| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2018 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Straight Lines & Coordinate Geometry |
| Type | Parallel line through point |
| Difficulty | Moderate -0.8 Part (i) requires finding the gradient of AB using two points, then writing y=mx for a line through the origin—straightforward coordinate geometry. Part (ii) involves applying the distance formula and solving a simple equation. Both are routine textbook exercises with no problem-solving insight required, making this easier than average. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships1.10f Distance between points: using position vectors |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Gradient of \(AB = -\frac{3}{4}\) | B1 | Accept \(-3a/4a\) |
| \(y = -\frac{3}{4}x\) | B1FT | Answer must not include \(a\). Ft on *their* numerical gradient |
| Total: 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \((4a)^2 + (3a)^2 = (10/3)^2\) | M1 | May be unsimplified |
| \(25a^2 = 100/9\) | A1 | |
| \(a = 2/3\) | A1 | |
| Total: 3 |
## Question 3:
**Part (i):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Gradient of $AB = -\frac{3}{4}$ | B1 | Accept $-3a/4a$ |
| $y = -\frac{3}{4}x$ | B1FT | Answer must not include $a$. Ft on *their* numerical gradient |
| | **Total: 2** | |
**Part (ii):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $(4a)^2 + (3a)^2 = (10/3)^2$ | M1 | May be unsimplified |
| $25a^2 = 100/9$ | A1 | |
| $a = 2/3$ | A1 | |
| | **Total: 3** | |
---3 Two points $A$ and $B$ have coordinates ( $3 a , - a$ ) and ( $- a , 2 a$ ) respectively, where $a$ is a positive constant.\\
(i) Find the equation of the line through the origin parallel to $A B$.\\
(ii) The length of the line $A B$ is $3 \frac { 1 } { 3 }$ units. Find the value of $a$.\\
\hfill \mbox{\textit{CAIE P1 2018 Q3 [5]}}