| Exam Board | OCR MEI |
|---|---|
| Module | Further Pure Core AS (Further Pure Core AS) |
| Session | Specimen |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear transformations |
| Type | Describe shear from matrix |
| Difficulty | Moderate -0.8 Part (i) requires recognizing a standard shear transformation from a 2×2 matrix—a direct recall task for Further Maths students. Part (ii) applies the determinant-area relationship (det = 1, so area preserved), which is a fundamental property taught explicitly. Both parts are routine applications of matrix transformation theory with no problem-solving or novel insight required, making this easier than average even for Further Maths. |
| Spec | 4.03d Linear transformations 2D: reflection, rotation, enlargement, shear4.03i Determinant: area scale factor and orientation |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | (i) | Shear |
| x-axis fixed, (0,1) to (2,1) | I |
| Answer | Marks |
|---|---|
| [2] | 1.2 |
| 1.1 | allow x-axis invariant, [shear] |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | (ii) | E |
| Answer | Marks |
|---|---|
| = 5 (square units) | B1 |
| Answer | Marks |
|---|---|
| [2] | 2.2a |
| 1.1 | Or det M = 1 |
Question 2:
2 | (i) | Shear
x-axis fixed, (0,1) to (2,1) | I
C
B1
B1
[2] | 1.2
1.1 | allow x-axis invariant, [shear]
factor 2.
2 | (ii) | E
Shear preserves area P
(cid:159) New area[ = 5 × 1]
= 5 (square units) | B1
B1
[2] | 2.2a
1.1 | Or det M = 1\begin{enumerate}[label=(\roman*)]
\item Describe fully the transformation represented by the matrix $\begin{pmatrix} 1 & 2 \\ 0 & 1 \end{pmatrix}$. [2]
\item A triangle of area 5 square units undergoes the transformation represented by the matrix $\begin{pmatrix} 1 & 2 \\ 0 & 1 \end{pmatrix}$.
Explaining your reasoning, find the area of the image of the triangle following this transformation. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Pure Core AS Q2 [4]}}