Form 5 Additional Mathematics Bab 1: Circular Measure
Instructions
Answer all questions. Show all relevant mathematical workings clearly. Where applicable, take π = 3.142 or leave answers in terms of π as requested.
10 questions · 21 marks total
1. A chord AB of length 10 cm subtends an angle of 1.2 rad at the centre O of a circle with radius r cm. Find the radius r of the circle, correct to 2 decimal places. [Hint: Use chord length = 2r sin(θ/2)]
Short Answer · 3m2. A sector AOB has a radius of 12 cm and an angle of 1.2 rad at the centre O. Find the area of the sector.
Short Answer · 2m3. The area of a sector of a circle with radius r cm is 40 cm². If the central angle is 0.8 rad, find the value of r.
Short Answer · 3m4. Which of the following gives the correct area of a sector with radius r and central angle θ in radians?
Multiple Choice · 1m5. Fill in the blank: The formula for the arc length s of a circle with radius r and central angle θ in radians is s = ________.
Fill in the Blank · 1m6. A sector of a circle with centre O has a radius of 8 cm and a central angle of 0.75 rad. Calculate the perimeter of the sector.
Short Answer · 2m7. State whether the following statement is True or False: 'One radian is the angle subtended at the centre of a circle by an arc whose length equals the diameter of the circle.'
True / False · 1m8. In a circle with centre O and radius 6 cm, a minor sector POQ has a central angle of 1.5 rad. Calculate (a) the area of triangle POQ, and (b) the area of the minor segment bounded by chord PQ and arc PQ. (Take sin(1.5 rad) = 0.9975)
Short Answer · 4m9. Convert 135° into radians in terms of π.
Short Answer · 2m10. Diagram shows a sector POQ of a circle with centre O and radius 10 cm. If the arc length PQ is 14 cm, calculate the angle θ subtended at the centre in radians.
Short Answer · 2m