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Date May 2015 Marks available 2 Reference code 15M.1.sl.TZ1.2
Level SL only Paper 1 Time zone TZ1
Command term Find Question number 2 Adapted from N/A

Question

The following diagram shows a circle with centre \(O\) and a radius of \(10\) cm. Points \(A\), \(B\) and \(C\) lie on the circle.

Angle \(AOB\) is \(1.2\) radians.

Find the length of \({\text{arc ACB}}\).

[2]
a.

Find the perimeter of the shaded region.

[3]
b.

Markscheme

correct substitution     (A1)

eg\(\;\;\;10(1.2)\)

\(ACB\) is \(12{\text{ (cm)}}\)     A1     N2

[2 marks]

a.

valid approach to find major arc     (M1)

eg\(\;\;\;\)circumference \( - {\text{AB}}\), major angle \({\text{AOB}} \times {\text{radius}}\)

correct working for arc length     (A1)

eg\(\;\;\;2\pi (10) - 12,{\text{ }}10(2 \times 3.142 - 1.2),{\text{ }}2\pi (10) - 12 + 20\)

perimeter is \(20\pi  + 8\;\;\;( = 70.8){\text{ (cm)}}\)     A1     N2

[3 marks]

Total [5 marks]

b.

Examiners report

Most candidates were able to find the minor arc length. Similarly most candidates successfully found the major arc length in part b) but did not go on to add the two radii. Quite a few candidates worked with decimal approximations, rather than in terms of \(\pi \).

a.

Most candidates were able to find the minor arc length. Similarly most candidates successfully found the major arc length in part b) but did not go on to add the two radii. Quite a few candidates worked with decimal approximations, rather than in terms of \(\pi \).

b.

Syllabus sections

Topic 3 - Circular functions and trigonometry » 3.1 » The circle: radian measure of angles; length of an arc; area of a sector.
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