Practise

Question bank

Original exam-style questions, mapped to your syllabus. Answers are checked for mathematical equivalence and every attempt updates your mastery.

TopicSkillDifficulty

12 questions

SA-FP-MAT-G011 markL1 FoundationNon-calculatorDeterminants

Find the determinant of

\begin{pmatrix}4&3\\2&5\end{pmatrix}

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SA-FP-MAT-Q011 markL1 FoundationNon-calculatorOperations

\mathbf A

2\times3

and

\mathbf B

3\times4

. What is the order of

\mathbf{AB}

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SA-FP-MAT-X011 markL1 FoundationNon-calculatorDeterminants

Find

\det\begin{pmatrix}2&1\\3&4\end{pmatrix}

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SA-FP-MAT-X041 markL1 FoundationNon-calculatorOperations

\mathbf A=\begin{pmatrix}1&2\\0&1\end{pmatrix}

\mathbf B=\begin{pmatrix}3&0\\1&2\end{pmatrix}

. Find the top-left entry of

\mathbf{AB}

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SA-FP-MAT-0012 marksL2 StandardNon-calculatorOperations

\mathbf A=\begin{pmatrix}1&2\\3&4\end{pmatrix}

\mathbf B=\begin{pmatrix}0&1\\5&2\end{pmatrix}

. Find the bottom-left entry of

\mathbf{AB}

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SA-FP-MAT-0022 marksL2 StandardNon-calculatorInverses

\mathbf A=\begin{pmatrix}5&2\\7&3\end{pmatrix}

. Find the top-right entry of

\mathbf A^{-1}

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SA-FP-MAT-X022 marksL2 StandardNon-calculatorInverses

Find the top-left entry of the inverse of

\begin{pmatrix}2&1\\3&4\end{pmatrix}

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SA-FP-MAT-X032 marksL2 StandardNon-calculatorDeterminants

Find

\det\begin{pmatrix}1&2&0\\0&1&3\\2&0&1\end{pmatrix}

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SA-FP-MAT-0033 marksL3 ExamNon-calculatorDeterminants

Find

\det\begin{pmatrix}2&1&0\\1&3&1\\0&1&2\end{pmatrix}

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SA-FP-MAT-0043 marksL3 ExamNon-calculatorDeterminants

Find the value of

k

for which

\begin{pmatrix}k&2\\3&k-1\end{pmatrix}

is singular, given

k>0

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SA-FP-MAT-0053 marksL3 ExamNon-calculatorInverses

Use an inverse matrix to solve

3x+y=7

5x+2y=12

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SA-FP-MAT-0063 marksL4 ChallengingNon-calculatorInverses

\det\mathbf A=4

and

\det\mathbf B=-3

for

3\times3

matrices. Find

\det\left((\mathbf{AB})^{-1}\right)

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