Date | November 2020 | Marks available | 1 | Reference code | 20N.2.SL.TZ0.S_7 |
Level | Standard Level | Paper | Paper 2 | Time zone | Time zone 0 |
Command term | Show that | Question number | S_7 | Adapted from | N/A |
Question
The following diagram shows a circle with centre O and radius 1 cm. Points A and B lie on the circumference of the circle and AˆOB=2θ, where 0<θ<π2.
The tangents to the circle at A and B intersect at point C.
Show that AC=tan θ.
Find the value of θ when the area of the shaded region is equal to the area of sector OADB.
Markscheme
* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.
correct working for AC (seen anywhere) A1
eg tan θ=ACOA, tan θ=AC1
AG N0
[1 mark]
METHOD 1 (working with half the areas)
area of triangle or triangle (A1)
eg
correct sector area (A1)
eg
correct approach using their areas to find the shaded area (seen anywhere) (A1)
eg
correct equation A1
eg
A2 N4
METHOD 2 (working with entire kite and entire sector)
area of kite (A1)
eg
correct sector area (A1)
eg
correct approach using their areas to find the shaded area (seen anywhere) (A1)
eg
correct equation A1
eg
A2 N4
[6 marks]