| Exam Board | WJEC |
|---|---|
| Module | Unit 1 (Unit 1) |
| Year | 2022 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | Parallel or perpendicular vectors condition |
| Difficulty | Moderate -0.8 This is a straightforward multi-part vectors question testing standard techniques: finding unit vectors (divide by magnitude), finding angles with axes (using tan^{-1}), and using the parallel condition (equating ratios of components). All parts are routine textbook exercises requiring only direct application of formulas with no problem-solving insight needed, making it easier than average. |
| Spec | 1.10a Vectors in 2D: i,j notation and column vectors1.10c Magnitude and direction: of vectors1.10d Vector operations: addition and scalar multiplication |
The vectors $\mathbf{a}$ and $\mathbf{b}$ are defined by $\mathbf{a} = 2\mathbf{i} - \mathbf{j}$ and $\mathbf{b} = \mathbf{i} - 3\mathbf{j}$.
\begin{enumerate}[label=(\alph*)]
\item Find a unit vector in the direction of $\mathbf{a}$. [2]
\item Determine the angle $\mathbf{b}$ makes with the $x$-axis. [2]
\item The vector $\mu\mathbf{a} + \mathbf{b}$ is parallel to $4\mathbf{i} - 5\mathbf{j}$.
\begin{enumerate}[label=(\roman*)]
\item Find the vector $\mu\mathbf{a} + \mathbf{b}$ in terms of $\mu$, $\mathbf{i}$ and $\mathbf{j}$. [1]
\item Determine the value of $\mu$. [4]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 1 2022 Q16 [9]}}