OCR MEI C1 — Question 8 5 marks

Exam BoardOCR MEI
ModuleC1 (Core Mathematics 1)
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicSimultaneous equations
TypeLine intersecting quadratic curve
DifficultyModerate -0.8 This is a straightforward simultaneous equations question requiring students to equate the expressions, form a quadratic, solve it, and substitute back to find coordinates. It's a standard C1 exercise with clear steps and no conceptual challenges, making it easier than average but not trivial since it requires accurate algebraic manipulation across multiple steps.
Spec1.02c Simultaneous equations: two variables by elimination and substitution
8 Find the points where the line \(y = 2 x - 3\) cuts the curve \(y = x ^ { 2 } - 4 x + 5\).
Question 8:
AnswerMarks
\(y=2x-3\) cuts \(y=x^2-4x+5\)M1
When \(2x-3=x^2-4x+5\)A1
\(\Rightarrow x^2-6x+8=0\)M1
\(\Rightarrow (x-4)(x-2)=0 \Rightarrow x=2,4\)A1 A1
\(\Rightarrow (2,1)\) and \((4,5)\)Total: 5 
## Question 8:
$y=2x-3$ cuts $y=x^2-4x+5$ | M1 |
When $2x-3=x^2-4x+5$ | A1 |
$\Rightarrow x^2-6x+8=0$ | M1 |
$\Rightarrow (x-4)(x-2)=0 \Rightarrow x=2,4$ | A1 A1 |
$\Rightarrow (2,1)$ and $(4,5)$ | **Total: 5**

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8 Find the points where the line $y = 2 x - 3$ cuts the curve $y = x ^ { 2 } - 4 x + 5$.

\hfill \mbox{\textit{OCR MEI C1  Q8 [5]}}
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Q1 2 Q2 3 Q3 4 Q4 4 Q5 4 Q6 4 Q7 5 Q8 5 Q9 5 Q10 12 Q11 12 Q12 12