CAIE P1 2016 November — Question 1 3 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2016
SessionNovember
Marks3
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Mark schemeDownload PDF ↗
TopicDiscriminant and conditions for roots
TypeRange of k, line not intersecting curve
DifficultyModerate -0.3 This is a straightforward discriminant problem requiring students to set the equations equal, rearrange to standard form, and apply b²-4ac < 0 for no intersection. The algebra is simple and the method is standard textbook material, making it slightly easier than average but still requiring correct execution of multiple steps.
Spec1.02d Quadratic functions: graphs and discriminant conditions1.02q Use intersection points: of graphs to solve equations
Find the set of values of \(k\) for which the curve \(y = kx^2 - 3x\) and the line \(y = x - k\) do not meet. [3]
Question 1:
AnswerMarks
1kx2 −3x= x−k ⇒ kx2 −4x+k (=0)
(−4)2 −4(k)(k) soi
AnswerMarks
k >2 , k<−2 cao Allow (2, ∞) etc. Allow 2<k<‒kM1
M1
AnswerMarks Guidance
A1[3] Eliminate y and rearrange into 3-
term quad
b2 −4ac.
Question 1:
1 | kx2 −3x= x−k ⇒ kx2 −4x+k (=0)
(−4)2 −4(k)(k) soi
k >2 , k<−2 cao Allow (2, ∞) etc. Allow 2<k<‒k | M1
M1
A1 | [3] | Eliminate y and rearrange into 3-
term quad
b2 −4ac.
Find the set of values of $k$ for which the curve $y = kx^2 - 3x$ and the line $y = x - k$ do not meet. [3]

\hfill \mbox{\textit{CAIE P1 2016 Q1 [3]}}
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Q1 3 Q2 4 Q3 4 Q4 4 Q5 6 Q6 7 Q7 7 Q8 8 Q9 8 Q10 12 Q11 12