OCR MEI AS Paper 1 Specimen — Question 11 6 marks

Exam BoardOCR MEI
ModuleAS Paper 1 (AS Paper 1)
SessionSpecimen
Marks6
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Mark schemeDownload PDF ↗
TopicSimultaneous equations
TypeIntersection existence or conditions
DifficultyModerate -0.3 This is a straightforward simultaneous equations problem requiring students to set the equations equal, rearrange to standard quadratic form, and apply the discriminant condition (b² - 4ac ≥ 0). While it requires multiple steps and understanding of the discriminant, it's a standard textbook exercise with no novel insight needed, making it slightly easier than average.
Spec1.02d Quadratic functions: graphs and discriminant conditions1.02q Use intersection points: of graphs to solve equations
11 In this question you must show detailed reasoning.
Determine for what values of \(k\) the graphs \(y = 2 x ^ { 2 } - k x\) and \(y = x ^ { 2 } - k\) intersect.
Question 11:
AnswerMarks Guidance
AnswerMarks Guidance
DR
\(2x^2-kx=x^2-k\)B1 3.1a — Equating the two expressions must be seen
\(x^2-kx+k=0\)M1 2.1 — Condone one error in rearranging
discriminant \(=k^2-4k\)B1 1.2
\(k^2-4k\geq 0\)M1 1.1
[sketch of parabola crossing \(x\)-axis at \(0\) and \(4\)]M1 2.4 — Or give table of values, oe
\(k\leq 0\) or \(k\geq 4\)A1 2.5 — or \(\{k:k\leq 0\}\cup\{k:k\geq 4\}\)
[6] 
## Question 11:

| Answer | Marks | Guidance |
|--------|-------|----------|
| **DR** | | |
| $2x^2-kx=x^2-k$ | B1 | 3.1a — Equating the two expressions **must** be seen |
| $x^2-kx+k=0$ | M1 | 2.1 — Condone one error in rearranging |
| discriminant $=k^2-4k$ | B1 | 1.2 |
| $k^2-4k\geq 0$ | M1 | 1.1 |
| [sketch of parabola crossing $x$-axis at $0$ and $4$] | M1 | 2.4 — Or give table of values, oe |
| $k\leq 0$ or $k\geq 4$ | A1 | 2.5 — or $\{k:k\leq 0\}\cup\{k:k\geq 4\}$ |
| **[6]** | | |

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11 In this question you must show detailed reasoning.\\
Determine for what values of $k$ the graphs $y = 2 x ^ { 2 } - k x$ and $y = x ^ { 2 } - k$ intersect.

\hfill \mbox{\textit{OCR MEI AS Paper 1  Q11 [6]}}
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Q1 2 Q2 3 Q3 3 Q4 3 Q5 5 Q6 4 Q7 4 Q8 11 Q9 8 Q10 12 Q11 6 Q12 9