1 | (IB/s1/2019/November/Paper2/q4)
[Maximum mark: 7] The following diagram shows a right-angled triangle, ABC, with AC=10 cm,AB=6 cm and BC=8 cm. The points D and F lie on [AC]. [BD] is perpendicular to [AC]. BEF is the arc of a circle, centred at A. The region R is bounded by [BD]. [DF] and are BEF.
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2 | (IB/sl/2019/May/paper2tz2/qu)
[Maximum mark: 7] OAB is a sector of the circle with centre O and radius r, as shown in the following diagram. The angle AOB is θ radians, where 0<θ<π2. The point C lies on OA and OA is perpendicular to BC.
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3 | (IB/s1/2018/November/Paper1/q1)
[Maximum mark: 6] The following diagram shows a circle with centre A and radius 6 cm. The points B,C, and D lie on the circle, and BˆAC=2 radians.
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4 | (IB/s1/2018/May/paper1tz2/q4)
[Maximum mark: 7] 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 AOB=θ. The area of the shaded sector AOB is 12 cm2 and the length of are AB is 6 cm. Find the value of r. |
5 | (IB/s1/2018/May/paper2tz1/q3)
[Maximum mark: 6] The diagram shows a circle, centre O, with radius 4 cm. Points A and B lie on the circumference of the circle and AOOB=θ, where 0≤θ≤π.
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6 | (IB/s1/2017/November/Paper1/q4)
[Maximum mark: 7 ] The following diagram shows triangle ABC, with AB=3 cm,BC=8 cm, and ABC=π3.
Find the exact perimeter of this shape. [3] |
7 | (IB/s1/2017/May/paper2tz1/q5)
[Maximum mark: 7] The following diagram shows the chord [AB] in a circle of radius 8 cm, where AB=12 cm. Find the area of the shaded segment. |
8 | (IB/s1/2017/May/paper2tz2/q1)
[Maximum mark: 6] The following diagram shows a circle with centre O and radius 40 cm. The points A,B and C are on the circumference of the circle and AOC=1.9 radians.
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9 | (IB/s1/2016/November/Paper2/q3)
[Maximum mark: 7] The following diagram shows a circle, centre O and radius r mm. The circle is divided into five equal sectors. One sector is OAB, and AOB=θ.
The area of sector AOB is 20πmm2.
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10 | (IB/s1/2016/May/paper1tz2/q5)
[Maximum mark: 8] The following diagram shows a triangle ABC and a sector BDC of a circle with centre B and radius 6 cm. The points A,B and D are on the same line. AB=2√3 cm,BC=6 cm, area of triangle ABC=3√3 cm2,ABC is obtuse.
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11 | (IB/s1/2015/November/Paper2/q1)
[Maximum mark: 6] The following diagram shows a circle with centre O and radius 3 cm. Points A,B, and C lie on the circle, and AOOC=1,3 radians.
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12 | (IB/s1/2015/May/paper1tz1/q2)
[Maximum mark: 5 ] The following diagram shows a circle with centre O and a radius of 10 cm. Points A,B and C. lie on the circle. Angle AOB is 1.2 radians.
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13 | (IB/sl/2015/May/paper2tz2/q10)
[Maximum mark: 16] The following diagram shows a square ABCD, and a sector OAB of a circle centre O, radius r. Part of the square is shaded and labelled R. AˆOB=θ, where 0.5≤θ<π.
(i) Write down the area of the sector when θ=α. (ii) Hence find α.
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Answer
[1](a) 0.927 (b) 8.05
[2](a) Show (b) A=12r2sinθcosθ (c) θ=.830
[3](a) Area =36 (b) Perimeter =12π
[4] r=4 cm
[5](a) A=8θ−8sinθ (b) θ=2.27
[6](a) Show (b) 11+72π
[7] Area =22.5
[8](a) 76 (b) 156 (c) 1520
[9](a) θ=2π5 (b) r=10 (c) 11.8
[10](a) 5π6(150∘),π6(30∘) (b) 3π
[11](a) l=3.9 (b) area =9π−5.85
[12](a) 12 (b) P=8+20π
[13](a) Show (b) (i) 12αr2 (ii) α=0.511 (c) 1.31<β<2.67
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