| Exam Board | WJEC |
|---|---|
| Module | Unit 1 (Unit 1) |
| Year | 2022 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Straight Lines & Coordinate Geometry |
| Type | Intersection of two lines |
| Difficulty | Moderate -0.8 This is a straightforward coordinate geometry question testing standard techniques: finding line equations from two points, perpendicular gradients, intersection points, and triangle areas. All parts follow routine procedures with no problem-solving insight required. The multi-part structure (11 marks total) adds length but not conceptual difficulty—each step is a textbook exercise that AS-level students practice extensively. |
| Spec | 1.02q Use intersection points: of graphs to solve equations1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships |
The line $L_1$ passes through the points $A(0, 5)$ and $B(3, -1)$.
\begin{enumerate}[label=(\alph*)]
\item Find the equation of the line $L_1$. [3]
\end{enumerate}
The line $L_2$ is perpendicular to $L_1$ and passes through the origin $O$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Write down the equation of $L_2$. [1]
\end{enumerate}
The lines $L_1$ and $L_2$ intersect at the point $C$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Calculate the area of triangle $OAC$. [4]
\item Find the equation of the line $L_3$ which is parallel to $L_1$ and passes through the point $D(4, 2)$. [2]
\item The line $L_3$ intersects the $y$-axis at the point $E$. Find the area of triangle $ODE$. [1]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 1 2022 Q3 [11]}}