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    A particle is projected from a point O on horizontal ground. The velocity of projection has magnitude 20ms^(-1) and direction upwards at an angle theta to the horizontal. The particle passes through the point 7m above the ground and 16m horizontally from O, and hits the ground at the point A.
    i) Using the equation of the particle's trajectory and the identity sec^(2)=1+tan^(2), show that the possible values of tan theta are 3/4 and 17/4
    ii) Find the distance of OA for each of the two possible values of tan theta
    iii) Sketch in the same diagram the two possible trajectories

    There are 12 people at an identification parade. Three witnesses are called to identify the accused person.

    Assuming they make their choice purely by random selection, draw a tree diagram showing the possible events
    i) From the tree diagram, calculate the following possibilities
    (a) that all three witnesses select the accused person
    (b) that none of the witnesses selects the accused person
    (c)at least two of the witnesses selects the accused person

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Updated: February 22, 2018
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