OCR MEI FP1 2012 January — Question 2 5 marks

Exam BoardOCR MEI
ModuleFP1 (Further Pure Mathematics 1)
Year2012
SessionJanuary
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicFactor & Remainder Theorem
TypePolynomial identity or expansion
DifficultyEasy -1.2 This is a straightforward polynomial identity question requiring expansion and coefficient comparison. While it's from FP1, the technique is mechanical: expand the right side, equate coefficients of like powers, and solve the resulting linear system. No conceptual insight or problem-solving is needed beyond applying a standard algorithm.
Spec1.02j Manipulate polynomials: expanding, factorising, division, factor theorem
2 Find the values of \(A , B , C\) and \(D\) in the identity \(2 x ^ { 3 } - 3 \equiv ( x + 3 ) \left( A x ^ { 2 } + B x + C \right) + D\).
Question 2:
AnswerMarks Guidance
AnswerMarks Guidance
\(2x^3 - 3 \equiv (x+3)(Ax^2 + Bx + C) + D\)B1 \(A = 2\)
M1Evidence of comparing coefficients or other valid method (may be implied)
\(B = -6,\ C = 18,\ D = -57\)A3 1 mark each for B, C and D, c.a.o.
[5] 
## Question 2:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $2x^3 - 3 \equiv (x+3)(Ax^2 + Bx + C) + D$ | B1 | $A = 2$ |
| | M1 | Evidence of comparing coefficients or other valid method (may be implied) |
| $B = -6,\ C = 18,\ D = -57$ | A3 | 1 mark each for B, C and D, c.a.o. |
| **[5]** | | |

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2 Find the values of $A , B , C$ and $D$ in the identity $2 x ^ { 3 } - 3 \equiv ( x + 3 ) \left( A x ^ { 2 } + B x + C \right) + D$.

\hfill \mbox{\textit{OCR MEI FP1 2012 Q2 [5]}}
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Q1 5 Q2 5 Q3 6 Q4 6 Q5 6 Q6 8 Q7 14 Q8 10 Q9 12