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O-LevelAdditional MathematicsSimultaneous equations4037/12 · May/June 2013 · Q89 Marks

(a) Given that the matrix A = (4 2 \ 3 -5), find

(a)(i)A²,[2]
(a)(ii)3A + 4I, where I is the identity matrix.[2]
(b)(i)Find the inverse matrix of (6 1 \ -9 3).[2]
(b)(ii)Hence solve the equations 6x + y = 5, -9x + 3y = 3/2.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2013). The mark or mark type is shown in brackets.

[2] (22 -2 \ -3 31) B2, 1, 0 -1 each element error
[2] (16 6 \ 9 -11) B2, 1, 0 -1 each element error
[1] B1 for 1/determinant (allow unsimplified)
[1] B1 for matrix
[1] M1 for correct use of inverse matrix, including correct multiplication to solve equation
[1] x = 0.5, y = 2 A1 for each
[1] x = 0.5, y = 2 A1 for each

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About this question

Topic: Simultaneous equations, O-Level Additional Mathematics (syllabus 4037). Structured question, 9 marks.
Source: O-Level Additional Mathematics, May/June 2013 Paper 1 Variant 2, question 8.

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