| Exam Board | CAIE |
|---|---|
| Module | P3 (Pure Mathematics 3) |
| Year | 2020 |
| Session | Specimen |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Modulus function |
| Type | Sketch y=|linear| then solve equation or inequality (numeric coefficients) |
| Difficulty | Easy -1.3 This is a straightforward modulus question requiring a basic V-shaped sketch and solving a simple linear modulus inequality. Both parts involve routine application of standard techniques with minimal steps, making it easier than average for A-level. |
| Spec | 1.02s Modulus graphs: sketch graph of |ax+b|1.02t Solve modulus equations: graphically with modulus function |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Make a recognisable sketch graph of \(y = | 2x - 3 | \) |
| Total | 1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| EITHER Solution 1: Find \(x\)-coordinate of intersection with \(y = 3x - 1\) | (M1) | |
| Obtain \(x = \frac{4}{5}\) | A1 | |
| State final answer \(x > \frac{4}{5}\) only | A1) | |
| OR Solution 2: Solve the linear inequality \(3x - 1 > 3 - 2x\), or corresponding equation | (M1 | |
| Obtain critical value \(x = \frac{4}{5}\) | A1 | |
| State final answer \(x > \frac{4}{5}\) only | A1) | |
| OR Solution 3: Solve the quadratic inequality \((3x-1)^2 > (3-2x)^2\), or corresponding equation | (M1 | |
| Obtain critical value \(x = \frac{4}{5}\) | A1 | |
| State final answer \(x > \frac{4}{5}\) only | A1) | |
| Total | 3 | Unsupported answer receives 0 marks |
## Question 3(a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Make a recognisable sketch graph of $y = |2x - 3|$ | B1 | |
| **Total** | **1** | |
## Question 3(b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| **EITHER** Solution 1: Find $x$-coordinate of intersection with $y = 3x - 1$ | (M1) | |
| Obtain $x = \frac{4}{5}$ | A1 | |
| State final answer $x > \frac{4}{5}$ only | A1) | |
| **OR** Solution 2: Solve the linear inequality $3x - 1 > 3 - 2x$, or corresponding equation | (M1 | |
| Obtain critical value $x = \frac{4}{5}$ | A1 | |
| State final answer $x > \frac{4}{5}$ only | A1) | |
| **OR** Solution 3: Solve the quadratic inequality $(3x-1)^2 > (3-2x)^2$, or corresponding equation | (M1 | |
| Obtain critical value $x = \frac{4}{5}$ | A1 | |
| State final answer $x > \frac{4}{5}$ only | A1) | |
| **Total** | **3** | Unsupported answer receives 0 marks |
---3 (a) Sketch the graph of $y = | 2 x - 3 |$.\\
(b) Solve the inequality $3 x - 1 > | 2 x - 3 |$.\\
\hfill \mbox{\textit{CAIE P3 2020 Q3 [4]}}