Find the length of OB.

Find the size of angle OBP.

Note: Unit penalty (UP) applies in this part

\({\rm{PB}} = \frac{1}{2}\sqrt {{{40}^2} + {{40}^2}}  = \sqrt {800}  = 28.28(28.3)\)     (M1)(A1)

Note: Award (M1) for correct substitutions, (A1) for correct answer.

(UP)     \({\rm{OB}} = \sqrt {{{40}^2} + {{28.28}^2}}  = 49.0{\text{ cm }}\left( {\sqrt {2400} {\text{ cm}}} \right)\)     (M1)(A1)(ft)     (C4)

Note: Award (M1) for correct substitution, can (ft) from any answer to PB.

[4 marks]

\({\sin ^{ - 1}}\left( {\frac{{40}}{{49}}} \right)\)

OR

\({\cos ^{ - 1}}\left( {\frac{{28.28}}{{49}}} \right)\)

OR

\({\tan ^{ - 1}}\left( {\frac{{40}}{{28.28}}} \right)\)     (M1)

= 54.7 (54.8)     (A1)(ft)     (C2)

Note: Award (M1) for any correct trig. ratio.

In radians = 0.616, award (M1)(A0).

Note: Common error: (a) \(OB = \sqrt {40^2 + 20^2} = 44.7 {\text{ cm}}\). Award (M0)(A0)(M1), (A1)(ft), and (b) angle OBP = 63.4° (63.5°) (M1)(A1)(ft).

[2 marks]

This question was well answered by many candidates although a number lost an accuracy penalty or a unit penalty in this question. A very common error was assuming PB to be 20 cm. The mark-scheme allowed for follow through marks to be awarded in this case. Most candidates could find the angle and very few did not use right angled trigonometry.

This question was well answered by many candidates although a number lost an accuracy penalty or a unit penalty in this question. A very common error was assuming PB to be 20 cm. The mark-scheme allowed for follow through marks to be awarded in this case. Most candidates could find the angle and very few did not use right angled trigonometry.