| Exam Board | Edexcel |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Session | Specimen |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | Geometric properties using vectors |
| Difficulty | Moderate -0.8 This is a straightforward vector question requiring basic vector subtraction (finding AB from position vectors) and showing two sides are parallel by demonstrating one is a scalar multiple of the other. Both parts are routine applications of fundamental vector concepts with no problem-solving insight needed, making it easier than average but not trivial since it requires understanding of parallel vectors. |
| Spec | 1.10a Vectors in 2D: i,j notation and column vectors1.10g Problem solving with vectors: in geometry |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(\overrightarrow{AB} = \overrightarrow{OB} - \overrightarrow{OA} = 6\mathbf{i} - 3\mathbf{j} - (4\mathbf{i} + 2\mathbf{j})\) | M1 | Attempts \(\overrightarrow{AB} = \overrightarrow{OB} - \overrightarrow{OA}\) or equivalent; may be implied by one correct component |
| \(= 2\mathbf{i} - 5\mathbf{j}\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Explains that \(\overrightarrow{OC}\) is parallel to \(\overrightarrow{AB}\) as \(8\mathbf{i} - 20\mathbf{j} = 4 \times (2\mathbf{i} - 5\mathbf{j})\) | M1 | Attempts to compare vectors \(\overrightarrow{OC}\) and \(\overrightarrow{AB}\) by considering their directions |
| As \(\overrightarrow{OC} = 4 \times \overrightarrow{AB}\) it is parallel to it and not the same length, hence \(OABC\) is a trapezium | A1 | Must state \(OC\) is parallel to \(AB\) but not the same length |
## Question 2:
**Part (a):**
| Answer/Working | Mark | Guidance |
|---|---|---|
| $\overrightarrow{AB} = \overrightarrow{OB} - \overrightarrow{OA} = 6\mathbf{i} - 3\mathbf{j} - (4\mathbf{i} + 2\mathbf{j})$ | M1 | Attempts $\overrightarrow{AB} = \overrightarrow{OB} - \overrightarrow{OA}$ or equivalent; may be implied by one correct component |
| $= 2\mathbf{i} - 5\mathbf{j}$ | A1 | |
**Part (b):**
| Answer/Working | Mark | Guidance |
|---|---|---|
| Explains that $\overrightarrow{OC}$ is parallel to $\overrightarrow{AB}$ as $8\mathbf{i} - 20\mathbf{j} = 4 \times (2\mathbf{i} - 5\mathbf{j})$ | M1 | Attempts to compare vectors $\overrightarrow{OC}$ and $\overrightarrow{AB}$ by considering their directions |
| As $\overrightarrow{OC} = 4 \times \overrightarrow{AB}$ it is parallel to it and not the same length, hence $OABC$ is a trapezium | A1 | Must state $OC$ is parallel to $AB$ but not the same length |
---\begin{enumerate}
\item The quadrilateral $O A B C$ has $\overrightarrow { O A } = 4 \mathbf { i } + 2 \mathbf { j } , \overrightarrow { O B } = 6 \mathbf { i } - 3 \mathbf { j }$ and $\overrightarrow { O C } = 8 \mathbf { i } - 20 \mathbf { j }$.\\
(a) Find $\overrightarrow { A B }$.\\
(b) Show that quadrilateral $O A B C$ is a trapezium.
\end{enumerate}
\hfill \mbox{\textit{Edexcel AS Paper 1 Q2 [4]}}