O-LevelAdditional MathematicsSimultaneous equations4037/12 · Oct/Nov 2019 · Q89 Marks

(a) Five teams took part in a competition in which each team played each of the other 4 teams. The following table represents the results after all the matches had been played. [Table showing Won, Drawn, Lost for Teams A, B, C, D, E] Points in the competition were awarded to the teams as follows: 4 for each match won, 2 for each match drawn, 0 for each match lost. (b) It is given that A = (6 -1 / 2 4) and B = (5 0 / 1 -2).

(a)(i)Write down two matrices whose product under matrix multiplication will give the total number of points awarded to each team.[2]
(a)(ii)Evaluate the matrix product from part (i) and hence state which team was awarded the most points.[2]
(b)(i)Find A⁻¹.[2]
(b)(ii)Hence find the matrix C such that AC = B.[3]

Mark scheme

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

[2] B2 For correct matrices in correct order or B1 if one correct matrix and a slip in one element of the other matrix
[1] M1 For matrix multiplication of their (i), with at least 2 elements correct, must be in correct form, may be unsimplified
[1] A1 All correct and identifying team E
[2] B2 B1 for 1/6 and B1 for (4 1 / -2 1)
[1] M1 For pre-multiplication by their inverse from (i)
[1] M1 Dep for matrix multiplication, using their inverse from (i), at least 2 elements correct
[1] A1

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