CAIE P1 2020 November — Question 1 3 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2020
SessionNovember
Marks3
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Mark schemeDownload PDF ↗
TopicInequalities
TypeLine-curve intersection conditions
DifficultyModerate -0.3 This is a standard discriminant problem requiring students to set mx - 3 = 2x² + 5, rearrange to 2x² - mx + 8 = 0, and apply b² - 4ac < 0 for no intersection. It's slightly easier than average as it's a routine textbook exercise with clear methodology, though students must remember the correct inequality direction.
Spec1.02c Simultaneous equations: two variables by elimination and substitution1.02g Inequalities: linear and quadratic in single variable
1 Find the set of values of \(m\) for which the line with equation \(y = m x - 3\) and the curve with equation \(y = 2 x ^ { 2 } + 5\) do not meet.
Question 1:
AnswerMarks Guidance
AnswerMarks Guidance
\(2x^2 + 5 = mx - 3 \rightarrow 2x^2 - mx + 8 (= 0)\)B1 Form 3-term quadratic
\(m^2 - 64\)M1 Find \(b^2 - 4ac\)
\(-8 < m < 8\)A1 Accept \((-8, 8)\) and equality included
3 
**Question 1:**

| Answer | Marks | Guidance |
|--------|-------|----------|
| $2x^2 + 5 = mx - 3 \rightarrow 2x^2 - mx + 8 (= 0)$ | B1 | Form 3-term quadratic |
| $m^2 - 64$ | M1 | Find $b^2 - 4ac$ |
| $-8 < m < 8$ | A1 | Accept $(-8, 8)$ and equality included |
| | **3** | |

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1 Find the set of values of $m$ for which the line with equation $y = m x - 3$ and the curve with equation $y = 2 x ^ { 2 } + 5$ do not meet.\\

\hfill \mbox{\textit{CAIE P1 2020 Q1 [3]}}
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Q1 3 Q2 4 Q3 3 Q4 3 Q5 5 Q6 5 Q7 6 Q8 7 Q9 8 Q10 10 Q11 9 Q12 12