O-LevelAdditional MathematicsVectors in two dimensions4037/22 · Oct/Nov 2015 · Q36 Marks

Relative to an origin O, points A, B and C have position vectors (5/4), (-10/12) and (-6/-18) respectively. All distances are measured in kilometres. A man drives at a constant speed directly from A to B in 20 minutes.

(i)Calculate the speed in kmh⁻¹ at which the man drives from A to B.[3]
(ii)He now drives directly from B to C at the same speed. Find how long it takes him to drive from B to C.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2015). The mark or mark type is shown in brackets.

[B1] (i) AB=(-15/8) Allow BA May be implied by later work.
[M1] (i) |AB| = √15² +8² (=17) Use of Pythagoras on their AB
[A1] (i) Speed = 17×3 = 51km/hr Must be exact
[B1] (ii) BC =(16/-30) Allow CB
[M1] (ii) |BC| = √16² +30² (=34) Use of Pythagoras on their BC
[A1] (ii) Time taken = 34/51 × 60 = 40 mins (or 2/3 hrs) Allow answers which round to 40 to 2sf. Accept 0.66 or 0.67 hrs. Mark final answer.

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Topic: Vectors in two dimensions, O-Level Additional Mathematics (syllabus 4037). Structured question, 6 marks.
Source: O-Level Additional Mathematics, Oct/Nov 2015 Paper 2 Variant 2, question 3.

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