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Cambridge IGCSE Mathematics practice

exam practice - Perform calculations related to the circumference and area of a circle, where answers may be expressed in terms of π. Additionally, calculate the arc length and sector area as fractions of the circle's circumference and area, including both minor and major sectors. - Circles, arcs and sectors

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2

Paper

5

Marks

Topic

Circles, arcs and sectors

Exam-style question

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Paper 2Core or Extended Mathematics5 marks

Calculations involving major and minor sectors and arcs of a circle.

Description

Circle with radius 10 cm and minor sector angle 120°

A circle has radius 10 cm. A minor sector has a central angle of 120°. Calculate the length of the major arc and the area of the major sector. Express your answers in terms of π.

QuantityFormulaCalculationAnswer
Major arc length((360 - θ)/360) × 2πr(240/360) × 2 × π × 10(2/3) × 20π = 40π/3 cm
Major sector area((360 - θ)/360) × πr²(240/360) × π × 10²(2/3) × 100π = 200π/3 cm²
  1. a

    Calculate the length of the major arc in terms of π.

    Aim for approximately 3 distinct marking points.

    [3]
  2. b

    Calculate the area of the major sector in terms of π.

    Aim for approximately 2 distinct marking points.

    [2]

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Maths method check

  • Topic focus: Circles, arcs and sectors.
  • Question style: structured_mathematics.
  • Reasoning demand: reasoning.
  • Check the operation, notation, units, and final answer form against the question before moving on.

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Paper 2 structured question: Circles, arcs and sectors

Paper 2Core or Extended Mathematics6 marks

Diagram Description

Circle with radius 7 cm and central angle 60°

A circle has radius 7 cm. A sector of the circle has a central angle of 60°. Calculate the circumference, area, arc length of the sector, and the area of the sector. Express all answers in terms of π where appropriate.

QuantityFormulaCalculationAnswer
Circumference2πr2 × π × 714π cm
Areaπr²π × 7²49π cm²
Arc length(θ/360) × 2πr(60/360) × 2 × π × 7(1/6) × 14π = 14π/6 = 7π/3 cm
Sector area(θ/360) × πr²(60/360) × π × 7²(1/6) × 49π = 49π/6 cm²
  1. a

    Calculate the circumference of the circle in terms of π.

    Aim for approximately 1 distinct marking point.

    [1]
  2. b

    Calculate the area of the circle in terms of π.

    Aim for approximately 1 distinct marking point.

    [1]
  3. c

    Calculate the length of the arc corresponding to the 60° sector, in terms of π.

    Aim for approximately 2 distinct marking points.

    [2]
  4. d

    Calculate the area of the sector with central angle 60°, in terms of π.

    Aim for approximately 2 distinct marking points.

    [2]