Symmetry — Paper 1 · IGCSE Mathematics 0580

12 Write down the order of rotational symmetry of each of the following shapes. (a) Equilateral Triangle Answer(a) [1] (b) Rhombus Answer(b) [1]

2 marks

Mark scheme: 12 (a) 3 1 Ignore any added words (b) 2 1

This question in 0580/11 Oct/Nov 2004

12 (a) Draw all the lines of symmetry on the following shapes. (Shape B is a regular polygon.) Shape A Shape B [2] (b) Write down the order of rotational symmetry of shape A. Answer(b) [1]

3 marks

Mark scheme: 12 (a) A-2 correct lines and B-6 correct lines 1, 1 Allow not ruled and small inaccuracies. (b) 2 1

This question in 0580/11 May/June 2006

20 (a) Draw the lines of symmetry on the two letters below. [2] (b) Write down the order of rotational symmetry for each of the figures below. Order Order [2]

4 marks

Mark scheme: 20 (a) 2 correct lines on H 1 Ruled not essential in either. Judge by eye. 1 correct line on W 1 No extraneous lines on either. (b) 1 1 Allow 0 or indication of no rotational symmetry. 2 1

This question in 0580/11 Oct/Nov 2006

8 (a) For Examiner's Use Draw all the lines of symmetry on the shape above. [1] (b) A quadrilateral has rotational symmetry of order 2 and no lines of symmetry. Write down the geometrical name of this shape. Answer(b) [1]

2 marks

Mark scheme: 8 1 Lines must be a minimum of length and height (a) Two correct lines of of the figure. symmetry, No extra lines (b) Parallelogram 1

This question in 0580/11 Oct/Nov 2007

2 Write down the order of rotational symmetry of the diagram above. Answer [1]

1 marks

Mark scheme: 2 2 1

This question in 0580/11 Oct/Nov 2008

18 The plan of a rectangular garden with 4 triangular flowerbeds is shown in the diagram. For Examiner's Use (a) Write down the name of the special triangles that are (i) shaded, Answer(a)(i) [1] (ii) unshaded. Answer(a)(ii) [1] (b) State the order of rotational symmetry of the plan. Answer(b) [1] (c) Draw the lines of symmetry on the plan. [2]

5 marks

Mark scheme: 18 (a) (i) Isosceles 1 (ii) Equilateral 1 (b) 2 or two 1 Allow order (=) 2 (c) Correct horizontal and vertical ruled 1, 1 SC1 Both freehand and ‘correct’ accuracy lines. By eye and to or beyond the by eye to or beyond edge of the plan or edges of the plan. both short of the full figure. −1 for each additional line.

This question in 0580/11 May/June 2009

16 Complete the information about each shape. Examiner's Use Shape Number of lines of symmetry Order of rotational symmetry [4]

4 marks

Mark scheme: 16 lines of symmetry 1 0 1, 1 order rotational 1 4 1, 1

This question in 0580/11 May/June 2010

10 (a) Examiner's Use Write down the order of rotational symmetry of the shape above. Answer(a) [1] (b) A M N O T X From the list, write down the letters which have only one line of symmetry. Answer(b) [2]

3 marks

Mark scheme: 10 (a) 2 1 (b) A M T 2 W1 for 4 letters listed, 3 of them correct or W1 for 2 and only 2 correct 2 1

This question in 0580/13 May/June 2010

11 (a) The diagram shows a rhombus. Draw all the lines of symmetry. [2] (b) Shade two squares in the diagram above so that the figure has one line of symmetry and no rotational symmetry. [1]

3 marks

Mark scheme: 11 (a) 2 lines joining opposite vertices 1, 1 Independent Accept reasonable freehand (b) Centre square and any other 1 Any of these diagrams: or 2 adjacent corner squares or 2 centre squares on adjacent edges May be rotated through 90, 180, 270 degrees IGCSE – October/November 2010 0580 11

This question in 0580/11 Oct/Nov 2010

3 For the diagram, write down (a) the number of lines of symmetry, Answer(a) [1] (b) the order of rotational symmetry. Answer(b) [1]

