Geometrical terms — Paper 1 · IGCSE Mathematics 0580

22 NOT TO SCALE A O B The diagram shows half of a circle, centre O. (a) What is the special name of the line AB? Answer(a) [1] (b) AB = 12 cm. (i) Calculate the perimeter of the shape. Answer(b)(i) cm [2] (ii) Calculate the area of the shape. Answer(b)(ii) cm2 [2]

5 marks

Mark scheme: 22 (a) diameter 1 (b)(i) rounds to 30.8 or 30.9 2 M1 for 0.5 x π x 12 or 12 + π x 12 (implied by rounding to18.8 or (ii) rounds to 56.5 or 56.6 2 18.9 or 49.7 seen) M1 for using π x 62 (implied by 113 (. ) seen

This question in 0580/11 Oct/Nov 2004

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

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

20 For D C Examiner's Use 32° 67° NOT TO SCALE w° p° t° A B M The diagram shows a quadrilateral ABCD with DC parallel to AB. (a) Write down the geometrical name for a quadrilateral with only one pair of parallel sides. Answer(a) [1] (b) ABM is a straight line and DC = AC. Angle DCA = 32° and angle ACB = 67°. Find the values of p, t and w, giving a reason for each answer. Answer (b) p = because [2] t = because [2] w = because [2]

7 marks

Mark scheme: 20 (a) Trapezium 1 (b) p = 32°, alternate 1, 1 Accept Z angles t = 99°, exterior angle (of) triangle 1ft, 1 ft if t = p + 67 Accept angle of triangles and angles on straight line w = 74°, (base angle) isosceles triangle 1 , 1 Accept 12 (180 − 32 ) with isosceles

This question in 0580/11 Oct/Nov 2010

4 A B Write down the geometrical name for (a) shape A, Answer(a) [1] (b) shape B. Answer(b) [1]

2 marks

Mark scheme: 4 (a) Trapezium 1 Do not allow Trapezoid (b) Parallelogram 1 600

This question in 0580/11 May/June 2011

17 (a) What type of angle is shown by the arc on the diagram? Answer(a) [1] (b) ABCD is a quadrilateral. • AB is parallel to DC. • BC is longer than AD. (i) Draw a possible quadrilateral ABCD. Answer(b)(i) [1] (ii) Write down the geometrical name for the quadrilateral ABCD. Answer(b)(ii) [1]

3 marks

Mark scheme: 17 (a) Reflex 1 (b) (i) Drawing of a trapezium 1 Ignore labels and no arrows as long as a reasonable sketch. (ii) Trapezium 1 2

This question in 0580/13 May/June 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

7 (a) A quadrilateral has four sides of equal length and two pairs of equal angles. For Examiner's Write down the mathematical name for this quadrilateral. Use Answer(a) [1] (b) 92° NOT TO SCALE 74° 63° Three of the angles in a quadrilateral are 63°, 74° and 92°. Work out the size of the fourth angle. Answer(b) [1]

2 marks

Mark scheme: 7 (a) Rhombus 1 (b) 131° 1 2 7

This question in 0580/11 May/June 2012

11 For E Examiner's D F Use b° 52° NOT TO SCALE a° A C B In the diagram lines AC and DF are parallel and AE = EB. Angle AEB = 52°. (a) Write down the mathematical name for triangle AEB. Answer(a) [1] (b) Work out the value of a. Answer(b) a = [1] (c) Explain why a = b. Answer(c) [1]

3 marks

Mark scheme: 11 (a) isosceles 1 (b) 64 1 (c) alternate (angle) 1 accept z angle IGCSE – May/June 2012 0580 13

This question in 0580/13 May/June 2012

13 Complete each statement with the correct mathematical term. For Examiner's Use (a) This solid is a … [1] (b) This polygon is a regular … [1] (c) A B C Angle ABC is an … angle [1] _____________________________________________________________________________________

3 marks

Mark scheme: 13 (a) cuboid 1 condone [rectangular] prism (b) pentagon 1 (c) obtuse 1

