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0580/32 Feb/Mar 2024, Question 1: Quadrilateral Properties

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 9 marks

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The question, in short

Geometry revision covering perpendicular construction, naming symmetric quadrilaterals, grid area, and angle facts in a quadrilateral with an extended side.

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

Part (a) · 1 mark

Construct a line passing through P at right angles to line l.

  1. 1Place a set square along l with its right angle at P
  2. 2Draw a ruled line through P at 90° to l

AnswerRuled line drawn through P, perpendicular to l

Part (b) · 2 marks

Name two distinct quadrilaterals each having two symmetry lines and order-two rotational symmetry.

  1. 1A rectangle has 2 lines of symmetry and rotational symmetry of order 2
  2. 2A rhombus has 2 lines of symmetry and rotational symmetry of order 2

Answerrectangle, rhombus

Part (c) · 1 mark

Determine the area of the quadrilateral shown on the 1 cm² grid.

  1. 1Vertical side = 3 cm, bottom side = 5 cm; the slanted corner is 4 across and 2 up from the bottom-left corner
  2. 2Rectangle 4 × 2 = 8 cm²
  3. 3Top triangle ½ × 4 × 1 = 2 cm²
  4. 4Right-hand triangle ½ × 1 × 2 = 1 cm²
  5. 5Area = 8 + 2 + 1 = 11 cm²

Answer11

Part (di) · 1 mark

State the mathematical term describing an angle measuring 82°.

  1. 182° is less than 90°
  2. 2It is an acute angle

Answeracute

Part (dii) · 2 marks

Calculate x, justifying your result with a geometric reason.

  1. 1x = 180 − 143
  2. 2x = 37
  3. 3Angles on a straight line add to 180°

Answer37, angles on a straight line add to 180

Part (diii) · 2 marks

Calculate y, justifying your result with a geometric reason.

  1. 1y = 360 − 82 − 103 − 143
  2. 2y = 32
  3. 3Angles in a quadrilateral add to 360°

Answer32, angles in a quadrilateral add to 360

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Also searched as: 0580/32/F/M/24 · 0580_m24_qp_32 · 0580 m24 32 · question 1.
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