2 marks

Mark scheme: 3 (a) 2 1 (b) 2 1

This question in 0580/13 Oct/Nov 2010

3 For an equilateral triangle, write down (a) the number of lines of symmetry, Answer(a) [1] (b) the order of rotational symmetry. Answer(b) [1]

2 marks

Mark scheme: 3 (a) 3 1cao (b) 3 1

This question in 0580/11 May/June 2011

7 For Examiner's Use For the diagram, write down (a) the number of lines of symmetry, Answer(a) [1] (b) the order of rotational symmetry. Answer(b) [1]

2 marks

Mark scheme: 7 (a) 0 1 (b) 2 1

This question in 0580/13 May/June 2011

10 (a) Write down the mathematical name of a quadrilateral that has exactly two lines of symmetry. Answer(a) [1] (b) Write down the mathematical name of a triangle with exactly one line of symmetry. Answer(b) [1] (c) Write down the order of rotational symmetry of a regular pentagon. Answer(c) [1]

3 marks

Mark scheme: 10 (a) Rectangle or rhombus 1 Either one or both given (b) Isosceles (triangle) 1 (c) 5 cao 1 IGCSE – October/November 2011 0580 11 11k

This question in 0580/11 Oct/Nov 2011

2 The lengths of each side of this triangle are the same. (a) Write down the mathematical name for this triangle. Answer(a) [1] (b) Write down the number of lines of symmetry for the triangle. Answer(b) [1]

2 marks

Mark scheme: 2 (a) Equilateral 1 (b) 3 1

This question in 0580/11 May/June 2012

1 Shade two more squares so that this pattern has rotational symmetry of order 2. For Examiner's Use [1]

1 marks

Mark scheme: Qu. Answers Mark Part Marks 1 1 cao

This question in 0580/11 Oct/Nov 2012

5 (a) Write down the order of rotational symmetry of this shape. Answer(a) … [1] (b) Draw the lines of symmetry on this shape. [1] _____________________________________________________________________________________

2 marks

Mark scheme: 5 (a) 2 1 (b) Both lines drawn 1

This question in 0580/11 Oct/Nov 2013

9 (a) Add one line to the diagram so that it has two lines of symmetry. For Examiner′s Use [1] (b) Add two lines to the diagram so that it has rotational symmetry of order 2. [1] _____________________________________________________________________________________

2 marks

Mark scheme: 9 (a) 1 (b) or or 1 Many other answers 2 2

This question in 0580/12 Oct/Nov 2013

20 For Examiner′s Use A (a) Construct the locus of all the points which are 3 cm from vertex A and outside the rectangle. [2] (b) Construct, using a straight edge and compasses only, one of the lines of symmetry of the rectangle. [2] _____________________________________________________________________________________

4 marks

Mark scheme: 20 (a) Circle, radius 3 cm, centre A, not inside the 2 M1 for arc or full circle centre rectangle A radius 3 cm or for an incorrect size circle at A outside rectangle (b) One line of symmetry with correct arcs E.g. 2 B1 for correct ruled line (must reach or cross two sides) B1 for 2 pairs of correct intersecting arcs IGCSE – October/November 2013 0580 13

This question in 0580/13 Oct/Nov 2013

21 The diagram shows a circle inside a square. The circumference of the circle touches all four sides of the square. (a) Calculate the area of the circle when the side of the square is 15 cm. Answer(a) … cm2 [2] (b) Draw all the lines of symmetry on the diagram. [2] __________________________________________________________________________________________ Question 22 is printed on the next page.

4 marks

Mark scheme: 21 (a) 177 or 176.7 to 176.74 2 M1 for π × 7.52 (b) 4 correct lines of symmetry drawn 2 B1 for 2 correct and no extra lines 27

This question in 0580/11 May/June 2014

3 Write down the letters in the word above that have (a) exactly one line of symmetry, Answer(a) … [1] (b) rotational symmetry of order 2. Answer(b) … [1] __________________________________________________________________________________________

2 marks

Mark scheme: 3 (a) E B A cao 1 (b) Z cao 1

This question in 0580/11 Oct/Nov 2014

3 Write down the order of rotational symmetry of this shape. Answer … [1] __________________________________________________________________________________________

