OCR MEI C1 — Question 8 4 marks

Exam BoardOCR MEI
ModuleC1 (Core Mathematics 1)
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicSolving quadratics and applications
TypeFinding quadratic constants from algebraic conditions
DifficultyModerate -0.8 This is a straightforward simultaneous equations problem requiring substitution of given values into a quadratic function and solving the resulting linear system. It tests basic algebraic manipulation with no conceptual difficulty or problem-solving insight required—simpler than average A-level questions.
Spec1.02c Simultaneous equations: two variables by elimination and substitution

You are given that \(f(x) = x^2 + kx + c\). Given also that \(f(2) = 0\) and \(f(-3) = 35\), find the values of the constants \(k\) and \(c\). [4]

Question 8:
AnswerMarks
84 + 2k + c = 0 or 22 + 2k + c = 0
9  3k + c = 35
correct method to eliminate one variable from
their eqns
k = 6, c = 8
or
[x2 + kx + c =] (x  2)(x  a)
 5 × (3  a) = 35 oe
a = 4
AnswerMarks
k = 6, c = 8B1
B1
M1
A1
or
M1
M1
A1
A1
AnswerMarks
[4]may be rearranged
may be rearranged; the (3)2 must be
evaluated / used as 9
eg subtraction or substitution for c; condone
one error
from fully correct method, allowing recovery
from slips
AnswerMarks
or (x  2)(x + b)condone 32 seen if used as 9
M0 for addition of eqns unless also
multiplied appropriately
if no errors and no method seen, allow
correct answers to imply M1 provided
B1B1 has been earned
Question 8:
8 | 4 + 2k + c = 0 or 22 + 2k + c = 0
9  3k + c = 35
correct method to eliminate one variable from
their eqns
k = 6, c = 8
or
[x2 + kx + c =] (x  2)(x  a)
 5 × (3  a) = 35 oe
a = 4
k = 6, c = 8 | B1
B1
M1
A1
or
M1
M1
A1
A1
[4] | may be rearranged
may be rearranged; the (3)2 must be
evaluated / used as 9
eg subtraction or substitution for c; condone
one error
from fully correct method, allowing recovery
from slips
or (x  2)(x + b) | condone 32 seen if used as 9
M0 for addition of eqns unless also
multiplied appropriately
if no errors and no method seen, allow
correct answers to imply M1 provided
B1B1 has been earned
You are given that $f(x) = x^2 + kx + c$.

Given also that $f(2) = 0$ and $f(-3) = 35$, find the values of the constants $k$ and $c$. [4]

\hfill \mbox{\textit{OCR MEI C1  Q8 [4]}}