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Date May 2014 Marks available 1 Reference code 14M.1.sl.TZ2.6
Level SL only Paper 1 Time zone TZ2
Command term Write down Question number 6 Adapted from N/A

Question

The surface of a red carpet is shown below. The dimensions of the carpet are in metres.

Write down an expression for the area, \(A\), in \({{\text{m}}^2}\), of the carpet.

[1]
a.

The area of the carpet is \({\text{10 }}{{\text{m}}^2}\).

Calculate the value of \(x\).

[3]
b.

The area of the carpet is \({\text{10 }}{{\text{m}}^2}\).

Hence, write down the value of the length and of the width of the carpet, in metres.

[2]
c.

Markscheme

\(2x(x - 4)\)   or   \(2{x^2} - 8x\)     (A1)     (C1)

 

Note: Award (A0) for \(x - 4 \times 2x\).

 

[1 mark]

a.

\(2x(x - 4) = 10\)     (M1)

 

Note: Award (M1) for equating their answer in part (a) to \(10\).

 

\({x^2} - 4x - 5 = 0\)     (M1)

OR

Sketch of \(y = 2{x^2} - 8x\) and \(y = 10\)     (M1)

OR

Using GDC solver \(x = 5\) and \(x =  - 1\)     (M1)

OR

\(2(x + 1)(x - 5)\)     (M1)

\(x = 5{\text{ (m)}}\)     (A1)(ft)     (C3)

 

Notes: Follow through from their answer to part (a).

     Award at most (M1)(M1)(A0) if both \(5\) and \(-1\) are given as final answer.

     Final (A1)(ft) is awarded for choosing only the positive solution(s).

 

[3 marks]

b.

\(2 \times 5 = 10{\text{ (m)}}\)     (A1)(ft)

\(5 - 4 = 1{\text{ (m)}}\)     (A1)(ft)     (C2)

 

Note: Follow through from their answer to part (b).

     Do not accept negative answers.

 

[2 marks]

c.

Examiners report

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

Syllabus sections

Topic 5 - Geometry and trigonometry » 5.0 » Simple two-dimensional shapes and their properties, including perimeters and areas of circles, triangles, quadrilaterals and compound shapes.
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