1 marks

Mark scheme: 3 8 1

This question in 0580/12 Oct/Nov 2014

2 Write down the order of rotational symmetry of this shape. Answer … [1] __________________________________________________________________________________________

1 marks

Mark scheme: 2 8 1

This question in 0580/12 Feb/March 2015

7 equilateral triangle square regular pentagon parallelogram regular hexagon circle From the list write down (a) the shape which has more than 6 lines of symmetry, Answer(a) … [1] (b) the shape which has both acute and obtuse interior angles. Answer(b) … [1] __________________________________________________________________________________________

2 marks

Mark scheme: 7 (a) circle 1 (b) parallelogram 1

This question in 0580/11 May/June 2015

12 (a) On the shape, draw the lines of symmetry. [2] (b) Write down the order of rotational symmetry of the shape. Answer(b) … [1] __________________________________________________________________________________________

3 marks

Mark scheme: 12 (a) correct horizontal and vertical lines only 2 B1 for one line only correct and no extras (b) 2 1

This question in 0580/13 May/June 2015

2 Parallelogram Trapezium Rhombus Write down which one of these shapes has • rotational symmetry of order 2 and • no line symmetry. Answer … [1] __________________________________________________________________________________________

1 marks

Mark scheme: 2 Parallelogram 1

This question in 0580/12 Oct/Nov 2015

3 Write down the order of rotational symmetry of this shape. Answer … [1] __________________________________________________________________________________________

1 marks

Mark scheme: 3 3 1

This question in 0580/13 Oct/Nov 2015

9 (a) Write down the order of rotational symmetry of the shape. … [1] (b) Draw all the lines of symmetry on the shape. [1]

2 marks

Mark scheme: 9 (a) 3 1 (b) All three correct lines 1 of symmetry drawn

This question in 0580/11 May/June 2016

4 A quadrilateral has rotational symmetry of order 2 and no lines of symmetry. Write down the mathematical name of this quadrilateral. … [1]

1 marks

Mark scheme: 4 Parallelogram 1

This question in 0580/12 May/June 2016

21 (a) The diagram shows an equilateral triangle. On the diagram, draw all the lines of symmetry. [2] (b) (i) In the space below, draw a quadrilateral that has 2 lines of symmetry and rotational symmetry of order 2. [1] (ii) Write down the mathematical name of your quadrilateral. … [1]

4 marks

Mark scheme: 21 (a) Three correct, ruled lines 2 B1 for two correct lines (b) (i) Drawing a rectangle or rhombus 1 (ii) FT their quadrilateral in (b)(i) 1

This question in 0580/13 Oct/Nov 2016

2 Shade two more squares so that this shape has rotational symmetry of order 2. [1]

1 marks

Mark scheme: 2 2 squares added correctly 1

This question in 0580/12 Feb/March 2017

9 The shape above is a rhombus. Draw all the lines of symmetry on the shape. [2]

2 marks

Mark scheme: 9 Two correct lines only 2 B1 for one correct line only

This question in 0580/12 May/June 2017

3 A quadrilateral has one line of symmetry and no rotational symmetry. Write down the name of this quadrilateral. … [1]

1 marks

Mark scheme: 3 Kite 1

This question in 0580/13 Oct/Nov 2017

8 For this diagram, write down (a) the number of lines of symmetry, … [1] (b) the order of rotational symmetry. … [1]

2 marks

Mark scheme: 8(a) 4 1 8(b) 4 1

This question in 0580/12 May/June 2018

7 (a) Draw the line of symmetry on the shape below. [1] (b) Shade one more square so that this pattern has rotational symmetry of order 2. [1]

2 marks

Mark scheme: 7(a) 1 7(b) 1

This question in 0580/11 Oct/Nov 2018

7 On the shape, draw all the lines of symmetry. [2]

2 marks

Mark scheme: 7 Both lines of symmetry only drawn 2 B1 each correct line Penalise 1 for each incorrect line

This question in 0580/13 Oct/Nov 2018

19 (a) On each shape, draw all the lines of symmetry. (i) [1] (ii) [2] (b) Write down the name of a quadrilateral that has • rotational symmetry of order 2 and • exactly two lines of symmetry. … [1]

