Sub-topic 1
2025 · National One-Eighth
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Determinant test: does $t(x,y)\to(x-y,\ x+y)$ have an inverse? (true/false)
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Sub-topic 2
2025 · National One-Eighth
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Zero determinant: transformations such as $t(x,y)\to(x-y,\ -x+y)$ with no inverse
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Sub-topic 3
2025 · National One-Eighth
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Matrix algebra: is $ab=ba$? distributive law and symmetric matrices (true/false)
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Sub-topic 4
2024 · National Preliminary
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Pre-image of $q(-3,9)$ under $t(x,y)\to(x-3y,\ x+3y)$
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Sub-topic 5
2022 · National Final
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Pre-image of $(3,-1)$ under $(x,y)\mapsto(x-2y,\ x+2y)$
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Sub-topic 6
2023 · National Preliminary
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Pre-image of $(-3,2)$ under $(x,y)\mapsto(4x+y,\ 3x+y)$
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Sub-topic 7
2024 · National Preliminary
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Riddles identifying transformations (linear map, dilation, isometry, reflection, rotation) from their properties
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Sub-topic 8
2026 · National One-Eighth
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Matrix of a linear transformation from the images of $\mathbf{i}(1,0)$ and $\mathbf{j}(0,1)$
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Sub-topic 9
2025 · National Preliminary
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Inverse of the $2\times2$ matrix $a=\begin{pmatrix}-2&-7\\1&3\end{pmatrix}$
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Sub-topic 10
2026 · National Quarterfinal
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Inverse of the linear transformation $(x,y)\mapsto(3x+4y,\ x+2y)$
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Sub-topic 11
2026 · National One-Eighth
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Image of $(3,-2)$ under $(x,y)\mapsto(2x+3y,\ x-2y)$
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Sub-topic 12
2026 · National One-Eighth
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Values of $x$ for which $\begin{pmatrix}3&6\\x&2x\end{pmatrix}$ has no inverse
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Sub-topic 13
2025 · National Quarterfinal
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Image of $a(-2,5)$ under a reflection in the point $p(3,-2)$
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Sub-topic 14
2024 · National One-Eighth
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Image of $a(2,-4)$ under a reflection in the point $p(3,-2)$
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Sub-topic 15
2024 · National Preliminary
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Image of a point under a reflection in another point $p$
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Sub-topic 16
2021 · National Preliminary
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Reflections of $a(5,-4)$ in the axes and the origin (true/false)
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Sub-topic 17
2021 · National Preliminary
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Finding $t$, its matrix and its inverse from $t(1,0)=(2,1)$ and $t(0,1)=(5,3)$
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Sub-topic 18
2024 · National One-Eighth
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Product $ab$ of $a=\begin{pmatrix}2&5\\1&3\end{pmatrix}$ and $b=\begin{pmatrix}7&-2\\-3&1\end{pmatrix}$
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Sub-topic 19
2026 · National Preliminary
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Determinants and invertibility of matrices (true/false)
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Sub-topic 20
2023 · National Preliminary
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Image of $y=x^2$, $y=x+4$ and $y=x^3$ under a reflection in the point $a(2,3)$
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Sub-topic 21
2013 · National Preliminary
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Image of $a(2,-5)$ under a $180^\circ$ rotation about the origin
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Sub-topic 22
2013 · National Preliminary
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Image of $b(-4,0)$ under a $90^\circ$ clockwise rotation about the origin
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Sub-topic 23
2013 · National Preliminary
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Image of $c(0,-4)$ under a $90^\circ$ anticlockwise rotation about the origin
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Sub-topic 24
2013 · National Preliminary
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Product of $\begin{bmatrix}2&1\\-2&1\end{bmatrix}$ and $\begin{bmatrix}2&-1\\1&2\end{bmatrix}$
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Sub-topic 25
2013 · National Preliminary
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Product of $\begin{bmatrix}3&-1\\2&2\end{bmatrix}$ and $\begin{bmatrix}-1&3\\1&3\end{bmatrix}$
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Sub-topic 26
2013 · National Preliminary
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Product of $\begin{bmatrix}1&0\\-1&2\end{bmatrix}$ and $\begin{bmatrix}2&-1\\0&1\end{bmatrix}$
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Sub-topic 27
2014 · National Quarterfinal
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Riddle: reflection in the line $y=x$
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Sub-topic 28
2016 · National One-Eighth
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Identifying the transformation $(x,y)\mapsto(-x,y)$
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Sub-topic 29
2016 · National One-Eighth
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Translation mapping $(2,4)$ onto $(4,2)$ applied to $a(3,1)$
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Sub-topic 30
2018 · National Preliminary
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Matrix for $(x,y)\mapsto(y,x)$ (reflection in the line $y=x$)
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Sub-topic 31
2018 · National Preliminary
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Matrix for $(x,y)\mapsto(-x,y)$ (reflection in the $y$-axis)
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Sub-topic 32
2018 · National Preliminary
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Matrix for $(x,y)\mapsto(x,-y)$ (reflection in the $x$-axis)
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Sub-topic 33
2018 · National Preliminary
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Image of $a(-2,1)$ under the translation mapping $(3,5)$ onto $(5,6)$
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Sub-topic 34
2019 · National Preliminary
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Image of the line $y=2x$ under a reflection in the $y$-axis
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Sub-topic 35
2021 · National Semifinal
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Image of $(-2,3)$ under the translation mapping $(2,5)$ onto $(3,2)$
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Sub-topic 36
2023 · National Preliminary
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Finding $p$ when $t(x,y)=(4x+y,\ 3x+y)$ maps $p$ onto $(-3,2)$
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Sub-topic 37
2023 · National Preliminary
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Finding $p$ when $(x,y)\mapsto(2x+y,\ 5x+3y)$ maps $p$ onto $b(1,2)$
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Sub-topic 38
2023 · National One-Eighth
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Product of a $2\times3$ matrix and a $3\times2$ matrix
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