Date | May 2018 | Marks available | 7 | Reference code | 18M.1.SL.TZ2.S_4 |
Level | Standard Level | Paper | Paper 1 (without calculator) | Time zone | Time zone 2 |
Command term | Find | Question number | S_4 | Adapted from | N/A |
Question
The following diagram shows a circle with centre O and radius r cm.
The points A and B lie on the circumference of the circle, and A∧OB = θ. The area of the shaded sector AOB is 12 cm2 and the length of arc AB is 6 cm.
Find the value of r.
Markscheme
* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.
evidence of correctly substituting into circle formula (may be seen later) A1A1
eg 12θr2=12,rθ=6
attempt to eliminate one variable (M1)
eg r=6θ,θ=1r,12θr2rθ=126
correct elimination (A1)
eg 12×6r×r2=12,12θ×(6θ)2=12,A=12×r2×lr,r22r=2
correct equation (A1)
eg 12×6r=12,12×36θ=12,12=12×r2×6r
correct working (A1)
eg 3r=12,18θ=12,r2=2,24=6r
r = 4 (cm) A1 N2
[7 marks]