| Exam Board | Edexcel |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Year | 2018 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Straight Lines & Coordinate Geometry |
| Type | Verify collinearity or parallel/perpendicular relationship |
| Difficulty | Moderate -0.8 This is a straightforward AS-level coordinate geometry question requiring students to find the gradient of l₂ from two points, rearrange l₁ into y = mx + c form to find its gradient, then compare the gradients using standard rules (equal for parallel, product = -1 for perpendicular). It involves only routine procedures with no problem-solving insight needed, making it easier than average but not trivial since it requires multiple steps and correct application of perpendicularity conditions. |
| Spec | 1.10d Vector operations: addition and scalar multiplication1.10e Position vectors: and displacement |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Mark | Guidance |
| Gradient of \(4y - 3x = 10\) is \(\frac{3}{4}\) | B1 | Or rewrites as \(y = \frac{3}{4}x + \ldots\) |
| Attempts gradient of line joining \((5,-1)\) and \((-1,8)\) | M1 | Using \(\frac{\Delta y}{\Delta x}\); condone one sign error |
| \(= \frac{-1-8}{5-(-1)} = -\frac{3}{2}\) | A1 | Accept \(-\frac{9}{6}\) or \(-1.5\) |
| States neither parallel nor perpendicular with reasons | A1 (CSO) | Gradients not equal (not parallel) AND \(\frac{3}{4} \times -\frac{3}{2} \neq -1\) (not perpendicular) |
# Question 4:
| Working/Answer | Mark | Guidance |
|---|---|---|
| Gradient of $4y - 3x = 10$ is $\frac{3}{4}$ | B1 | Or rewrites as $y = \frac{3}{4}x + \ldots$ |
| Attempts gradient of line joining $(5,-1)$ and $(-1,8)$ | M1 | Using $\frac{\Delta y}{\Delta x}$; condone one sign error |
| $= \frac{-1-8}{5-(-1)} = -\frac{3}{2}$ | A1 | Accept $-\frac{9}{6}$ or $-1.5$ |
| States neither parallel nor perpendicular with reasons | A1 (CSO) | Gradients not equal (not parallel) AND $\frac{3}{4} \times -\frac{3}{2} \neq -1$ (not perpendicular) |\begin{enumerate}
\item The line $l _ { 1 }$ has equation $4 y - 3 x = 10$
\end{enumerate}
The line $l _ { 2 }$ passes through the points $( 5 , - 1 )$ and $( - 1,8 )$.\\
Determine, giving full reasons for your answer, whether lines $l _ { 1 }$ and $l _ { 2 }$ are parallel, perpendicular or neither.
\hfill \mbox{\textit{Edexcel AS Paper 1 2018 Q4 [4]}}