4 marks

Mark scheme: 19(a)(i) 2 correct lines of symmetry only 1 19(a)(ii) 4 correct lines of symmetry only 2 B1 for only 2 or 3 correct lines of symmetry 19(b) Rectangle or rhombus 1

This question in 0580/11 May/June 2019

7 (a) Shade five-eighths of this rectangle. [1] (b) Shade two more squares so that this grid has rotational symmetry of order 4. [1]

2 marks

Mark scheme: 7(a) Any 15 blocks shaded 1 7(b) 2 correct squares shaded 1

This question in 0580/12 May/June 2019

2 Write down the order of rotational symmetry of this regular pentagon. … [1]

1 marks

Mark scheme: 2 5 1

This question in 0580/11 Oct/Nov 2019

14 (a) Shade two more small squares to give a pattern with exactly one line of symmetry. [1] (b) Complete the description of this pattern. The pattern has … lines of symmetry and order of rotational symmetry … [2]

3 marks

Mark scheme: 14(a) • 1 • or • • 14(b) 2 2 B1 for each 2

This question in 0580/12 Oct/Nov 2019

4 (a) On each shape draw all the lines of symmetry. [3] (b) Write down the order of rotational symmetry of this shape. … [1]

4 marks

Mark scheme: 4(a) Three correct lines B2 B1 for one or more correct lines and no wrong lines One correct line B1 4(b) 2 1

This question in 0580/11 May/June 2020

9 Write down the order of rotational symmetry of the diagram. … [1]

1 marks

Mark scheme: 9 2 1

This question in 0580/12 May/June 2020

7 (a) Write down the mathematical name of a quadrilateral that has • rotational symmetry of order 1 and • only one line of symmetry. … [1] (b) Reflect the shape in line L. L [2]

3 marks

Mark scheme: 7(a) Kite or isosceles trapezium 1 7(b) Correct shape drawn 2 M1 for 3 sides correctly reflected or 4 correct vertices

This question in 0580/13 May/June 2020

5 (a) The diagram shows a rhombus. On the diagram, draw all the lines of symmetry. [2] (b) Shade two squares so that the diagram has rotational symmetry of order 2. [1]

3 marks

Mark scheme: 5(a) Two diagonal lines only 2 B1 for one correct line with one incorrect or missing line or for two correct lines with maximum one incorrect line 5(b) 1

This question in 0580/11 Oct/Nov 2020

3 Write down the order of rotational symmetry of this regular octagon. … [1]

1 marks

Mark scheme: 3 8 cao 1

This question in 0580/12 Oct/Nov 2020

4 Write down the order of rotational symmetry of each shape. … … [2]

2 marks

Mark scheme: 4 4 2 2 B1 for each

This question in 0580/13 Oct/Nov 2020

1 (a) Complete this statement. The diagram has rotational symmetry of order … [1] (b) On the diagram, draw all the lines of symmetry. [2]

3 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 2 1 1(b) 2 correct lines 2 B1 for each

This question in 0580/12 Feb/March 2021

3 (a) Write down the order of rotational symmetry of this diagram. … [1] (b) On the diagram, draw all the lines of symmetry. [2]

3 marks

Mark scheme: 3(a) 4 1 3(b) 2 B1 for 2 or 3 correct lines drawn or for 4 correct lines and one wrong extra line

This question in 0580/11 May/June 2021

1 Draw the line of symmetry on this shape. [1]

1 marks

Mark scheme: Question Answer Marks Partial Marks 1 1 correct line of symmetry 1

This question in 0580/12 May/June 2021

3 Write down the order of rotational symmetry of this shape. … [1]

1 marks

Mark scheme: 3 2 1

This question in 0580/11 Oct/Nov 2021

6 (a) Write down the order of rotational symmetry of a rectangle. … [1] (b) Draw all the lines of symmetry on this equilateral triangle. [2]

3 marks

Mark scheme: 6(a) 2 1 6(b) Three correct lines only 2 B1 for 1 or 2 correct lines and no incorrect lines If zero scored, SC1 for 3 correct lines and 1 additional incorrect line

This question in 0580/12 Oct/Nov 2021

5 Draw all the lines of symmetry on this shape. [2]

2 marks

Mark scheme: 5 Two correct lines and no extras 2 B1 for one line and no extra or two correct lines and one extra

