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Junior Cycle · Junior Cycle Maths

Junior Cycle Maths: Constructions

How often Constructions comes up on the Maths papers, every year it was asked, and questions to try.

HL Asked on 3 of the last 5 Higher Level papers, most recently in 2026. most years

OL Asked on 2 of the last 5 Ordinary Level papers, most recently in 2024.

Constructions, Higher Level(7 marks)

Quick ones on Constructions.

(a)Every point on the perpendicular bisector of [AB] is…
  1. on the line through A and B
  2. equally far from A and B
  3. closer to A than to B
(b)A point P is the same distance from both arms of angle ABC. P lies on…
  1. the line through A and C
  2. the perpendicular bisector of [AB]
  3. the bisector of angle ABC
(c)Constructing a triangle from SAS data means you are given…
  1. two sides and the angle between them
  2. all three sides
  3. two angles and the side between them
Show the answers

(a) equally far from A and B

(b) the bisector of angle ABC

(c) two sides and the angle between them

Your turn: Higher Level questions on Constructions.

Higher Level

Asked on 3 of the last 5 Higher Level papers, most recently in 2026. most years

Every paper, year by year

YearWhere it came up
2026Q12
2025Q6
2024Not asked
2023Q12
2022Not asked

Links open the State Examinations Commission’s paper for that year.

More Constructions questions

Constructions, 3 marks

Dividing [AB] into 5 equal parts without measuring it relies on which fact?

  1. Angles in a semicircle are 90°
  2. Base angles of an isosceles triangle are equal
  3. Parallel lines cut off equal segments
Show the answer

Parallel lines cut off equal segments

Mark 5 equal steps along a ray from A, join the last mark to B, then draw parallels through the other marks. Equal steps on the ray give equal parts on [AB] (theorem 11).

Ordinary Level

Asked on 2 of the last 5 Ordinary Level papers, most recently in 2024.

Every paper, year by year

YearWhere it came up
2026Not asked
2025Not asked
2024Q6
2023Not asked
2022Q11

Links open the State Examinations Commission’s paper for that year.

More Constructions questions

Constructions, 2 marks

The standard construction to bisect an angle uses only which instruments?

  1. Protractor and set square
  2. Protractor only
  3. Compass and straight edge
Show the answer

Compass and straight edge

Bisecting an angle, like the perpendicular bisector, uses only a compass and a straight edge. Leave your construction arcs showing.

Constructions, 2 marks

Where does the perpendicular bisector of [AB] cross [AB]?

  1. One third of the way along
  2. At the midpoint of [AB]
  3. At the point A
Show the answer

At the midpoint of [AB]

Bisect means cut into two equal halves, and perpendicular means at 90°. So the line crosses [AB] at right angles at its midpoint.

Constructions, 2 marks

Constructing a triangle from three side lengths (SSS): after drawing one side, what do you use?

  1. A compass, to draw arcs
  2. A protractor, to measure angles
  3. A set square, for a right angle
Show the answer

A compass, to draw arcs

Set the compass to each of the other two lengths and draw an arc from each end of the first side. The arcs cross at the third corner.

Other Maths topics

All of Junior Cycle Maths