| Exam Board | WJEC |
|---|---|
| Module | Unit 1 (Unit 1) |
| Year | 2022 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Laws of Logarithms |
| Type | Simultaneous equations with logarithms |
| Difficulty | Challenging +1.2 This question requires systematic manipulation of logarithm laws (product, quotient, power rules) across multiple terms, followed by solving simultaneous equations. While the algebraic manipulation is lengthy and requires care, the techniques are standard A-level content with no novel insight needed. The 8-mark allocation reflects the extended working rather than conceptual difficulty, placing it moderately above average. |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution1.06f Laws of logarithms: addition, subtraction, power rules |
Solve the simultaneous equations
$$3\log_u(x^2y) - \log_u(x^2y^2) + \log_u\left(\frac{9}{x^2y^2}\right) = \log_u 36,$$
$$\log_u y - \log_u(x + 3) = 0.$$ [8]
\hfill \mbox{\textit{WJEC Unit 1 2022 Q15 [8]}}