This question in 0580/11 May/June 2013

17 For Examiner′s F Use NOT TO SCALE C D E 6 cm A 4 cm B The diagram shows a triangular prism. Triangle ABC is equilateral. AB = 4 cm and BE = 6 cm. (a) Write down the size of angle ABC. Answer(a) Angle ABC = … [1] (b) On the 1 cm2 grid, draw an accurate net of the prism. The line BE has been drawn for you. B E [3] _____________________________________________________________________________________

4 marks

Mark scheme: 17 (a) 60 1 (b) Correct net 3 B1 for 3 rectangles and a triangle to the right and left of rectangles. B1 for 3 accurate (6 by 4) rectangles joined. B1 for 2 equilateral triangles joined in correct positions

This question in 0580/13 May/June 2013

19 similar acute line perpendicular radius refl ex obtuse parallel congruent isosceles Choose the correct word from this box to complete each of these statements. (a) A Angle A is … [1] (b) B Angle B is … [1] (c) These lines are … [1] (d) These lines are … [1] __________________________________________________________________________________________

4 marks

Mark scheme: 19 (a) acute 1 (b) reflex 1 (c) parallel 1 (d) perpendicular 1 3

This question in 0580/12 May/June 2014

22 This is an accurate drawing of quadrilateral ABCD. D C A B (a) Write down the mathematical name for quadrilateral ABCD. Answer(a) … [1] (b) Measure the size of the acute angle. Answer(b) … [1] (c) By taking suitable measurements from the diagram, work out the area of ABCD. Answer(c) … cm2 [3] __________________________________________________________________________________________

5 marks

Mark scheme: 22 (a) Trapezium 1 (b) 55o 1 (c) 21.4 or 19.55 to 23.37 nfww 3 B1 for [AB =] 7.2, [DC =] 4.7, and [height =] 3.6 seen and M1 for 5.0 × their 6.3 × their (7.4 + 2.7 )

This question in 0580/13 Oct/Nov 2014

8 The diagram shows a circle, centre O. A NOT TO A, B and C are points on the circumference. SCALE B O C Write down the mathematical name of the straight line (a) OC, Answer(a) … [1] (b) AB. Answer(b) … [1] __________________________________________________________________________________________

2 marks

Mark scheme: 8 (a) radius 1 (b) chord 1

This question in 0580/12 Feb/March 2015

15 (a) NOT TO 44° SCALE x° The diagram shows an isosceles triangle. Find the value of x. Answer(a) x = … [1] (b) (i) The exterior angle of a regular polygon is 24°. Find the number of sides of this regular polygon. Answer(b)(i) … [2] (ii) Write down the mathematical name for a 5-sided polygon. Answer(b)(ii) … [1] __________________________________________________________________________________________

4 marks

Mark scheme: 15 (a) 68 1 360 (b) (i) 15 2 M1 for = 24 or (n − 2 )180 = 156n n (ii) pentagon 1 25 25

This question in 0580/12 Feb/March 2015

7 Write down the mathematical name for (a) an angle that is less than 90°, … [1] (b) a five-sided polygon. … [1]

2 marks

Mark scheme: 7 (a) Acute 1 (b) Pentagon 1  6 

This question in 0580/11 May/June 2016

2 B O C A A, B and C are points on the circumference of a circle, centre O. Write down the mathematical name for (a) the line OA, … [1] (b) the line BC. … [1]

2 marks

Mark scheme: 2(a) radius 1 2(b) chord 1

This question in 0580/13 May/June 2017

20 (a) Here is a description of a quadrilateral. It has 4 right angles. It has 2 lines of symmetry. It has rotational symmetry of order 2. Write down the mathematical name of this quadrilateral. … [1] (b) Write down two geometrical properties of a parallelogram. 1. … 2. … [2]

3 marks

Mark scheme: 20(a) Rectangle 1 20(b) Two correct properties 2 B1 for one correct property e.g. 2 pairs of parallel sides Opposite angles are equal Opposite sides are same length Rotational symmetry order 2 Diagonals are not equal

