| Exam Board | AQA |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2006 |
| Session | June |
| Marks | 10 |
| 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 C1 coordinate geometry question testing standard techniques: gradient formula, equation of a line, solving simultaneous equations, and perpendicular gradients. All parts are routine textbook exercises requiring direct application of formulas with no problem-solving insight needed, making it easier than average but not trivial due to the multi-step nature. |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships |
1 The point $A$ has coordinates $( 1,7 )$ and the point $B$ has coordinates $( 5,1 )$.
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Find the gradient of the line $A B$.
\item Hence, or otherwise, show that the line $A B$ has equation $3 x + 2 y = 17$.
\end{enumerate}\item The line $A B$ intersects the line with equation $x - 4 y = 8$ at the point $C$. Find the coordinates of $C$.
\item Find an equation of the line through $A$ which is perpendicular to $A B$.
\end{enumerate}
\hfill \mbox{\textit{AQA C1 2006 Q1 [10]}}