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O-LevelAdditional MathematicsSimultaneous equations4037/21 · Oct/Nov 2010 · Q45 Marks

Students take three multiple-choice tests, each with ten questions. A correct answer earns 5 marks. If no answer is given 1 mark is scored. An incorrect answer loses 2 marks. A student's final total mark is the sum of 20% of the mark in test 1, 30% of the mark in test 2 and 50% of the mark in test 3. One student's responses are summarized in the table below. Test 1 Test 2 Test 3 Correct answer 7 6 5 No answer 1 3 5 Incorrect answer 2 1 0 Write down three matrices such that matrix multiplication will give this student's final total mark and hence find this total mark.

  1. (a)Write down three matrices such that matrix multiplication will give this student's final total mark and hence find this total mark.[5]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2010). The mark or mark type is shown in brackets.

  1. [B1] (7 6 5) or (0.2 0.3 0.5)
  2. (1 3 5) (7 1 2)
  3. (2 1 0) (6 3 1)
  4. (5 5 0)
  5. (5 1 -2)
  6. [M1] Matrix multiplication using 3 × 3 matrix
  7. [A1] (32 31 30) or (5.7) (3.6) (0.7)
  8. [DM1] Matrix multiplication of 1 × 3 with 3 × 1
  9. [A1] 30.7

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About this question

Topic
Simultaneous equations, O-Level Additional Mathematics (syllabus 4037). Structured question, 5 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2010 Paper 2 Variant 1, question 4.

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