| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Simultaneous equations |
| Type | Line intersecting quadratic curve |
| Difficulty | Moderate -0.8 This is a straightforward C1 simultaneous equations question with clear scaffolding. Part (a) guides students through the algebraic manipulation, and part (b) requires only routine application of the quadratic formula followed by back-substitution. The surd form answer is standard for this level, requiring no novel insight. |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution1.02f Solve quadratic equations: including in a function of unknown |
| 5. continued | Leave blank |
Question 5:
M1: 1.6, 1.2, 1.5
A1: 4
B1: 1
DM1: 25. (a) Show that eliminating $y$ from the equations
$$\begin{gathered}
2 x + y = 8 \\
3 x ^ { 2 } + x y = 1
\end{gathered}$$
produces the equation
$$x ^ { 2 } + 8 x - 1 = 0$$
(b) Hence solve the simultaneous equations
$$\begin{gathered}
2 x + y = 8 \\
3 x ^ { 2 } + x y = 1
\end{gathered}$$
giving your answers in the form $a + b \sqrt { } 17$, where $a$ and $b$ are integers.\\
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5. continued & Leave blank \\
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\hfill \mbox{\textit{Edexcel C1 Q5 [7]}}