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Olympiad (Class 7) Constructions and Tilings — practice questions

Explore 55 free Constructions and Tilings questions in Olympiad (Class 7) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Constructions and Tilings questions and exercises with answers

Showing questions 1–30 of 55.

A point is equally far from the ends of segment XY. Where must it lie?Read the answer and worked solution →Which two tools alone are used for the constructions here?Read the answer and worked solution →Eight lines through a point make equal angles. What is the angle between neighbours?Read the answer and worked solution →Angle bisection by compass works because two triangles are congruent by which condition?Read the answer and worked solution →Which route gives a 45 degree angle using only ruler and compass?Read the answer and worked solution →Starting from a constructed 90 degree angle, how many successive bisections give 22.5 degrees?Read the answer and worked solution →Which shape, once built, hands you a 60 degree angle with ruler and compass?Read the answer and worked solution →How many congruent equilateral triangles fit around the centre to form a regular hexagon?Read the answer and worked solution →Two 60 degree angles meet at a hexagon corner. What is the hexagon angle?Read the answer and worked solution →Around a point lie angles of 40, 60, 50, 30, 40 and 90 degrees. How big is the remaining gap angle?Read the answer and worked solution →Five equilateral triangles are joined at one vertex without overlap. How large is the gap left around that vertex?Read the answer and worked solution →Around a point there are angles of 90, 120 and 80 degrees. What angle fills the rest of the full turn?Read the answer and worked solution →Five equal angles fill the whole space around a point exactly. How large is each one?Read the answer and worked solution →Each angle of a regular hexagon is 120 degrees. How many hexagons meet at a vertex of a hexagonal tiling?Read the answer and worked solution →Which regular polygon cannot tile a flat plane by itself?Read the answer and worked solution →How many equilateral triangles meet at each point in a tiling of the plane by such triangles?Read the answer and worked solution →What is the name for covering a region with shapes leaving no gaps and no overlaps?Read the answer and worked solution →How many 2 x 1 tiles cover a 4 x 6 grid exactly?Read the answer and worked solution →Why can a 5 x 7 grid never be covered by 2 x 1 tiles?Read the answer and worked solution →Which grid cannot be covered exactly by 2 x 1 tiles?Read the answer and worked solution →A 5 x 3 grid has 8 white and 7 black squares. Removing which square makes it tileable by 2 x 1 tiles?Read the answer and worked solution →A coloured region has 8 white squares and 6 black squares. Can 2 x 1 tiles cover it exactly?Read the answer and worked solution →Two opposite corners are cut from an 8 x 8 chessboard. Can 2 x 1 tiles cover the rest?Read the answer and worked solution →How many pieces make up the tangram puzzle?Read the answer and worked solution →Tangram puzzles originated in which country?Read the answer and worked solution →Which Dutch artist explored tiling by covering a plane with animal shapes?Read the answer and worked solution →What were the construction methods of the Sulba-Sutras used for in the Vedic period?Read the answer and worked solution →A rope on pegs X, Y is pulled tight at its midpoint A. Why is A on the perpendicular bisector?Read the answer and worked solution →To draw a line parallel to m by ruler and compass, which is copied on a transversal?Read the answer and worked solution →When an angle is copied by compass, the new triangle matches the first by which rule?Read the answer and worked solution →

Worked practice questions

A point is equally far from the ends of segment XY. Where must it lie?

  1. On the bisector of angle X
  2. On the perpendicular bisector
  3. On line XY, beyond Y
  4. At the midpoint of XY
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Correct answer: B. On the perpendicular bisector

Every point with equal distance from X and Y lies on the one line that bisects XY at a right angle.

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Which two tools alone are used for the constructions here?

  1. Protractor and ruler
  2. Set square and protractor
  3. Divider and set square
  4. Unmarked ruler and compass
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Correct answer: D. Unmarked ruler and compass

The constructions are carried out with only an unmarked straightedge and a compass, with no angle measuring.

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Eight lines through a point make equal angles. What is the angle between neighbours?

  1. 30 degrees
  2. 60 degrees
  3. 90 degrees
  4. 45 degrees
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Correct answer: D. 45 degrees

A full turn of 360 degrees shared equally among 8 rays gives 360 divided by 8, which is 45 degrees each.

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More Mathematics topics

Data interpretation and analysisRational numbersSimple Linear EquationsPerimeter and areaTriangles and congruence of trianglesIntegersFractions and DecimalsFactors and Multiples