AQA Further Paper 2 2023 June — Question 3 1 marks

Exam BoardAQA
ModuleFurther Paper 2 (Further Paper 2)
Year2023
SessionJune
Marks1
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
Topic3x3 Matrices
TypeDeterminant calculation and singularity
DifficultyStandard +0.3 This is a 1-mark multiple choice question testing basic determinant properties (row operations, row swaps, transposition). Students need to recognize that swapping rows changes the sign, while row operations and transposition preserve or predictably change the determinant. This is straightforward recall and application of standard determinant rules, making it easier than average even for Further Maths.
Spec4.03j Determinant 3x3: calculation

The determinant \(A = \begin{vmatrix} 1 & 1 & 1 \\ 2 & 0 & 2 \\ 3 & 2 & 1 \end{vmatrix}\) Which one of the determinants below has a value which is not equal to the value of \(A\)? Tick (\(\checkmark\)) one box. [1 mark] \(\begin{vmatrix} 3 & 1 & 3 \\ 2 & 0 & 2 \\ 3 & 2 & 1 \end{vmatrix}\) \quad \(\square\) \(\begin{vmatrix} 1 & 2 & 3 \\ 1 & 0 & 2 \\ 1 & 2 & 1 \end{vmatrix}\) \quad \(\square\) \(\begin{vmatrix} 2 & 2 & 2 \\ 1 & 0 & 1 \\ 3 & 2 & 1 \end{vmatrix}\) \quad \(\square\) \(\begin{vmatrix} 1 & 1 & 1 \\ 3 & 2 & 1 \\ 2 & 0 & 2 \end{vmatrix}\) \quad \(\square\)

Question 3:
AnswerMarks Guidance
3Ticks correct answer 1.1b
3 2 1
2 0 2
AnswerMarks Guidance
Question total1
QMarking Instructions AO
Question 3:
3 | Ticks correct answer | 1.1b | B1 | 1 1 1
3 2 1
2 0 2
Question total | 1
Q | Marking Instructions | AO | Marks | Typical solution
The determinant $A = \begin{vmatrix} 1 & 1 & 1 \\ 2 & 0 & 2 \\ 3 & 2 & 1 \end{vmatrix}$

Which one of the determinants below has a value which is not equal to the value of $A$?

Tick ($\checkmark$) one box.
[1 mark]

$\begin{vmatrix} 3 & 1 & 3 \\ 2 & 0 & 2 \\ 3 & 2 & 1 \end{vmatrix}$ \quad $\square$

$\begin{vmatrix} 1 & 2 & 3 \\ 1 & 0 & 2 \\ 1 & 2 & 1 \end{vmatrix}$ \quad $\square$

$\begin{vmatrix} 2 & 2 & 2 \\ 1 & 0 & 1 \\ 3 & 2 & 1 \end{vmatrix}$ \quad $\square$

$\begin{vmatrix} 1 & 1 & 1 \\ 3 & 2 & 1 \\ 2 & 0 & 2 \end{vmatrix}$ \quad $\square$

\hfill \mbox{\textit{AQA Further Paper 2 2023 Q3 [1]}}