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0580/33 Oct/Nov 2021, Question 4: Multi-Step Angle Reasoning

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 9 marks

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The question, in short

Measure an angle from a diagram, name its type, find y using an isosceles triangle on a straight line, and work with a circle of diameter 12 cm.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (ai) · 1 mark

Measure the size of angle x from the diagram.

  1. 1Measure with a protractor: x = 42°

Answer42 (accept 40 to 44)

Part (aii) · 1 mark

State the mathematical name for this type of angle.

  1. 142° is less than 90°, so it is acute

AnswerAcute

Part (b) · 3 marks

Given DA = DB, angle ADB = 74° and ABC straight, find y, the angle DBC.

  1. 1DA = DB, so angle DBA = (180 − 74) ÷ 2 = 53°
  2. 2y = 180 − 53 = 127 (angles on a straight line)

Answer127

Part (ci) · 1 mark

Give the mathematical name for line FG in the circle.

  1. 1FG joins two points on the circle, so it is a chord

AnswerChord

Part (cii) · 1 mark

Explain why angle EFG equals 90°.

  1. 1EG is a diameter, and the angle in a semicircle = 90°

AnswerAngle in a semicircle = 90°

Part (ciii) · 2 marks

Calculate the area of the circle with EG = 12 cm.

  1. 1Radius = 12 ÷ 2 = 6 cm
  2. 2Area = π × 6² = 113.0… ≈ 113 cm²

Answer113 or 113.0 to 113.1

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Also searched as: 0580/33/O/N/21 · 0580_w21_qp_33 · 0580 w21 33 · question 4.
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