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0580/32 Feb/Mar 2022, Question 4: Simultaneous Equations by Elimination

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 10 marks

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The question, in short

Circle geometry: name lines OX and YZ, measure OX, find circumference for radius 18 cm, then form and solve simultaneous equations from tangent and angle facts.

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

Part (aia) · 1 mark

Give the mathematical name of line OX, where O is the centre and X on the circle.

  1. 1OX joins the centre to the circle: radius

AnswerRadius

Part (aib) · 1 mark

Give the mathematical name of line YZ, a chord joining two points on the circle.

  1. 1YZ joins two points on the circle: chord

AnswerChord

Part (aii) · 1 mark

Measure the length of line segment OX from the diagram.

  1. 1Measure with a ruler: OX = 3.5 cm

Answer3.5

Part (b) · 2 marks

Calculate the circumference of a circle with radius 18 cm.

  1. 1Circumference = 2 × 18 × π
  2. 2= 113.09… ≈ 113 cm

Answer113 or 113.09… to 113.112

Part (ci) · 2 marks

Complete two simultaneous equations using the tangent angle and angle ABC values shown.

  1. 1Angle XDO = 90° (tangent is perpendicular to the radius): 9x + 3y = 90
  2. 2Angle ABC = 90° (angle in a semicircle): 18x − 4y = 90

Answer9x + 3y = 90; 18x − 4y = 90

Part (cii) · 3 marks

Solve the simultaneous equations 9x + 3y = 90 and 18x − 4y = 90, showing all working.

  1. 1Angle ABC = 90° (angle in a semicircle): 18x − 4y = 90
  2. 2Angle XDO = 90° (tangent ⊥ radius): 9x + 3y = 90
  3. 3Double the second: 18x + 6y = 180, then subtract the first: 10y = 90, so y = 9
  4. 49x + 27 = 90, so 9x = 63 and x = 7
  5. 5x = 7, y = 9

Answerx = 7, y = 9

Stuck on a step? Read the free lesson: Simultaneous Equations by Elimination

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Also searched as: 0580/32/F/M/22 · 0580_m22_qp_32 · 0580 m22 32 · question 4.
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