| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2003 |
| Session | November |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Straight Lines & Coordinate Geometry |
| Type | Rectangle or parallelogram vertices |
| Difficulty | Moderate -0.3 This is a straightforward coordinate geometry problem requiring finding perpendicular and parallel line equations, then solving simultaneously. While it involves multiple steps (finding gradients, using point-slope form, solving system of equations), each step uses standard techniques with no conceptual challenges. The trapezium context provides clear geometric constraints that guide the solution method. Slightly easier than average due to the structured nature and routine application of formulas. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships |
| Answer | Marks | Guidance |
|---|---|---|
| eqn CD: \(y=5-2(x-12)\) | B1, M1, A1, ∇, M1, A1, ∇ [5] | Co. Correct form of eqn. \(\surd\) on m\(=-\frac{1}{2}\). Use of m\(_1m_2=-1\). \(\surd\) on his "\(\frac{1}{2}\)" but needs both M marks. |
| Answer | Marks | Guidance |
|---|---|---|
| \(\rightarrow C(10,9)\) | M1, A1 [2] | Method for solving. Co. Diagram only for (ii), allow B1 for (10,9). |
**(i)** m of BC $= \frac{1}{2}$
Eqn BC: $y-6=\frac{1}{2}(x-4)$
m of CD $= -2$
eqn CD: $y=5-2(x-12)$ | B1, M1, A1, ∇, M1, A1, ∇ [5] | Co. Correct form of eqn. $\surd$ on m$=-\frac{1}{2}$. Use of m$_1m_2=-1$. $\surd$ on his "$\frac{1}{2}$" but needs both M marks.
**(ii)** Sim eqns $2y=x+8$ and $y+2x=29$
$\rightarrow C(10,9)$ | M1, A1 [2] | Method for solving. Co. Diagram only for (ii), allow B1 for (10,9).5\\
\includegraphics[max width=\textwidth, alt={}, center]{1cf37a58-8a7f-4dc8-9e35-2e8badf3eb83-2_594_778_1360_682}
The diagram shows a trapezium $A B C D$ in which $B C$ is parallel to $A D$ and angle $B C D = 90 ^ { \circ }$. The coordinates of $A , B$ and $D$ are $( 2,0 ) , ( 4,6 )$ and $( 12,5 )$ respectively.\\
(i) Find the equations of $B C$ and $C D$.\\
(ii) Calculate the coordinates of $C$.
\hfill \mbox{\textit{CAIE P1 2003 Q5 [7]}}