Moderate -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.
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]}}