| Date | May 2009 | Marks available | 2 | Reference code | 09M.1.sl.TZ1.4 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Calculate | Question number | 4 | Adapted from | N/A |
Question
A and B are points on a straight line as shown on the graph below.
Write down the y-intercept of the line AB.
Calculate the gradient of the line AB.
The acute angle between the line AB and the x-axis is θ.
Show θ on the diagram.
The acute angle between the line AB and the x-axis is θ.
Calculate the size of θ.
Markscheme
6
OR
(0, 6) (A1) (C1)
[1 mark]
\(\frac{{(2 - 5)}}{{(8 - 2)}}\) (M1)
Note: Award (M1) for substitution in gradient formula.
\( = - \frac{1}{2}\) (A1) (C2)
[2 marks]
Angle clearly identified. (A1) (C1)
[1 mark]
\(\tan \theta = \frac{1}{2}\) (or equivalent fraction) (M1)
\(\theta = 26.6^\circ\) (A1)(ft) (C2)
Note: (ft) from (b).
Accept alternative correct trigonometrical methods.
[2 marks]
Examiners report
This was generally well answered.
This was generally well answered, the errors coming from incorrect substitution into the gradient formula rather than using the two intercepts.
There was often a lack of accuracy in the answers. Also, the use of the sine rule overly complicated matters for many.
