| Exam Board | WJEC |
|---|---|
| Module | Further Unit 3 (Further Unit 3) |
| Year | 2024 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Work done and energy |
| Type | Work done by constant force - vector setup |
| Difficulty | Moderate -0.8 This is a straightforward two-part question requiring basic vector addition to find the resultant force, then applying the standard work formula W = F·s to find an unknown constant. Both parts involve routine calculations with no problem-solving insight needed, making it easier than average for A-level Further Maths mechanics. |
| Spec | 1.10d Vector operations: addition and scalar multiplication1.10f Distance between points: using position vectors6.02b Calculate work: constant force, resolved component |
3. Three forces $( 4 \mathbf { i } - 7 \mathbf { j } + 9 \mathbf { k } ) \mathrm { N } , ( 5 \mathbf { i } + 3 \mathbf { j } - 8 \mathbf { k } ) \mathrm { N }$ and $( - 2 \mathbf { i } + 6 \mathbf { j } - 11 \mathbf { k } ) \mathrm { N }$ act on a particle.
\begin{enumerate}[label=(\alph*)]
\item Find the resultant $\mathbf { R }$ of the three forces.
\item The points $A$ and $B$ have position vectors $( 3 \mathbf { i } + 4 \mathbf { j } - 12 \mathbf { k } ) \mathrm { m }$ and $( a \mathbf { i } + 7 \mathbf { j } - 10 \mathbf { k } ) \mathrm { m }$ respectively, where $a$ is a constant. The work done by $\mathbf { R }$ in moving the particle from $A$ to $B$ is 21 J . Calculate the value of $a$.\\
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\end{enumerate}
\hfill \mbox{\textit{WJEC Further Unit 3 2024 Q3 [5]}}