O-LevelAdditional MathematicsSimultaneous equations4037/21 · May/June 2017 · Q65 Marks

Four cinemas, P, Q, R and S each sell adult, student and child tickets. The number of tickets sold by each cinema on one weekday were P: 90 adult, 10 student, 30 child Q: 45 student R: 25 adult, 15 child S: 10 adult, 100 child.

(i)Given that L = (1 1 1), construct a matrix, M, of the number of tickets sold, such that the matrix product LM can be found.[1]
(ii)Find the matrix product LM.[1]
(iii)State what information is represented by the matrix product LM.[1]
(iv)An adult ticket costs $5, a student ticket costs $4 and a child ticket costs $3. Construct a matrix, N, of the ticket costs, such that the matrix product LMN can be found and state what information is represented by the matrix product LMN.[2]

Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

[B1] (M =) [ [90 10 30] ; [0 45 0] ; [25 0 15] ; [10 0 100] ] columns and/or rows may be interchanged but must be consistent
[B1] (LM =)(1 1 1 1) [ [90 10 30] ; [0 45 0] ; [25 0 15] ; [10 0 100] ] = (125 55 145) Answer must be of correct order and must be consistent with a correct M
[B1] The total numbers of each type of ticket sold by all 4 cinemas oe
[B1] (N =) [ [5] ; [4] ; [3] ] Calculation not required
[B1] The total income of all (4) cinemas or other valid comment e.g. total income from all ticket sales

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