Edexcel C1 — Question 5 7 marks

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicSimultaneous equations
TypeLine intersecting general conic
DifficultyModerate -0.3 This is a standard C1 simultaneous equations question combining one linear and one quadratic equation. It requires substitution (y = 2 - x into the second equation) followed by solving a quadratic, then back-substitution. While it involves multiple steps for 7 marks, the technique is routine and commonly practiced, making it slightly easier than average but not trivial due to the algebraic manipulation required.
Spec1.02c Simultaneous equations: two variables by elimination and substitution1.02f Solve quadratic equations: including in a function of unknown
Solve the simultaneous equations \begin{align} x + y &= 2
3x^2 - 2x + y^2 &= 2 \end{align} [7]
AnswerMarks
\(x + y = 2 \Rightarrow y = 2 - x\)M1
sub. into \(3x^2 - 2x + y^2 = 2\)
\(3x^2 - 2x + (2 - x)^2 = 2\)M1
\(2x^2 - 3x + 1 = 0\)A1
\((2x - 1)(x - 1) = 0\)M1
\(x = \frac{1}{2}, 1\)A1
\(\therefore x = \frac{1}{2}, y = \frac{3}{2}\) or \(x = 1, y = 1\)M1 A1
Total: 7 marks
$x + y = 2 \Rightarrow y = 2 - x$ | M1 | 
sub. into $3x^2 - 2x + y^2 = 2$ | 
$3x^2 - 2x + (2 - x)^2 = 2$ | M1 | 
$2x^2 - 3x + 1 = 0$ | A1 | 
$(2x - 1)(x - 1) = 0$ | M1 | 
$x = \frac{1}{2}, 1$ | A1 | 
$\therefore x = \frac{1}{2}, y = \frac{3}{2}$ or $x = 1, y = 1$ | M1 A1 | 
**Total: 7 marks**

---
Solve the simultaneous equations
\begin{align}
x + y &= 2\\
3x^2 - 2x + y^2 &= 2
\end{align} [7]

\hfill \mbox{\textit{Edexcel C1  Q5 [7]}}
This paper (10 questions)
View full paper
Q1 3 Q2 4 Q3 4 Q4 6 Q5 7 Q6 7 Q7 10 Q8 10 Q9 11 Q10 13