| Exam Board | WJEC |
|---|---|
| Module | Unit 1 (Unit 1) |
| Year | 2019 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Increasing/decreasing intervals |
| Difficulty | Moderate -0.5 This is a straightforward calculus question requiring students to find f'(x) = 3x² - 12x + 13, then show it's always positive by completing the square or using the discriminant. While it requires multiple steps (differentiate, analyze sign, conclude), it's a standard textbook exercise with no problem-solving insight needed—slightly easier than average. |
| Spec | 1.01a Proof: structure of mathematical proof and logical steps1.07o Increasing/decreasing: functions using sign of dy/dx |
Prove that $f(x) = x^3 - 6x^2 + 13x - 7$ is an increasing function. [4]
\hfill \mbox{\textit{WJEC Unit 1 2019 Q15 [4]}}