O-LevelMathematicsVectors and transformations4024/21 · May/June 2019 · Q912 Marks

In the diagram, PQ = 4p, QR = 3q and PT=p+2q. QỦ = 2/3 QR and PT = 2/3 PS.

(a)In the diagram, PQ = 4p, QR = 3q and PT=p+2q. QỦ = 2/3 QR and PT = 2/3 PS.
(a)(i)Express, as simply as possible, in terms of p and/or q,
(a)(i)(a)PS,[1]
(a)(i)(b)SR.[2]
(a)(ii)State the name of the special quadrilateral PQRS. Using vectors, give a reason for your answer.[2]
(a)(iii)Find, in its simplest form, the ratio |PQ| : |SR|.[2]
(b)AB=(3/2) BC=(6/-2) CD=(-7/-3)
(b)(i)Find AD.[1]
(b)(ii)Find |BC|.[2]
(b)(iii)Given that E is the midpoint of BC, find AE.[2]

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Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

[1] 3/2 (p + 2q) oe simplified expression
[2] 5/2 p or 2.5p M1 for a correct vector route
[2] Trapezium B1 PQ is a multiple of SR B1 or PQ is parallel to SR since PQ=4p and SR=2.5p oe
[2] 8:5 FT their SR of form kp B1 for 4: 2.5 oe
[1] (2/-3) final answer
[2] 6.32 or 6.324 to 6.325 M1 for √6² + (-2)²
[2] (6/1) final answer B1 for (3/-1)

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