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Date May 2018 Marks available 3 Reference code 18M.2.hl.TZ2.4
Level HL only Paper 2 Time zone TZ2
Command term Find Question number 4 Adapted from N/A

Question

Consider the following diagram.

The sides of the equilateral triangle ABC have lengths 1 m. The midpoint of [AB] is denoted by P. The circular arc AB has centre, M, the midpoint of [CP].

Find AM.

[3]
a.i.

Find AMP in radians.

[2]
a.ii.

Find the area of the shaded region.

[3]
b.

Markscheme

METHOD 1

PC =32 or 0.8660       (M1)

PM =12PC =34 or 0.4330     (A1)

AM =14+316

=74 or 0.661 (m)     A1

 

METHOD 2

using the cosine rule

AM2 =12+(34)22×34×cos(30)      M1A1

AM =74 or 0.661 (m)     A1

[3 marks]

a.i.

tan (AMP=23 or equivalent      (M1)

= 0.857      A1

[2 marks]

a.ii.

EITHER

12AM2(2AMPsin(2AMP))     (M1)A1

OR

12AM2×2AMP=38     (M1)A1

= 0.158(m2)      A1

Note: Award M1 for attempting to calculate area of a sector minus area of a triangle.

[3 marks]

b.

Examiners report

[N/A]
a.i.
[N/A]
a.ii.
[N/A]
b.

Syllabus sections

Topic 3 - Core: Circular functions and trigonometry » 3.1 » The circle: radian measure of angles.
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