CAIE P1 2015 November — Question 1 3 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2015
SessionNovember
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicInequalities
TypeLine-curve intersection conditions
DifficultyStandard +0.3 This is a standard discriminant problem requiring students to set the equations equal, form a quadratic, and apply the condition b²-4ac < 0 for no intersection. It's slightly easier than average as it's a direct application of a well-practiced technique with straightforward algebra and no conceptual surprises.
Spec1.02d Quadratic functions: graphs and discriminant conditions1.02q Use intersection points: of graphs to solve equations
1 A line has equation \(y = 2 x - 7\) and a curve has equation \(y = x ^ { 2 } - 4 x + c\), where \(c\) is a constant. Find the set of possible values of \(c\) for which the line does not intersect the curve.
Question 1:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(x^2 - 4x + c = 2x - 7 \rightarrow x^2 - 6x + c + 7 (= 0)\)M1 All terms on one side
\(36 - 4(c + 7) < 0\)DM1 Apply \(b^2 - 4ac < 0\). Allow \(\leqslant\)
\(c > 2\)A1
[3] 
## Question 1:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $x^2 - 4x + c = 2x - 7 \rightarrow x^2 - 6x + c + 7 (= 0)$ | M1 | All terms on one side |
| $36 - 4(c + 7) < 0$ | DM1 | Apply $b^2 - 4ac < 0$. Allow $\leqslant$ |
| $c > 2$ | A1 | |
| **[3]** | | |

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1 A line has equation $y = 2 x - 7$ and a curve has equation $y = x ^ { 2 } - 4 x + c$, where $c$ is a constant. Find the set of possible values of $c$ for which the line does not intersect the curve.

\hfill \mbox{\textit{CAIE P1 2015 Q1 [3]}}
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