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Question bank

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

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12 questions

SA-FP-MTR-G011 markL1 FoundationNon-calculatorStandard matrices
The matrix (3003)\begin{pmatrix}3&0\\0&3\end{pmatrix} is an enlargement about OO. Find its area scale factor.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-MTR-Q011 markL1 FoundationNon-calculatorCombining
Transformation A\mathbf A is followed by B\mathbf B. The single matrix is
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Salam Academy Original Practice · Proposed mark scheme
SA-FP-MTR-X011 markL1 FoundationNon-calculatorStandard matrices
The point (1,0)(1,0) is rotated 90∘90^\circ anticlockwise about the origin. Find its new yy-coordinate.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-MTR-X021 markL1 FoundationNon-calculatorStandard matrices
Find the area scale factor of the transformation (3124)\begin{pmatrix}3&1\\2&4\end{pmatrix}.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-MTR-X051 markL1 FoundationNon-calculatorCombining
Transformation A\mathbf A followed by transformation B\mathbf B is represented by
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-MTR-0012 marksL2 StandardNon-calculatorStandard matrices
The matrix (12−323212)\begin{pmatrix}\frac12&-\frac{\sqrt3}2\\\frac{\sqrt3}2&\frac12\end{pmatrix} is a rotation about OO. Find the anticlockwise angle in degrees (0≤θ<3600\le\theta<360).

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-MTR-0022 marksL2 StandardNon-calculatorCombining
P=(2001)\mathbf P=\begin{pmatrix}2&0\\0&1\end{pmatrix} (stretch) and Q=(0−110)\mathbf Q=\begin{pmatrix}0&-1\\1&0\end{pmatrix} (rotation). The point (1,3)(1,3) undergoes P\mathbf P then Q\mathbf Q. Find the xx-coordinate of its image.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-MTR-X032 marksL2 StandardNon-calculatorCombining
An enlargement with scale factor 33 is followed by a reflection in the xx-axis. Find the determinant of the combined matrix.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-MTR-X041 markL2 StandardNon-calculatorInvariance
Reflection in y=xy=x has a line of invariant points y=mxy=mx. Find mm.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-MTR-0033 marksL3 ExamNon-calculatorInvariance
Find the gradients of the invariant lines through OO of (3122)\begin{pmatrix}3&1\\2&2\end{pmatrix}.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-MTR-0043 marksL3 ExamNon-calculatorInvariance
M=(2112)\mathbf M=\begin{pmatrix}2&1\\1&2\end{pmatrix} has a line of invariant points y=kxy=kx. Find kk.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-MTR-0053 marksL4 ChallengingNon-calculatorStandard matrices
The matrix (0110)\begin{pmatrix}0&1\\1&0\end{pmatrix} is a reflection in y=(tan⁡θ)xy=(\tan\theta)x. Find θ\theta in degrees (0≤θ<1800\le\theta<180).

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Salam Academy Original Practice · Proposed mark scheme