O-LevelMathematicsVectors and transformations4024/11 · Oct/Nov 2025 · Q267 Marks
The diagram shows triangle OAB. [Figure 26.1] OA = a and OB = 4b. T is a point on AB such that AT : TB = 3 : 2.
- (a)Find AB in terms of a and b.[1]
- (b)Show that the position vector of T is (2/5)a + (6/5)b.[3]
- (c)Q is a point on OB and QT = (1/5)(2a - 3b). Find OQ : QB.[3]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.
- [1] (a) 4b - a
- [M2] (b) a + (3/5)(4b - a) or 4b - (2/5)(4b - a)
- [M1] for correct vector route for OT soi or for AT = (3/5)(their (4b-a)) oe or TB = (2/5)(their (4b-a)) oe
- [A1] With no errors
- [3] (c) 3:1 oe
- [M2] for [OQ=] a + (2/5)b - (2/5)a + (3/5)b oe or [QB=] (3/5)b - (2/5)a + (8/5)b oe or M1 for OQ = OT + TQ or better or for QB = QT + TB or better or for QT = QO + OA + AT or better
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