| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2016 |
| Session | November |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Straight Lines & Coordinate Geometry |
| Type | Coordinates from geometric constraints |
| Difficulty | Moderate -0.3 This is a straightforward coordinate geometry problem requiring midpoint formula application and perpendicular gradient conditions. Part (i) is routine algebraic manipulation; part (ii) involves setting up two simultaneous equations from given conditions. While multi-step, it uses only standard AS-level techniques with no novel insight required, making it slightly easier than average. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships |
| Answer | Marks |
|---|---|
| 6 (i) | 2+x |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | B1 | |
| B1 | [2] | No MR for (½(2+n), |
| Answer | Marks | Guidance |
|---|---|---|
| Page 5 | Mark Scheme | Syllabus |
| Cambridge International AS/A Level – October/November 2016 | 9709 | 13 |
| (ii) | Sub their x, y into y= x+1 → −12−m=2n−2+1 |
| Answer | Marks |
|---|---|
| m=−9, n=−1 | M1* |
| Answer | Marks | Guidance |
|---|---|---|
| A1A1 | [5] | Expect m+2n=−11 |
Question 6:
--- 6 (i) ---
6 (i) | 2+x
=n ⇒ x=2n−2
2
m+ y
=−6 ⇒ y=−12−m
2 | B1
B1 | [2] | No MR for (½(2+n),
½(m – 6))
Expect (2n−2, −12−m)
Page 5 | Mark Scheme | Syllabus | Paper
Cambridge International AS/A Level – October/November 2016 | 9709 | 13
(ii) | Sub their x, y into y= x+1 → −12−m=2n−2+1
m+6
=−1 oe Not nested in an equation
2−n
Eliminate a variable
m=−9, n=−1 | M1*
B1
DM1
A1A1 | [5] | Expect m+2n=−11
Expect m−n=−8
Note: other methods possibleThree points, $A$, $B$ and $C$, are such that $B$ is the mid-point of $AC$. The coordinates of $A$ are $(2, m)$ and the coordinates of $B$ are $(n, -6)$, where $m$ and $n$ are constants.
\begin{enumerate}[label=(\roman*)]
\item Find the coordinates of $C$ in terms of $m$ and $n$. [2]
\end{enumerate}
The line $y = x + 1$ passes through $C$ and is perpendicular to $AB$.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Find the values of $m$ and $n$. [5]
\end{enumerate}
\hfill \mbox{\textit{CAIE P1 2016 Q6 [7]}}