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Date November 2019 Marks available 2 Reference code 19N.1.SL.TZ0.T_2
Level Standard Level Paper Paper 1 Time zone Time zone 0
Command term Find Question number T_2 Adapted from N/A

Question

M-Line is a company that prints and sells custom designs on T-shirts. For each order, they charge an initial design fee and then an additional fee for each printed T-shirt.

M-Line charges M euros per order. This charge is modelled by the linear function M ( x ) = 5 x + 40 , where x is the number of T-shirts in the order.

EnYear is another company that prints and sells T-shirts. The price, N euros, that they charge for an order can be modelled by the linear function N ( x ) = 9 x , where x is the number of T-shirts in the order.

Write down the initial design fee charged for each order.

[1]
a.

Find the total amount charged for an order of 94 T-shirts.

[2]
b.

Write down the number of T-shirts in an order for which EnYear charged 63 euros.

[1]
c.

An order of p T-shirts will be charged the same price by both M-Line and EnYear.

Find the value of p .

[2]
d.

Markscheme

40 (euros)      (A1)  (C1)

[1 mark]

a.

( M ( 94 ) = ) 5 ( 94 ) + 40         (M1)

Note: Award (M1) for correct substitution of 94 into given function.

510 (euros)       (A1)  (C2)

[2 marks]

b.

7 (T-shirts)      (A1)  (C1)

[1 mark]

c.

9 p = 5 p + 40       (M1)

Note: Award (M1) for equating the given functions. Accept a sketch showing both functions.

( p = ) 10   (T-shirts)      (A1)  (C2)

[2 marks]

d.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.
[N/A]
d.

Syllabus sections

Topic 2—Functions » SL 2.5—Modelling functions
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Topic 2—Functions

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