O-LevelAdditional MathematicsQuadratic functions4037/21 · May/June 2019 · Q66 Marks

A = ((x+3), -x; (2x), (x-3)). Given that A does not have an inverse, find the exact values of x.

(a)A = ((x+3), -x; (2x), (x-3)). Given that A does not have an inverse, find the exact values of x.[3]
(b)(i)Write down the order of matrix B.[1]
(b)(ii)The matrix BC = ((9), (-12), (15); (3), (-8), (-3); (6), (-3), (20)). Explain why CB ≠ BC.[2]

Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

[B1] (x+3)(x-3) - 2x(-x)
[M1] their det A = 0 (Can be implied by later work)
[A1] [x=] ±√3 isw
[B1] 3 × 2 or 3 by 2
[B2] BC is a 3 by 3 matrix and CB is a 2 by 2 matrix [so they cannot be the same] oe OR [B1] for a partially correct statement e.g. The orders are not the same or BC is a 3 by 3 matrix or CB is a 2 by 2 matrix OR [B1] for 3 correct elements for CB = ((6, 5), (41, 15)) [so not equal] OR [B1] for finding one correct element of CB as being different from BC and commenting that the elements are different, [the matrices cannot be the same] oe

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Topic: Quadratic functions, O-Level Additional Mathematics (syllabus 4037). Structured question, 6 marks.
Source: O-Level Additional Mathematics, May/June 2019 Paper 2 Variant 1, question 6.

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