| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Simultaneous equations |
| Type | Line intersecting general conic |
| Difficulty | Moderate -0.3 This is a straightforward two-part question where part (a) requires basic index law manipulation (converting 9 to 3²) and part (b) involves standard substitution into a simple system with one linear and one quadratic equation. While it requires multiple steps, each step uses routine C1 techniques with no conceptual challenges or novel problem-solving required, making it slightly easier than average. |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution1.06g Equations with exponentials: solve a^x = b |
(a) Given that $3^x = 9^{y-1}$, show that $x = 2y – 2$.
(2)
(b) Solve the simultaneous equations $x = 2y – 2$, $x^2 = y^2 + 7$.
(6)3. (a) Given that $3 ^ { x } = 9 ^ { y - 1 }$, show that $x = 2 y - 2$.\\
(b) Solve the simultaneous equations
$$\begin{aligned}
& x = 2 y - 2 \\
& x ^ { 2 } = y ^ { 2 } + 7
\end{aligned}$$
\hfill \mbox{\textit{Edexcel C1 Q3 [8]}}