O-LevelAdditional MathematicsSimultaneous equations4037/22 · May/June 2015 · Q25 Marks

The table shows the number of passengers in Economy class and in Business class on 3 flights from London to Paris. The table also shows the departure times for the 3 flights and the cost of a single ticket in each class. Departure time | Number of passengers in Economy class | Number of passengers in Business class ---|---|--- 0930 | 60 | 50 1330 | 70 | 52 1545 | 58 | 34 Single ticket price (£) | 120 | 300

(i)Write down a matrix, P, for the numbers of passengers and a matrix, Q, of single ticket prices, such that the matrix product QP can be found.[2]
(ii)Find the matrix product QP.[2]
(iii)Given that R = [1/1], explain what information is found by evaluating the matrix product QPR.[1]

Mark scheme

Marking points from the official mark scheme (May/June 2015). The mark or mark type is shown in brackets.

[B2] or [P=] [[60, 70, 58], [50, 52, 34]] and [Q =] [120, 300]
or [P=] [[50, 52, 34], [60, 70, 58]] and [Q=] [300, 120]
or B1 if one error
may be written as an unevaluated product; B0 if choice of P and Q offered
[B2] must have brackets and must not have commas; must be a 1 by 3 matrix; must be from correct product; working may be seen in (i)
or B1 for any two elements correct
[B1] do not accept, e.g. The total amount from each flight; must be a comment not just a figure; must not contain a contradiction

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