This question in 0580/12 Oct/Nov 2022

4 The diagram shows a shape with four sides of equal length. (a) Write down the mathematical name of this shape. … [1] (b) Write down the order of rotational symmetry of this shape. … [1]

2 marks

Mark scheme: 4(a) Rhombus 1 4(b) 2 1

This question in 0580/13 Oct/Nov 2022

4 Write down the mathematical name of a 4-sided shape that has rotational symmetry of order 2 and no lines of symmetry. … [1]

1 marks

Mark scheme: 4 Parallelogram 1

This question in 0580/11 May/June 2023

3 Shade two squares so that the diagram has rotational symmetry of order 4. [2]

2 marks

Mark scheme: 3 2 B1 for one correct square and a maximum of one incorrect square

This question in 0580/12 May/June 2023

5 (a) Complete the statement. The diagram has rotational symmetry of order … . [1] (b) On the diagram, draw all the lines of symmetry. [2]

3 marks

Mark scheme: 5(a) 2 1 5(b) 2 B1 for one correct line and no extras or two correct lines and one extra

This question in 0580/13 May/June 2023

3 Draw the lines of symmetry on this rhombus. [2]

2 marks

Mark scheme: 3 2 correct lines of symmetry 2 B1 for 1 correct line and no incorrect lines or 2 correct lines and 1 incorrect line

This question in 0580/13 Oct/Nov 2023

4 Write down the order of rotational symmetry of a rhombus. … [1]

1 marks

Mark scheme: 4 2 1

This question in 0580/11 May/June 2024

8 Draw all the lines of symmetry on this shape. [2]

2 marks

Mark scheme: 8 2 correct lines of symmetry 2 B1 for one correct line and no extras or two correct lines and one extra

This question in 0580/11 May/June 2024

5 (a) Draw all the lines of symmetry on this quadrilateral. [2] (b) Write down the mathematical name of a quadrilateral that has rotational symmetry of order 2. … [1]

3 marks

Mark scheme: 5(a) 4 correct lines of symmetry 2 B1 for two or three correct lines drawn and none incorrect or 4 correct and one additional line. 5(b) Rectangle or rhombus or parallelogram 1

This question in 0580/12 May/June 2024

5 (a) On the diagram, draw any lines of symmetry. [1] (b) Write down the order of rotational symmetry of this shape. … [1]

2 marks

Mark scheme: 5(a) Correct line of symmetry 1 5(b) 3 1

This question in 0580/13 May/June 2024

12 The grid shows half of a shape which has a line of symmetry, L. Complete the shape. L [2]

2 marks

Mark scheme: 12 2 B1 for 1 line correct

This question in 0580/11 Oct/Nov 2024

4 The diagram shows a regular polygon. (a) Write down the mathematical name for this polygon. … [1] (b) On the diagram, draw all the lines of symmetry. [2] (c) Write down the order of rotational symmetry. … [1]

4 marks

Mark scheme: 4(a) Pentagon 1 4(b) all 5 lines of symmetry drawn 2 B1 for 3 lines of symmetry and no extras or all 5 lines and 1 extra line 4(c) 5 1

This question in 0580/12 Oct/Nov 2024

5 (a) On the diagram, draw all the lines of symmetry. [2] (b) Shade one square so that the diagram has rotational symmetry of order 2. [1]

3 marks

Mark scheme: 5(a) 2 correct lines of symmetry drawn 2 B1 for one line correct and no extras or for 2 lines correct and one extra 5(b) 1 square correctly shaded 1

This question in 0580/12 Feb/March 2025

6 Shade one square so that the diagram has rotational symmetry of order 4. [1]

1 marks

Mark scheme: 6 1

This question in 0580/11 Oct/Nov 2025

5 The diagram is made from equilateral triangles. (a) On the diagram, draw all the lines of symmetry. [2] (b) Write down the order of rotational symmetry. … [1]

3 marks

Mark scheme: 5(a) 3 correct lines 2 B1 for two correct lines and no extras or 3 correct lines and one extra 5(b) 3 1

This question in 0580/12 Oct/Nov 2025