Symmetry

Revise Symmetry for Mathematics A 4MA1 (O Level) — revision notes, 32 practice questions and instant AI marking.

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Pearson Edexcel International GCSE Mathematics A (4MA1)

Symmetry

The big idea: A line of symmetry folds a shape onto itself; rotational symmetry turns it onto itself. Count both separately, and remember that every shape fits onto itself at least once in a full turn.

Summary — What This Chapter Covers

A line of symmetry (mirror line) divides a shape into two halves that are mirror images.
The order of rotational symmetry is the number of times a shape looks the same in one full turn.
A shape with no rotational symmetry has order 1.
A regular polygon with n sides has n lines of symmetry and rotational symmetry of order n.

1. Line and Rotational Symmetry

Foundation & Higher

Counting both

To find lines of symmetry, imagine folding along a line: both halves must match exactly. Tracing paper helps in the exam. To find the order of rotational symmetry, trace the shape and turn it about its centre, counting how many positions match in 360°.

Shape	Lines of symmetry	Order of rotational symmetry
Square	4	4
Rectangle	2	2
Rhombus	2 (the diagonals)	2
Parallelogram	0	2
Kite	1	1
Isosceles trapezium	1	1
Equilateral triangle	3	3
Isosceles triangle	1	1
Regular hexagon	6	6

Worked Example

Name a quadrilateral with no lines of symmetry and order of rotational symmetry of 2.

Practice Question 1

A regular pentagon is drawn. Write down (a) the number of lines of symmetry, (b) the order of rotational symmetry.

Order 1, not 0

Every shape matches itself after a full 360° turn, so the lowest possible order of rotational symmetry is 1. Writing 0 loses the mark.

Memorise

Line symmetry

Fold so the halves match exactly.

Rotational order

Regular n-gon

Parallelogram

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Past papers that test Symmetry

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4MA1 Jun 2026 · Paper 2F · Variant R Edexcel · mark scheme Open → 4MA1 Nov 2025 · Paper 2F Edexcel · mark scheme Open → 4MA1 Jun 2025 · Paper 2F · Variant R Edexcel · mark scheme Open → 4MA1 Jun 2024 · Paper 1F · Variant R Edexcel · mark scheme Open → 4MA1 Nov 2023 · Paper 1F Edexcel · mark scheme Open → 4MA1 Jun 2023 · Paper 2F · Variant R Edexcel · mark scheme Open →

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Symmetry

Symmetry

Counting both

Line symmetry

Rotational order

Regular n-gon

Parallelogram

Past papers that test Symmetry

More Mathematics A topics