This question in 0580/11 May/June 2018

6 (a) Write down the mathematical name of the type of angle marked. … [1] (b) A and B are points on the circumference of a circle, centre O. O B A Write down the mathematical name of the line AB. … [1]

2 marks

Mark scheme: 6(a) acute 1 6(b) diameter 1

This question in 0580/13 May/June 2018

24 ABCD is a quadrilateral. A D B C (a) Using a straight edge and compasses only, construct the perpendicular bisector of BC. Show all your construction arcs. [2] (b) Using a straight edge and compasses only, construct the bisector of angle BCD. Show all your construction arcs. [2] (c) Shade the region inside ABCD that is • nearer to B than to C and • nearer to CD than to BC. [1]

5 marks

Mark scheme: 24(a) correct perpendicular bisector with 2 B1 for correct perpendicular bisector correct arcs without any arcs or with incorrect arcs 24(b) correct angle bisector with correct arcs 2 B1 for correct angle bisector without any arcs or with incorrect arcs 24(c) correct region shaded 1 Dep on B1, B1

This question in 0580/13 May/June 2018

5 (a) O Measure the radius of the circle, centre O. Give your answer in centimetres. … cm [1] (b) Write down the mathematical name of this polygon. … [1]

2 marks

Mark scheme: 5(a) 3.7 1 5(b) [Regular] hexagon 1

This question in 0580/11 Oct/Nov 2018

2 Write down the size of one angle in an equilateral triangle. … [1]

1 marks

Mark scheme: 2 60[°] 1

This question in 0580/12 Oct/Nov 2018

23 The diagram shows a quadrilateral on a 1 cm2 grid. (a) Write down the mathematical name of this quadrilateral. … [1] (b) Work out the area of this quadrilateral. Give the units of your answer. … … [3]

4 marks

Mark scheme: 23(a) kite 1 23(b) 24 2 B1 for any relevant correct area calculated or M1 for a fully correct method cm2 1

This question in 0580/12 Feb/March 2019

6 Complete each statement. (a) A quadrilateral with only one pair of parallel sides is called a … . [1] (b) An angle greater than 90° but less than 180° is called … . [1]

2 marks

Mark scheme: 6(a) Trapezium 1 6(b) Obtuse 1

This question in 0580/12 May/June 2019

21 A B C D E F G H The diagram shows some quadrilaterals. Complete the statements. (a) Quadrilateral … is a rhombus. [1] (b) Quadrilateral A is a … [1] (c) Quadrilaterals … and … are congruent. [1] (d) Quadrilaterals … and … are similar. [1]

4 marks

Mark scheme: 21(a) C 1 21(b) Trapezium 1 21(c) B and G 1 Both correct 21(d) D and F or B and G 1 Both correct

This question in 0580/12 Oct/Nov 2019

20 y 6 A 5 4 B 3 2 1 C 0 1 2 3 4 5 6 7 8 x (a) Write down the co-ordinates of point B. ( … , … ) [1] (b) The quadrilateral ABCD has x = 4 as a line of symmetry. On the grid, plot point D. [1] (c) Write down the mathematical name of quadrilateral ABCD. … [1] (d) Write down the order of rotational symmetry of quadrilateral ABCD. … [1]

4 marks

Mark scheme: 20(a) 7 3 1 20(b) point plotted at (1, 3) 1 20(c) rhombus 1 20(d) 2 1 strict FT their diagram

This question in 0580/13 Oct/Nov 2019

2 (a) Write down the mathematical name for this type of angle. … [1] (b) NOT TO B SCALE A O A and B lie on a circle, centre O. (i) Write down the mathematical name for line AB. … [1] (ii) OA = 8cm Write down the length of the diameter of this circle. … cm [1]

