| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2020 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Linear transformations |
| Type | Combined transformation matrix product |
| Difficulty | Standard +0.3 This is a straightforward Further Maths question testing standard matrix transformations. Part (i) involves recognizing a stretch, writing down a standard rotation matrix, and computing a 2×2 matrix product—all routine procedures. Part (ii) uses the determinant-area relationship, which is a direct application of a key formula. While it's Further Maths content, it requires only recall and basic computation with no novel problem-solving, making it easier than average overall. |
| Spec | 4.03d Linear transformations 2D: reflection, rotation, enlargement, shear4.03e Successive transformations: matrix products4.03h Determinant 2x2: calculation4.03i Determinant: area scale factor and orientation |
| VIXV SIHIANI III IM IONOO | VIAV SIHI NI JYHAM ION OO | VI4V SIHI NI JLIYM ION OO |
6. (i)
$$\mathbf { A } = \left( \begin{array} { l l }
1 & 0 \\
0 & 3
\end{array} \right)$$
\begin{enumerate}[label=(\alph*)]
\item Describe fully the single transformation represented by the matrix $\mathbf { A }$.
The matrix $\mathbf { B }$ represents a rotation of $45 ^ { \circ }$ clockwise about the origin.
\item Write down the matrix $\mathbf { B }$, giving each element of the matrix in exact form.
The transformation represented by matrix $\mathbf { A }$ followed by the transformation represented by matrix $\mathbf { B }$ is represented by the matrix $\mathbf { C }$.
\item Determine $\mathbf { C }$.\\
(ii) The trapezium $T$ has vertices at the points $( - 2,0 ) , ( - 2 , k ) , ( 5,8 )$ and $( 5,0 )$, where $k$ is a positive constant. Trapezium $T$ is transformed onto the trapezium $T ^ { \prime }$ by the matrix
$$\left( \begin{array} { r r }
5 & 1 \\
- 2 & 3
\end{array} \right)$$
Given that the area of trapezium $T ^ { \prime }$ is 510 square units, calculate the exact value of $k$.
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VIXV SIHIANI III IM IONOO & VIAV SIHI NI JYHAM ION OO & VI4V SIHI NI JLIYM ION OO \\
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\hfill \mbox{\textit{Edexcel F1 2020 Q6 [10]}}