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Date	May 2022	Marks available	2	Reference code	22M.1.SL.TZ2.1
Level	Standard Level	Paper	Paper 1	Time zone	Time zone 2
Command term	Calculate	Question number	1	Adapted from	N/A

Question

The straight metal arm of a windscreen wiper on a car rotates in a circular motion from a pivot point, $O$ , through an angle of $140 °$ . The windscreen is cleared by a rubber blade of length $46 cm$ that is attached to the metal arm between points $A$ and $B$ . The total length of the metal arm, $OB$ , is $56 cm$ .

The part of the windscreen cleared by the rubber blade is shown unshaded in the following diagram.

Calculate the length of the arc made by $B$ , the end of the rubber blade.

[2]

Determine the area of the windscreen that is cleared by the rubber blade.

[3]

Markscheme

attempt to substitute into length of arc formula (M1)

$\frac{140 °}{360 °} \times 2 π \times 56$

$137 cm (136.833 \dots, \frac{392 π}{9} cm)$ A1

[2 marks]

subtracting two substituted area of sectors formulae (M1)

$(\frac{140 °}{360 °} \times π \times 56^{2}) - (\frac{140 °}{360 °} \times π \times 10^{2})$ OR $\frac{140 °}{360 °} \times π \times (56^{2} - 10^{2})$ (A1)

$3710 {cm}^{2} (3709.17 \dots {cm}^{2})$ A1

[3 marks]

Examiners report

There was some difficulty determining the correct radius to substitute, with several candidates substituting a radius of 46.

It was common to see candidates subtracting the radii before substituting into the area formula, rather than subtracting the sector areas after calculating each. Using the π key on the calculator rather than an approximated value was prevalent and pleasing to see.

Syllabus sections

Topic 3—Geometry and trigonometry » SL 3.4—The circle, arc and area of sector, degrees only

18N.2.AHL.TZ0.H_7:
Boat A is situated 10km away from boat B, and each boat has a marine radio transmitter on board. The range of the transmitter on boat A is 7km, and the range of the transmitter on boat B is 5km. The region in which both transmitters can be detected is represented by the shaded region in the following diagram. Find the area of this region.
22M.2.SL.TZ1.4a.ii:
Find the area of the shaded segment.
22M.2.SL.TZ1.4b.ii:
Find the area of the field that can be reached by the goat.
22M.2.AHL.TZ1.2a.ii:
Find the area of the shaded segment.
22M.2.SL.TZ1.4a.i:
Find the angle $AÔB$ .
21N.1.SL.TZ0.8b:
Find the surface area of the outside of the hat.
22M.1.SL.TZ2.1b:
Determine the area of the windscreen that is cleared by the rubber blade.
22M.1.AHL.TZ2.8a:
Use Sam’s measurements to calculate the area of the sector. Give your answer to four significant figures.
22M.2.AHL.TZ1.2a.i:
Find the angle $AÔB$ .
21M.2.SL.TZ1.2d:
Calculate the length of arc $AC$ .
SPM.1.SL.TZ0.11:
Helen is building a cabin using cylindrical logs of length 2.4 m and radius 8.4 cm. A wedge is cut from one log and the cross-section of this log is illustrated in the following diagram.

Find the volume of this log.
21M.2.SL.TZ1.2e:
Calculate the area of the shaded sector, $AOC$ .
21M.2.SL.TZ1.2c:
Find the size of angle $θ$ in degrees.
21M.2.SL.TZ1.2f:
Write down the height of the endpoint of the minute hand above the bookshelf at $6 : 00$ am.
17M.2.SL.TZ1.S_5:
The following diagram shows the chord [AB] in a circle of radius 8 cm, where ${\text{AB}} = 12{\text{ cm}}$ .

Find the area of the shaded segment.
21M.1.SL.TZ2.9a:
A footpath is to be laid around the curved side of the lawn. Find the length of the footpath.
21M.1.SL.TZ2.9b:
Find the area of the lawn.
21N.1.SL.TZ0.8a.i:
Write down the perimeter of the base of the hat in terms of $π$ .
21N.1.SL.TZ0.8a.ii:
Find the value of $θ$ .

Topic 3—Geometry and trigonometry

Question

Markscheme

Examiners report

Syllabus sections

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