3 marks

Mark scheme: 2(a) Acute 1 2(b)(i) Chord 1 2(b)(ii) 16 1

This question in 0580/12 May/June 2020

1 Write down the mathematical name for (a) an angle which is less than 90°, … [1] (b) a polygon with 5 sides, … [1] (c) a quadrilateral with exactly one pair of parallel sides. … [1]

3 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) Acute 1 1(b) Pentagon 1 1(c) Trapezium 1

This question in 0580/11 Oct/Nov 2020

2 hexagon perpendicular isosceles regular congruent Put a ring around the word that describes two polygons that are the same shape and size. [1]

1 marks

Mark scheme: 2 Congruent indicated only 1

This question in 0580/11 Oct/Nov 2020

2 (a) On the grid, draw a kite. [1] (b) Write down two geometrical properties of a rhombus. 1. … 2. … [2]

3 marks

Mark scheme: 2(a) Any kite drawn 1 2(b) Two correct geometrical properties 2 B1 for 1 correct property

This question in 0580/12 Feb/March 2021

11 (a) Write down the mathematical name for a polygon with 5 sides. … [1] (b) Work out the interior angle of a regular 18‑sided polygon. … [2]

3 marks

Mark scheme: 11(a) Pentagon 1 11(b) 160 2 360 (18 − 2 ) × 180 M1 for 180 − or oe 18 18

This question in 0580/11 May/June 2021

17 A rhombus has side length 6.5 cm. The rhombus can be constructed by drawing two triangles. Using a ruler and compasses only, construct the rhombus. Leave in your construction arcs. One diagonal of the rhombus has been drawn for you. [2]

2 marks

Mark scheme: 17 Accurate construction of rhombus with 2 B1 for accurate diagram with no/wrong sides 6.5 cm and correct construction arcs arcs or for one triangle (6.5 cm, 6.5 cm, 8 cm) correctly constructed with correct arcs or for four correct arcs

This question in 0580/12 May/June 2021

2 NOT TO SCALE O B A Points A and B lie on a circle, centre O. (a) Write down the mathematical name for line AB. … [1] (b) The circle has a diameter of 16.8 cm. Write down the radius of the circle. … cm [1]

2 marks

Mark scheme: 2(a) Chord 1 2(b) 8.4 oe 1

This question in 0580/13 May/June 2021

10 Write down the mathematical name of this polygon. … [1]

1 marks

Mark scheme: 10 Pentagon 1

This question in 0580/12 Oct/Nov 2021

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

20 C x° B NOT TO SCALE O 32° A The diagram shows a circle, centre O, diameter AB. A, B and C lie on the circumference of the circle. (a) Write down the mathematical name of the line AC. … [1] (b) Find the value of x. Give a geometrical reason for your answer. x = … because … [2]

3 marks

Mark scheme: 20(a) Chord 1 20(b) 58 1 Angle in a semicircle = 90° 1

This question in 0580/13 May/June 2023

17 A B NOT TO O SCALE C A, B and C are points on a circle, centre O. (a) Draw a tangent to the circle at point A. [1] (b) The circumference of the circle is 22.3 cm. Calculate the radius of the circle. … cm [2] (c) Give a geometrical reason why angle BCA is 90°. … [1]

4 marks

Mark scheme: 17(a) Ruled tangent drawn at A 1 17(b) 3.55 or 3.548 to 3.549… 2 M1 for [r =] 22.3 ÷ 2π 17(c) Angle in a semicircle is 90º oe 1

This question in 0580/12 Oct/Nov 2023

14 B NOT TO 112° SCALE 44° C M A The diagram shows triangle ABC. M is the midpoint of AC. Triangle ABC is rotated 180° about centre M. The image and the original triangle together form a quadrilateral ABCD. (a) Write down the mathematical name of the quadrilateral ABCD. … [1] (b) Find angle BAD. Angle BAD = … [2]

3 marks

Mark scheme: 14(a) Parallelogram 1 14(b) 68 2 M1 for 180 – 112 or for 180 – 112 – 44 oe

