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Symmetry and Tessellations — Free MYP3 Mathematics Practice Questions
1QuestionTessellating Shapes and PatternsConcept Practice
2 marks~3 minCriterion B
The four regular polygons shown are an equilateral triangle, a square, a regular pentagon, and a regular hexagon.
a
Calculate the interior angle of each polygon using the formula , where is the number of sides. [1]
b
Explain which of the four polygons can tessellate a plane, justifying your answer using the angles found in part (a). [1]
Solutions
2QuestionExploring Regular and Irregular TessellationsAssessment Practice
6 marks~9 minCriterion C
A shape is formed by taking a regular hexagon with side length 2 cm and removing one corner equilateral triangle of side length 1 cm.
a
Calculate the interior angle at the concave (indented) vertex of the new shape. [2]
b
Explain why the angles at the concave vertex cannot combine with angles from other copies of the shape to sum to . [2]
c
Justify whether this shape can tessellate the plane. [2]
Solutions
3QuestionCreating Symmetrical DesignsConcept Practice
2 marks~3 minCriterion A
A regular hexagon is shown in the diagram with one line of symmetry indicated by a dashed line.
a
State the total number of lines of symmetry of a regular hexagon. [1]
b
Explain how you know that a regular hexagon has two distinct types of lines of symmetry. [1]
Solutions
4QuestionCreating Symmetrical DesignsAssessment Practice
6 marks~9 minCriterion D
A graphic designer proposes a logo for a wind turbine company using -fold rotational symmetry, where the design repeats every . The manufacturer states it can only reproduce designs with a maximum of -fold rotational symmetry, where the design repeats every .
a
Describe what -fold rotational symmetry means for the appearance of the logo. [1]
b
Explain how the manufacturing limitation affects both the logo's appearance and the production process. [3]
c
The designer proposes switching to -fold rotational symmetry ( rotation) as a compromise. Analyse whether this compromise is suitable for the wind turbine company, identifying one advantage and one limitation. [2]
Solutions
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