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O-LevelAdditional MathematicsSimultaneous equations4037/22 · Oct/Nov 2017 · Q87 Marks

The matrix A is (2 1 / 4 3).

  1. (i)Find (2A)⁻¹.[3]
  2. (ii)Hence solve the simultaneous equations 2y + 4x + 5 = 0, 6y + 8x + 9 = 0.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

  1. [B1] 2A=(4 2 / 8 6)
  2. [B2] (2A)^(-1) = 1/8 (6 -2 / -8 4); B1 for (6 -2 / -8 4) B1 for 1/8
  3. [B1] 4x + 2y = -5; 8x + 6y = -9
  4. [M1] Pre multiply (-5 / -9) by a 2x2 matrix.; Allow recovery
  5. [M1] (x / y) = 1/8 (6 -2 / -8 4) (-5 / -9); Pre multiply their (-5 / -9) by their answer to (i)
  6. [A2] (x / y) = 1/8 (-12 / 4) (= -1.5 / 0.5); A1 for x value A1 for y value oe Allow both unsimplified

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About this question

Topic
Simultaneous equations, O-Level Additional Mathematics (syllabus 4037). Structured question, 7 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2017 Paper 2 Variant 2, question 8.

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