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Practise

Question bank

Original exam-style questions, mapped to your syllabus. Answers are checked for mathematical equivalence and every attempt updates your mastery.

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18 questions

SA-9709-P1-CM-0022 marksL1 FoundationCalculatorArc length
Find the length of an arc of a circle of radius 66 cm that subtends an angle of 0.80.8 radians at the centre.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CM-0032 marksL1 FoundationCalculatorSector area
Find the area of a sector of radius 55 cm and angle 1.21.2 radians.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CM2-G013 marksL1 FoundationCalculatorSector area
A sector has radius 1010 cm and angle 0.60.6 radians. Find its arc length, its area and its perimeter.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CM2-Q011 markL1 FoundationCalculatorSector area
The radius of a sector is doubled and its angle stays the same. Its area is multiplied by
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CM-Q021 markL1 FoundationCalculatorSector area
With θ\theta in radians, the area of a sector of radius rr is
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CM-0042 marksL2 StandardCalculatorSector area
A sector has radius 99 cm and angle π3\dfrac{\pi}{3} radians. Find its area, giving an exact answer.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CM-0053 marksL2 StandardCalculatorArc length
Find the perimeter of a sector of radius 88 cm and angle 1.51.5 radians.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CM-0062 marksL2 StandardCalculatorSector area
A sector of a circle of radius 44 cm has area 2424 cm². Find the angle of the sector in radians.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CM2-0012 marksL2 StandardCalculatorSector area
A sector has radius 66 cm and angle 5π6\dfrac{5\pi}{6}. Find the exact arc length and the exact area.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CM2-0022 marksL2 StandardCalculatorArc length
A sector of radius 99 cm has angle 40∘40^\circ. Find the exact arc length.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CM2-0032 marksL2 StandardCalculatorBackwards
A sector of radius 55 cm has area 1515 cm². Find the angle of the sector in radians.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CM2-0043 marksL2 StandardCalculatorBackwards
An arc of length 1212 cm subtends an angle of 1.51.5 radians at the centre of a circle. Find the radius and the area of the sector.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CM2-0062 marksL2 StandardCalculatorSector area
A pizza of diameter 3030 cm is cut into 88 equal slices. Find, exactly, the area of one slice and the length of its crust (the arc).

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CM-0074 marksL3 ExamCalculatorSector area
A sector has arc length 1010 cm and area 4040 cm². Find the radius and the angle of the sector.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CM-0153 marksL3 ExamCalculatorArc length
An arc of length 7π3\dfrac{7\pi}{3} cm subtends an angle of 70∘70^\circ at the centre of a circle. Find the radius.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CM2-0053 marksL3 ExamCalculatorBackwards
A sector of radius 66 cm has perimeter 2121 cm. Find the angle of the sector and its area.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CM-0125 marksL4 ChallengingCalculatorSector area
A sector of radius rr cm and angle θ\theta radians has perimeter 2020 cm. (a) Show that its area is A=10r−r2A=10r-r^2. (b) Find the value of rr that makes AA as large as possible, the maximum area, and the corresponding angle θ\theta.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CM2-0073 marksL4 ChallengingCalculatorSector area
A windscreen wiper is 6060 cm long, but only the outer 4040 cm is rubber blade (the inner 2020 cm is the arm). It turns through 1.81.8 radians about the pivot. Find the area of windscreen cleaned, in cm².

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Salam Academy Original Practice · Proposed mark scheme