OCR MEI Paper 1 Specimen — Question 13 4 marks

Exam BoardOCR MEI
ModulePaper 1 (Paper 1)
SessionSpecimen
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicDiscriminant and conditions for roots
TypeFind range for two distinct roots
DifficultyStandard +0.3 This is a straightforward discriminant problem requiring students to find when a quadratic has real roots (Δ > 0), then solve the resulting quadratic inequality k² - 8k > 0. While it requires understanding the connection between roots and the graph being below the x-axis, it's a standard textbook exercise with routine algebraic steps, making it slightly easier than average.
Spec1.02d Quadratic functions: graphs and discriminant conditions1.02g Inequalities: linear and quadratic in single variable
13 In this question you must show detailed reasoning. Determine the values of \(k\) for which part of the graph of \(y = x ^ { 2 } - k x + 2 k\) appears below the \(x\)-axis.
Question 13:
AnswerMarks Guidance
AnswerMarks Guidance
discriminant \(= k^2 - 8k\)B1
\(\Rightarrow k^2 - 8k > 0\)M1
[sketch showing roots at \((0,0)\) and \((8,0)\)]E1 Or give table of values, oe
\(\Rightarrow k < 0\) or \(k > 8\)A1 or \((-\infty, 0) \cup (8, \infty)\); or \(\{k: k<0\} \cup \{k: k>8\}\)
[4] 
## Question 13:

| Answer | Marks | Guidance |
|--------|-------|----------|
| discriminant $= k^2 - 8k$ | B1 | |
| $\Rightarrow k^2 - 8k > 0$ | M1 | |
| [sketch showing roots at $(0,0)$ and $(8,0)$] | E1 | Or give table of values, oe |
| $\Rightarrow k < 0$ or $k > 8$ | A1 | or $(-\infty, 0) \cup (8, \infty)$; or $\{k: k<0\} \cup \{k: k>8\}$ |
| **[4]** | | |

---
13 In this question you must show detailed reasoning.
Determine the values of $k$ for which part of the graph of $y = x ^ { 2 } - k x + 2 k$ appears below the $x$-axis.

\hfill \mbox{\textit{OCR MEI Paper 1  Q13 [4]}}
This paper (15 questions)
View full paper
Q1 2 Q2 3 Q3 4 Q4 6 Q5 4 Q6 4 Q7 10 Q8 7 Q9 8 Q10 15 Q11 9 Q12 9 Q13 4 Q14 9 Q15 6