| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2013 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Matrices |
| Type | Determinant calculation |
| Difficulty | Moderate -0.8 This is a straightforward Further Maths question requiring basic determinant calculation (2×2 matrix formula) and understanding that zero area means zero determinant. Both parts are direct application of standard techniques with minimal problem-solving, making it easier than average even for Further Maths. |
| Spec | 4.03h Determinant 2x2: calculation4.03i Determinant: area scale factor and orientation |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\det \mathbf{M} = a(2-a)-1\) | M1A1 | M1 for "\(ad-bc\)" |
| (2) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\det \mathbf{M} = 0\) | M1 | First M for setting \(\det \mathbf{M} = 0\) |
| \(a^2 - 2a + 1 = 0\) | M1 | Second M for attempt to solve their 3 term quadratic |
| \((a-1)^2 = 0\) | Method mark for solving 3 term quadratic: factorisation, formula, or completing the square | |
| \(a = 1\) | A1 | |
| (3) [5] |
# Question 1:
## Part (a)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\det \mathbf{M} = a(2-a)-1$ | M1A1 | M1 for "$ad-bc$" |
| | **(2)** | |
## Part (b)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\det \mathbf{M} = 0$ | M1 | First M for setting $\det \mathbf{M} = 0$ |
| $a^2 - 2a + 1 = 0$ | M1 | Second M for attempt to solve their 3 term quadratic |
| $(a-1)^2 = 0$ | | Method mark for solving 3 term quadratic: factorisation, formula, or completing the square |
| $a = 1$ | A1 | |
| | **(3) [5]** | |
---\begin{enumerate}
\item $\mathbf { M } = \left( \begin{array} { c c } a & 1 \\ 1 & 2 - a \end{array} \right)$, where $a$ is a constant.\\
(a) Find det M in terms of $a$.\\
(2)
\end{enumerate}
A triangle $T$ is transformed to $T ^ { \prime }$ by the matrix M .\\
Given that the area of $T ^ { \prime }$ is 0 ,\\
(b) find the value of $a$.\\
(3)\\
\hfill \mbox{\textit{Edexcel FP1 2013 Q1 [5]}}