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Date November 2017 Marks available 1 Reference code 17N.1.SL.TZ0.T_6
Level Standard Level Paper Paper 1 Time zone Time zone 0
Command term Write down Question number T_6 Adapted from N/A

Question

The size of a computer screen is the length of its diagonal. Zuzana buys a rectangular computer screen with a size of 68 cm, a height of y cm and a width of x cm, as shown in the diagram.

N17/5/MATSD/SP1/ENG/TZ0/06

The ratio between the height and the width of the screen is 3:4.

Use this information to write down an equation involving x and y .

[1]
a.

Use this ratio to write down y in terms of x .

[2]
b.

Find the value of x and of y .

[3]
c.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

x 2 + y 2 = 68 2 (or 4624 or equivalent)     (A1)     (C1)

[1 mark]

a.

y x = 3 4     (M1)

 

Note:     Award (M1) for a correct equation.

 

y = 3 4 x   ( y = 0.75 x )     (A1)     (C2)

[2 marks]

b.

x 2 + ( 3 4 x ) 2 = 68 2   ( or  x 2 + 9 16 x 2 = 4624  or equivalent )     (M1)

 

Note:     Award (M1) for correct substitution of their expression for y into their answer to part (a). Accept correct substitution of x in terms of y .

 

x = 54.4  (cm),  y = 40.8  (cm)     (A1)(ft)(A1)(ft)     (C3)

 

Note:     Follow through from parts (a) and (b) as long as x > 0 and y > 0 .

 

[3 marks]

c.

Examiners report

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

Syllabus sections

Topic 2—Functions » SL 2.5—Modelling functions
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