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