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.
Find the area of the shaded segment.
Markscheme
attempt to find the central angle or half central angle (M1)
eg, cosine rule, right triangle
correct working (A1)
egcosθ=82+82−1222∙8∙8, sin−1(68), 0.722734, 41.4096∘, π2−sin−1(68)cosθ=82+82−1222∙8∙8, sin−1(68), 0.722734, 41.4096∘, π2−sin−1(68)
correct angle AˆOBA^OB (seen anywhere)
eg1.69612, 97.1807∘, 2×sin−1(68)1.69612, 97.1807∘, 2×sin−1(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×√64−36×12, 31.749012(8)(8)sin1.70, 12(8)(12)sin0.722, 12×√64−36×12, 31.7490
appropriate approach (seen anywhere) (M1)
egAtriangle−AsectorAtriangle−Asector, 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]