| Exam Board | OCR |
|---|---|
| Module | Further Pure Core 2 (Further Pure Core 2) |
| Year | 2021 |
| Session | June |
| Marks | 5 |
| Topic | Linear transformations |
| Type | Determine unknown matrix from conditions |
| Difficulty | Moderate -0.3 This is a straightforward application of shear transformation properties. Part (a) requires knowing that a y-axis invariant shear has form [[1,0],[k,1]] and solving for k using the given point mapping (one equation, one unknown). Part (b) is direct recall that det(A)=1 implies area preservation. While it's a Further Maths topic, the question requires minimal problem-solving beyond applying standard definitions. |
| Spec | 4.03d Linear transformations 2D: reflection, rotation, enlargement, shear |
2 A 2-D transformation $T$ is a shear which leaves the $y$-axis invariant and which transforms the object point $( 2,1 )$ to the image point $( 2,9 )$. $A$ is the matrix which represents the transformation $T$.
\begin{enumerate}[label=(\alph*)]
\item Find A .
\item By considering the determinant of A , explain why the area of a shape is invariant under T .
\end{enumerate}
\hfill \mbox{\textit{OCR Further Pure Core 2 2021 Q2 [5]}}