This question in 0580/13 Oct/Nov 2023

17 The diagram shows a circle, centre O. P lies on the circle. P O (a) Write down the mathematical name of the line OP. … [1] (b) Draw a tangent to the circle at P. [1]

2 marks

Mark scheme: 17(a) radius 1 17(b) Ruled line drawn through P 1 perpendicular to OP

This question in 0580/11 May/June 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

15 D NOT TO SCALE y° A B C The diagram shows a triangle BCD and a straight line ABC. DB=DC=BC. (a) Write down the mathematical name for triangle BCD. … [1] (b) Work out the value of y. Give two geometrical reasons for your answer. y = … because 1. … 2. … [4]

5 marks

Mark scheme: 15(a) equilateral 1 15(b) 120 2 B1 for DBC=60 Angles in an equilateral triangle are 1 equal Angles on a straight line add to 180 1

This question in 0580/12 Feb/March 2025

13 (a) A quadrilateral has the geometrical properties • 4 equal length sides • 2 lines of symmetry • rotational symmetry of order 2. Write down the mathematical name of this quadrilateral. … [1] (b) Write down two geometrical properties of a rectangle. 1. … 2. … [2] (c) The parallel sides of a trapezium have lengths 6 cm and 4 cm. The area of the trapezium is 15 cm2. On the 1 cm2 grid, draw a trapezium with these lengths and area. [3]

6 marks

Mark scheme: 13(a) rhombus 1 13(b) two properties stated that are better 2 B1 for one property than any applying to all quadrilaterals. 13(c) A correct drawing of a trapezium with 3 B2 for trapezium perpendicular height 3 cm perpendicular height 3 cm and parallel or B1 for a trapezium drawn with sides 4 cm sides 4 cm and 6 cm and 6 cm but height ≠ 3 Or 1 M1 for ( 4 + 6 )  h = 15 or better 2 A1 [h =] 3 If 0 scored, SC1 for a parallelogram or rectangle drawn with height 3 cm or h = 3 with no/wrong working

This question in 0580/12 May/June 2025

4 The diagram shows a quadrilateral with sides of equal length. NOT TO SCALE a° 2a° (a) Write down the mathematical name for this quadrilateral. … [1] (b) Work out the value of a. a = … [2]

3 marks

Mark scheme: 4(a) Rhombus 1 4(b) 60 2 M1 for a + 2a = 180 oe or better

This question in 0580/13 May/June 2025

9 The diagram shows the net of a square-based pyramid. 4 cm NOT TO SCALE 5 cm The perpendicular height of each triangle is 4 cm. The base has side length 5 cm. (a) Calculate the surface area of the pyramid. … cm2 [2] (b) Write down the number of edges of the square-based pyramid. … [1]

3 marks

Mark scheme: 9(a) 65 2 1 M1 for 4  5 4 + 5  5 oe 2 9(b) 8 1

This question in 0580/13 May/June 2025

3 Write down the mathematical name of this polygon. … [1]

1 marks

Mark scheme: 3 Hexagon 1

This question in 0580/11 Oct/Nov 2025

1 A B (a) Measure the length of line AB in centimetres. … cm [1] (b) Draw a line that is parallel to line AB. [1]

2 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 5.6 1 1(b) Ruled line parallel to AB 1

This question in 0580/13 Oct/Nov 2025

5 The diagram shows quadrilateral ABCD on a 1 cm 2 grid. y 4 3 B C 2 1 – 4 – 3 – 2 – 1 0 1 2 3 4 x – 1 – 2 A D – 3 – 4 (a) Write down the coordinates of point B. ( … , … ) [1] (b) Write down the mathematical name of quadrilateral ABCD. … [1] (c) Find the area of quadrilateral ABCD. … cm2 [1] (d) On the grid, plot the point E at ( –3 , 2) . [1]

4 marks

Mark scheme: 5(a) (–1, 2) 1 5(b) trapezium 1 5(c) 16 1 5(d) Point plotted at (–3,2) 1

This question in 0580/13 Oct/Nov 2025