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0580/32 May/Jun 2022, Question 3: Simultaneous Equations by Elimination

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 11 marks

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The question, in short

Answer questions on angle types and measurement, sketch and name a quadrilateral with equal sides and two symmetry lines, find its missing angles, then form and solve simultaneous equations from triangle and straight-line diagrams.

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

Part (ai) · 1 mark

Give the mathematical name for the angle labelled a in the triangle.

  1. 1Angle a is between 90° and 180°: obtuse

AnswerObtuse

Part (aii) · 1 mark

Measure the size of angle a.

  1. 1Measure with a protractor: a = 113°

Answer113 (accept 111 to 115)

Part (bi) · 1 mark

Sketch a quadrilateral whose sides are all equal and which has exactly two lines of symmetry.

  1. 1Sketch four equal sides with opposite sides parallel and no right angles (a slanted diamond shape)

AnswerSketch of a rhombus

Part (bii) · 1 mark

State the mathematical name of this quadrilateral.

  1. 1All sides equal with only two lines of symmetry: rhombus

AnswerRhombus

Part (biii) · 2 marks

Given one interior angle is 70°, work out the remaining three interior angles.

  1. 1Opposite angles of a rhombus are equal: 70°
  2. 2Other two angles = (360 − 70 − 70) ÷ 2 = 110°
  3. 370°, 110°, 110°

Answer70, 110, 110

Part (ci) · 1 mark

Explain the geometrical reason that the triangle's angles give 2x + 2y = 180.

  1. 1x + x + 2y = 180 because angles in a triangle add to 180°

AnswerAngles in a triangle add to 180

Part (cii) · 1 mark

Using the straight-line diagram, write a second equation linking x and y.

  1. 1Angles on a straight line add to 180°
  2. 2x + 6y = 180

Answerx + 6y = 180

Part (ciii) · 3 marks

Solve the simultaneous equations 2x + 2y = 180 and x + 6y = 180, showing all working.

  1. 12x + 2y = 180 → x + y = 90
  2. 2(x + 6y) − (x + y) = 180 − 90, so 5y = 90, y = 18
  3. 3x = 90 − 18 = 72
  4. 4x = 72, y = 18

Answerx = 72, y = 18

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

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Also searched as: 0580/32/M/J/22 · 0580_s22_qp_32 · 0580 s22 32 · question 3.
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