OCR MEI FP1 2010 June — Question 1 4 marks

Exam BoardOCR MEI
ModuleFP1 (Further Pure Mathematics 1)
Year2010
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicSolving quadratics and applications
TypeAlgebraic identity, find constants
DifficultyModerate -0.8 This is a straightforward algebraic manipulation requiring students to expand the right-hand side and equate coefficients. While it's from FP1, the technique is routine and involves only basic algebra with no problem-solving insight needed—simpler than typical A-level questions.
Spec1.02e Complete the square: quadratic polynomials and turning points
1 Find the values of \(A , B\) and \(C\) in the identity \(4 x ^ { 2 } - 16 x + C \equiv A ( x + B ) ^ { 2 } + 2\).
Question 1:
AnswerMarks Guidance
AnswerMark Guidance
\(4x^2 - 16x + C \equiv A(x^2 + 2Bx + B^2) + 2\)B1 \(A = 4\)
\(\Leftrightarrow 4x^2 - 16x + C \equiv Ax^2 + 2ABx + AB^2 + 2\)M1 Attempt to expand RHS or other valid method (may be implied)
\(\Leftrightarrow A = 4, B = -2, C = 18\)A2, 1 [4] 1 mark each for B and C, c.a.o. 
# Question 1:

| Answer | Mark | Guidance |
|--------|------|----------|
| $4x^2 - 16x + C \equiv A(x^2 + 2Bx + B^2) + 2$ | B1 | $A = 4$ |
| $\Leftrightarrow 4x^2 - 16x + C \equiv Ax^2 + 2ABx + AB^2 + 2$ | M1 | Attempt to expand RHS or other valid method (may be implied) |
| $\Leftrightarrow A = 4, B = -2, C = 18$ | A2, 1 **[4]** | 1 mark each for B and C, c.a.o. |

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1 Find the values of $A , B$ and $C$ in the identity $4 x ^ { 2 } - 16 x + C \equiv A ( x + B ) ^ { 2 } + 2$.

\hfill \mbox{\textit{OCR MEI FP1 2010 Q1 [4]}}
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