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O-LevelAdditional MathematicsVectors in two dimensions4037/11 · May/June 2022 · Q55 Marks

Find the vector which is in the opposite direction to `( (15), (-8) )` and has a magnitude of 8.5.

  1. (a)Find the vector which is in the opposite direction to `( (15), (-8) )` and has a magnitude of 8.5.[2]
  2. (b)Find the values of a and b such that `5( (3a), (b) ) + ( (2a+1), (2) ) = 6( (b+a), (2) )`.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.

  1. [2] B1 for ( ( -7.5 ), ( 4 ) ) oe (This is the required vector or a scalar multiple, e.g. 1/2 (15 / -8) or (-15 / 8) and magnitude check)
  2. B1 for (-15 / 8) oe (This is the direction vector, or other intermediate step showing components)

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About this question

Topic
Vectors in two dimensions, O-Level Additional Mathematics (syllabus 4037). Structured question, 5 marks.
Source
O-Level Additional Mathematics, May/June 2022 Paper 1 Variant 1, question 5.

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