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O-LevelAdditional MathematicsVectors in two dimensions4037/21 · May/June 2020 · Q55 Marks

The vectors a and b are such that a = αi+j and b = 12i+βj.

  1. (a)Find the value of each of the constants α and β such that 4a-b = (α+3)i-2j.[3]
  2. (b)Hence find the unit vector in the direction of b-4a.[2]

Mark scheme

Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.

  1. [M1] 4α-12 = α+3 and 4 – β = −2
  2. [A1] α = 5
  3. [A1] β = 6
  4. [M1] √(their(α+3)² + (-2)²)
  5. [A1] (2j - their8i) / their 68

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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 2020 Paper 2 Variant 1, question 5.

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