketch graph of |ax+b| |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Show a recognizable sketch graph of \(y = | 2x - 3 | \) |
| Total | 1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Find \(x\)-coordinate of intersection with \(y = 3x + 2\) | M1 | |
| Obtain \(x = \frac{1}{5}\) | A1 | |
| State final answer \(x > \frac{1}{5}\) only | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Solve the linear inequality \(3 - 2x < 3x + 2\), or corresponding equation | M1 | |
| Obtain critical value \(x = \frac{1}{5}\) | A1 | |
| State final answer \(x > \frac{1}{5}\) only | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Solve the quadratic inequality \((2x-3)^2 < (3x+2)^2\), or corresponding equation | M1 | |
| Obtain critical value \(x = \frac{1}{5}\) | A1 | |
| State final answer \(x > \frac{1}{5}\) only | A1 |
**Question 2(a):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Show a recognizable sketch graph of $y = |2x - 3|$ | B1 | |
| **Total** | **1** | |
## Question 2(b):
| Answer | Mark | Guidance |
|--------|------|----------|
| Find $x$-coordinate of intersection with $y = 3x + 2$ | M1 | |
| Obtain $x = \frac{1}{5}$ | A1 | |
| State final answer $x > \frac{1}{5}$ only | A1 | |
**Alternative method:**
| Answer | Mark | Guidance |
|--------|------|----------|
| Solve the linear inequality $3 - 2x < 3x + 2$, or corresponding equation | M1 | |
| Obtain critical value $x = \frac{1}{5}$ | A1 | |
| State final answer $x > \frac{1}{5}$ only | A1 | |
**Alternative method 2:**
| Answer | Mark | Guidance |
|--------|------|----------|
| Solve the quadratic inequality $(2x-3)^2 < (3x+2)^2$, or corresponding equation | M1 | |
| Obtain critical value $x = \frac{1}{5}$ | A1 | |
| State final answer $x > \frac{1}{5}$ only | A1 | |
---2
\begin{enumerate}[label=(\alph*)]
\item Sketch the graph of $y = | 2 x - 3 |$.
\item Solve the inequality $| 2 x - 3 | < 3 x + 2$.
\end{enumerate}
\hfill \mbox{\textit{CAIE P3 2021 Q2 [4]}}