In the diagram, ABCD is a parallelogram. P is the midpoint of BC. DQ: QP = 1 : 2. AB = p and AD = q. [Figure 24.1]

1. (a)Express DP in terms of p and q.[1]
2. (b)Express DQ in terms of p and q.[1]
3. (c)Express AQ in terms of p and q, giving your answer in its simplest form.[1]
4. (d)R is the point on BC produced such that BR = k BP.
5. (d)(i)Express AR in terms of p and q and k.[1]
6. (d)(ii)Given that A, Q and R lie on a straight line, find the value of k.[1]

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