O-LevelAdditional MathematicsVectors in two dimensions4037/12 · May/June 2015 · Q79 Marks
In the diagram AB = 4a, BC = b and DC = 7a. The lines AC and DB intersect at the point X. Find, in terms of a and b,
- (i)DA,[1]
- (ii)DB.[1]
- (iii)AX, Given that AX = λAC, find, in terms of a, b and λ,[1]
- (iv)DX.[2]
- (v)find the value of λ and of μ. (Given that DX = μDB,)[4]
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Mark scheme
Marking points from the official mark scheme (May/June 2015). The mark or mark type is shown in brackets.
- [1] (i) B1 mark final answer, allow unsimplified
- [1] (ii) B1 mark final answer, allow unsimplified
- [1] (iii) B1 mark final answer, allow unsimplified
- [2] (iv) M1 their (i) + their (iii) or equivalent valid method or 3a − b + their (iii)
- [2] (iv) A1 Allow unsimplified
- [4] (v) M1 equating their (iv) and μ× their (ii)
- [4] (v) DM1 for an attempt to equate like vectors and attempt to solve 2 linear equations for λ and μ
- [4] (v) A1,A1 A1 for each λ and μ
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