IGCSE Maths 0580 Geometrical Constructions Past Paper Questions and Worked Solutions

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IGCSE Maths (0580) · Geometry · 4.2

Every geometrical constructions question from 6 Cambridge IGCSE Mathematics (0580) past papers (Oct/Nov 2025 to May/June 2026), syllabus section 4.2. 6 questions covering Core and Extended tiers, ordered from Core to Extended. Each question is labelled with its question paper code (for example 0580/11/M/J/26) and every final answer matches the official Cambridge mark scheme. Try each question first, then click “Show solution” to check your working. This page is part of our IGCSE Maths 0580 Geometry past paper questions.

0580 Geometrical Constructions past paper questions: Core (Papers 1 and 3)

12 marksCore

May/June 2026 · Paper 1 · 0580/11/M/J/26 · Q6

Triangle ABC has sides AC = 7.4 cm and BC = 4.6 cm. Using a ruler and compasses only, construct triangle ABC. Leave in your construction arcs. The side AB has been drawn for you.

0580/11 May/June 2026 Q6 – line AB drawn for the triangle constructionAB
Show solution
  1. Open the compasses to 7.4 cm (the length AC). Put the point on A and draw an arc above AB.
  2. Open the compasses to 4.6 cm (the length BC). Put the point on B and draw an arc that crosses the first arc.
  3. Label the crossing point C.
  4. Join AC and BC with a ruler. Leave both arcs showing because they are your working.
0580/11 May/June 2026 Q6 solution – triangle ABC with arcs of radius 7.4 cm from A and 4.6 cm from BABC
24 marksCore

Feb/Mar 2026 · Paper 1 · 0580/12/F/M/26 · Q6

An isosceles triangle has a side length 4 cm and a side length 6 cm. There are two possible triangles that can be drawn that are not congruent to each other. Construct these two triangles. One 4 cm side has been drawn for each of the triangles.

0580/12 February/March 2026 Q6 – two 4 cm lines drawn for the constructions4 cm4 cm
Show solution
  1. An isosceles triangle has two equal sides. With sides of 4 cm and 6 cm, the third side must equal one of them.
  2. So the two triangles are 4 cm, 4 cm, 6 cm and 4 cm, 6 cm, 6 cm
  3. Triangle 1: from one end of the 4 cm line draw an arc of radius 4 cm. From the other end draw an arc of radius 6 cm.
  4. Join both ends of the line to the point where the arcs cross.
  5. Triangle 2: from both ends of the other 4 cm line draw arcs of radius 6 cm, and join both ends to where they cross.
  6. Leave all the arcs showing.
0580/12 February/March 2026 Q6 solution – the 4-4-6 and 4-6-6 isosceles triangles with construction arcs4 cm6 cm4 cm6 cm6 cm4 cm4 cm, 4 cm, 6 cm4 cm, 6 cm, 6 cm
Answer 4 cm, 4 cm, 6 cm 4 cm, 6 cm, 6 cm
34 marksCore

Feb/Mar 2026 · Paper 3 · 0580/32/F/M/26 · Q7

(a) Measure the length of line AB.

(b) The point P lies on the line AB. Draw a straight line, PQ, that is perpendicular to line AB and 60% longer than line AB.

0580/32 February/March 2026 Q7 – line AB with point P on itABP
Show solution
Part (a)
  1. Put the 0 of the ruler exactly on A and read the scale at B.
  2. AB = 5 cm
Answer 5 cm
Part (b)
  1. 60% longer than 5 cm means 160% of 5 cm: 5 × 1.6 = 8 cm.
  2. Use a set square or protractor at P to make a right angle with AB.
  3. Draw a ruled line 8 cm long from P at 90° to AB
0580/32 February/March 2026 Q7(b) solution – 8 cm line PQ perpendicular to AB8 cmABPQNOT TOSCALE
Answer ruled line 8 cm long from P at 90° to AB
42 marksCore

Oct/Nov 2025 · Paper 1 · 0580/11/O/N/25 · Q5

In triangle ABC, AB = 8 cm and BC = 6.4 cm. Using a ruler and compasses only, construct triangle ABC. Leave in your construction arcs. The line AC has been drawn for you.

0580/11 October/November 2025 Q5 – line AC drawn for the triangle constructionAC
Show solution
  1. Open the compasses to 8 cm (the length AB). Put the point on A and draw an arc.
  2. Open the compasses to 6.4 cm (the length BC). Put the point on C and draw an arc that crosses the first arc.
  3. Label the crossing point B.
  4. Join AB and BC with a ruler and leave both arcs showing.
0580/11 October/November 2025 Q5 solution – triangle ABC with construction arcs8 cm6.4 cmACBNOT TOSCALE

0580 Geometrical Constructions past paper questions: Extended (Papers 2 and 4)

52 marksExtended

May/June 2026 · Paper 4 · 0580/42/M/J/26 · Q3

In triangle ABC, AC = 10 cm and BC = 8.5 cm. Using a ruler and compasses only, construct triangle ABC. The line AB has been drawn for you.

0580/42 May/June 2026 Q3 – line AB drawn for the triangle constructionAB
Show solution
  1. C is 10 cm from A and 8.5 cm from B, so it lies on two circles. Use arcs to find where they cross.
  2. Set the compasses to 10 cm and draw an arc centred on A.
  3. Set the compasses to 8.5 cm and draw an arc centred on B so that it crosses the first arc. Label the crossing point C.
  4. Join AC and BC with a ruler. Leave both arcs showing as your construction lines.
0580/42 May/June 2026 Q3 solution – triangle ABC with construction arcs10 cm8.5 cmABC
63 marksExtended

Oct/Nov 2025 · Paper 4 · 0580/41/O/N/25 · Q5(a,b)

(a) In triangle ABC, AB = 8 cm, AC = 7 cm and BC = 5 cm. Using a ruler and compasses only, construct triangle ABC. The side AB has been drawn for you.

(b) Measure angle ACB.

0580/41 October/November 2025 Q5 – line AB drawn for the triangle constructionAB
Show solution
Part (a)
  1. Open the compasses to 7 cm (this is AC). Put the point on A and draw an arc above AB.
  2. Open the compasses to 5 cm (this is BC). Put the point on B and draw an arc that crosses the first arc.
  3. Label the crossing point C. Join AC and BC with a ruler and leave both arcs showing.
0580/41 October/November 2025 Q5(a) solution – triangle ABC with construction arcs7 cm5 cmABC
Part (b)
  1. Put the centre of the protractor on C, line the zero up along CA and read the angle where CB crosses.
  2. Angle ACB = about 82°
Note: This is a measured answer. Any value from 80° to 85° is accepted.
Answer about 82°

Question papers used on this page

All geometrical constructions questions above, listed by 0580 question paper code.

QP codeFile namePaperQuestions
0580/11/M/J/260580_s26_qp_11May/June 2026 · Paper 1 (Core)Q6
0580/42/M/J/260580_s26_qp_42May/June 2026 · Paper 4 (Extended)Q3
0580/12/F/M/260580_m26_qp_12Feb/Mar 2026 · Paper 1 (Core)Q6
0580/32/F/M/260580_m26_qp_32Feb/Mar 2026 · Paper 3 (Core)Q7
0580/11/O/N/250580_w25_qp_11Oct/Nov 2025 · Paper 1 (Core)Q5
0580/41/O/N/250580_w25_qp_41Oct/Nov 2025 · Paper 4 (Extended)Q5(a,b)

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