OCR FP1 2014 June — Question 1 3 marks

Exam BoardOCR
ModuleFP1 (Further Pure Mathematics 1)
Year2014
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
Topic3x3 Matrices
TypeDeterminant calculation and singularity
DifficultyModerate -0.5 This is a straightforward 3×3 determinant calculation with a parameter, requiring application of the standard formula (cofactor expansion or rule of Sarrus). While it involves algebraic manipulation with the parameter 'a', it's a routine Further Maths exercise with no conceptual difficulty beyond the mechanical process.
Spec4.03j Determinant 3x3: calculation

1 Find the determinant of the matrix \(\left( \begin{array} { r r r } a & 4 & - 1 \\ 3 & a & 2 \\ a & 1 & 1 \end{array} \right)\).

Question 1:
AnswerMarks Guidance
AnswerMarks Guidance
Show correct expansion process for \(3 \times 3\)M1 Condone sign errors for first M1; M2 for the "diagonal" method
Correct evaluation of any \(2 \times 2\)M1
\(2a^2 + 6a - 15\)A1 \(\text{Det} = 1/(2a^2 + 6a - 15)\) only A0
[3]
# Question 1:
| Answer | Marks | Guidance |
|--------|-------|----------|
| Show correct expansion process for $3 \times 3$ | M1 | Condone sign errors for first M1; M2 for the "diagonal" method |
| Correct evaluation of any $2 \times 2$ | M1 | |
| $2a^2 + 6a - 15$ | A1 | $\text{Det} = 1/(2a^2 + 6a - 15)$ **only** A0 |
| **[3]** | | |

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1 Find the determinant of the matrix $\left( \begin{array} { r r r } a & 4 & - 1 \\ 3 & a & 2 \\ a & 1 & 1 \end{array} \right)$.

\hfill \mbox{\textit{OCR FP1 2014 Q1 [3]}}