User interface language: English | Español

Date May 2017 Marks available 7 Reference code 17M.2.sl.TZ1.5
Level SL only Paper 2 Time zone TZ1
Command term Find Question number 5 Adapted from N/A

Question

The following diagram shows the chord [AB] in a circle of radius 8 cm, where AB=12 cmAB=12 cm.

M17/5/MATME/SP2/ENG/TZ1/05

Find the area of the shaded segment.

Markscheme

attempt to find the central angle or half central angle     (M1)

egM17/5/MATME/SP2/ENG/TZ1/05/M, cosine rule, right triangle

correct working     (A1)

egcosθ=82+82122288, sin1(68), 0.722734, 41.4096, π2sin1(68)cosθ=82+82122288, sin1(68), 0.722734, 41.4096, π2sin1(68)

correct angle AˆOBA^OB (seen anywhere) 

eg1.69612, 97.1807, 2×sin1(68)1.69612, 97.1807, 2×sin1(68)     (A1)

correct sector area

eg12(8)(8)(1.70), 97.1807360(64π), 54.275912(8)(8)(1.70), 97.1807360(64π), 54.2759     (A1) 

area of triangle (seen anywhere)     (A1) 

eg12(8)(8)sin1.70, 12(8)(12)sin0.722, 12×6436×12, 31.749012(8)(8)sin1.70, 12(8)(12)sin0.722, 12×6436×12, 31.7490

appropriate approach (seen anywhere)     (M1)

egAtriangleAsectorAtriangleAsector, their sector-their triangle

22.5269

area of shaded region =22.5 (cm2)=22.5 (cm2)     A1     N4

 

Note:     Award M0A0A0A0A1 then M1A0 (if appropriate) for correct triangle area without any attempt to find an angle in triangle OAB.

 

[7 marks]

Examiners report

[N/A]

Syllabus sections

Topic 3 - Circular functions and trigonometry » 3.6 » The cosine rule.
Show 58 related questions

View options