| Date | May 2009 | Marks available | 3 | Reference code | 09M.1.sl.TZ2.7 |
| Level | SL only | Paper | 1 | Time zone | TZ2 |
| Command term | Find | Question number | 7 | Adapted from | N/A |
Question
The diagram below shows the line PQ, whose equation is x + 2y = 12. The line intercepts the axes at P and Q respectively.
Find the coordinates of P and of Q.
A second line with equation x − y = 3 intersects the line PQ at the point A. Find the coordinates of A.
Markscheme
\(0 + 2y = 12\) or \(x + 2(0) = 12\) (M1)
P(0, 6) (accept \(x = 0\), \(y = 6\)) (A1)
Q(12, 0) (accept \(x = 12\), \(y = 0\)) (A1) (C3)
Notes: Award (M1) for setting either value to zero.
Missing coordinate brackets receive (A0) the first time this occurs.
Award (A0)(A1)(ft) for P(0, 12) and Q(6, 0).
[3 marks]
\(x + 2(x - 3) = 12\) (M1)
(6, 3) (accept \(x = 6\), \(y = 3\)) (A1)(A1) (C3)
Note: (A1) for each correct coordinate.
Missing coordinate brackets receive (A0)(A1) if this is the first time it occurs.
[3 marks]
Examiners report
Most candidates could find the x and y intercepts but many wrote the coordinates the wrong way around. A number of candidates did not label their coordinates as P and Q or did not include parentheses.
In this part many had trouble recognising the need to solve the two simultaneous equations.
