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O-LevelAdditional MathematicsSimultaneous equations4037/12 · Oct/Nov 2018 · Q88 Marks

A = ( (a 3) / (4 a+4) )

  1. (i)Find the values of the constant a for which A⁻¹ does not exist.[3]
  2. (ii)Given that a = 4, find A⁻¹.[2]
  3. (iii)Hence find the matrix B such that AB = ( (2 3) / (4 -5) ).[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

  1. [M1] For correct use of det = 0
  2. [M1] Dep For solution of resulting quadratic equation
  3. [A1] For both
  4. [B2] oe
  5. [B1] for (1/20)
  6. [B1] for ( (8 -3) / (-4 4) )
  7. [M1] For pre-multiplication by their A⁻¹
  8. [M1] Dep For multiplication of 2 matrices – need to see at least 2 correct elements – may be unsimplified
  9. [A1] For final matrix oe

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About this question

Topic
Simultaneous equations, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2018 Paper 1 Variant 2, question 8.

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