17N.1.SL.TZ0.T_6

pestleMathematicsAISLPaper 117N· sl-2-5-modelling-functionssource ↗

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]

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

[2]

Find the value of $x$ and of $y$ .

[3]

Markscheme / solution

* 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]

$\frac{y}{x} = \frac{3}{4}$ (M1)

Note: Award (M1) for a correct equation.

$y = \frac{3}{4}x{\text{ }}(y = 0.75x)$ (A1) (C2)

[2 marks]

${x^2} + {\left( {\frac{3}{4}x} \right)^2} = {68^2}{\text{ }}\left( {{\text{or }}{x^2} + \frac{9}{{16}}{x^2} = 4624{\text{ or equivalent}}} \right)$ (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 $y$ .

$x = 54.4{\text{ (cm), }}y = 40.8{\text{ (cm)}}$ (A1)(ft)(A1)(ft) (C3)

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

[3 marks]

Examiners’ report

[N/A]