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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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15 questions

SA-9709-P1-CM3-Q011 markL1 FoundationCalculatorSegments
The area of a segment with angle θ\theta (radians) in a circle of radius rr is
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CM3-0012 marksL2 StandardCalculatorChords
A chord ABAB of a circle of radius 55 cm subtends an angle of 2π3\dfrac{2\pi}{3} at the centre. Find the exact length of ABAB.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CM3-0032 marksL2 StandardCalculatorSegments
A sector OABOAB has radius 88 cm and angle 11 radian. Find the area of triangle OABOAB, correct to 2 decimal places.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CM3-0061 markL2 StandardCalculatorChords
A chord of a circle is exactly as long as the radius. The angle it subtends at the centre is
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CM3-G013 marksL2 StandardCalculatorSegments
A chord ABAB of a circle with centre OO and radius 44 cm has ∠AOB=π2\angle AOB=\dfrac{\pi}{2}. Find, exactly, the area of the sector OABOAB, the area of triangle OABOAB and the area of the minor segment.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CM-0084 marksL3 ExamCalculatorSegments
A chord ABAB of a circle with centre OO and radius 66 cm subtends angle AOB=π3AOB=\dfrac{\pi}{3}. Find the exact area of the minor segment cut off by ABAB.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CM-0092 marksL3 ExamCalculatorSegments
A chord ABAB of a circle of radius 1010 cm subtends an angle of 1.21.2 radians at the centre. Find the length of ABAB, correct to 2 decimal places.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CM-0144 marksL3 ExamCalculatorSegments
A sector OABOAB has radius 1010 cm and angle 0.80.8 radians. Find the area of triangle OABOAB and the area of the segment, each correct to 2 decimal places.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CM3-0023 marksL3 ExamCalculatorSegments
For the same circle (radius 55 cm, ∠AOB=2π3\angle AOB=\dfrac{2\pi}{3}), find the exact perimeter of the minor segment.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CM3-0043 marksL3 ExamCalculatorSegments
A chord of a circle of radius 66 cm subtends π3\dfrac{\pi}{3} at the centre. Find the exact area of the major segment.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CM3-0072 marksL3 ExamCalculatorChords
A chord of length 1212 cm is drawn in a circle of radius 1010 cm. Find the angle it subtends at the centre, in radians, correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CM-0104 marksL4 ChallengingCalculatorSegments
A sector OABOAB has radius 1212 cm and angle 2π3\dfrac{2\pi}{3}. Find the exact area of the segment between the chord ABAB and the arc ABAB.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CM-0114 marksL4 ChallengingCalculatorSegments
For the same sector (r=12r=12 cm, angle 2π3\dfrac{2\pi}{3}), find the exact perimeter of the segment.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CM3-0055 marksL4 ChallengingCalculatorComposite
OABOAB is a sector of radius 55 cm and angle 11 radian. The tangent to the arc at AA meets OBOB extended at TT. Find (a) ATAT and (b) the area of the region bounded by ATAT, BTBT and the arc ABAB, each correct to 2 decimal places.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CM3-0085 marksL5 ExtensionCalculatorComposite
Two circles, each of radius 66 cm, have their centres 66 cm apart. Find the exact area of the region inside both circles.

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Salam Academy Original Practice · Proposed mark scheme