Moderate -0.8 This is a straightforward simultaneous equations problem requiring substitution of given values into a quadratic function. It involves basic algebraic manipulation with no conceptual difficulty beyond GCSE-level equation solving, making it easier than a typical A-level question which would require more sophisticated techniques or problem-solving.
5 You are given that \(\mathrm { f } ( x ) = x ^ { 2 } + k x + c\).
Given also that \(\mathrm { f } ( 2 ) = 0\) and \(\mathrm { f } ( - 3 ) = 35\), find the values of the constants \(k\) and \(c\).
May be rearranged; \((-3)^2\) must be evaluated/used as 9. Condone \(-3^2\) seen if used as 9
Correct method to eliminate one variable from their equations
M1
e.g. subtraction or substitution for \(c\); condone one error. M0 for addition of equations unless also multiplied appropriately
\(k = -6\), \(c = 8\)
A1
From fully correct method, allowing recovery from slips. If no errors and no method seen, allow correct answers to imply M1 provided B1B1 has been earned
or \([x^2 + kx + c =] (x-2)(x-a)\)
M1
or \((x-2)(x+b)\)
\(-5 \times (-3-a) = 35\) oe
M1
\(a = 4\)
A1
\(k = -6\), \(c = 8\)
A1
[4]
## Question 5:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $4 + 2k + c = 0$ or $2^2 + 2k + c = 0$ | B1 | May be rearranged |
| $9 - 3k + c = 35$ | B1 | May be rearranged; $(-3)^2$ must be evaluated/used as 9. Condone $-3^2$ seen if used as 9 |
| Correct method to eliminate one variable from their equations | M1 | e.g. subtraction or substitution for $c$; condone one error. M0 for addition of equations unless also multiplied appropriately |
| $k = -6$, $c = 8$ | A1 | From fully correct method, allowing recovery from slips. If no errors and no method seen, allow correct answers to imply M1 provided B1B1 has been earned |
| **or** $[x^2 + kx + c =] (x-2)(x-a)$ | M1 | or $(x-2)(x+b)$ |
| $-5 \times (-3-a) = 35$ oe | M1 | |
| $a = 4$ | A1 | |
| $k = -6$, $c = 8$ | A1 | |
| **[4]** | | |
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5 You are given that $\mathrm { f } ( x ) = x ^ { 2 } + k x + c$.\\
Given also that $\mathrm { f } ( 2 ) = 0$ and $\mathrm { f } ( - 3 ) = 35$, find the values of the constants $k$ and $c$.
\hfill \mbox{\textit{OCR MEI C1 2013 Q5 [4]}}