Compound shapes and parts of shapes — Paper 1 · IGCSE Mathematics 0580

13 For Examiner's Use The diagram shows a pyramid with a square base. All the sloping edges are the same length. In the space below sketch a net of the pyramid. [2]

2 marks

Mark scheme: 13 Net of the pyramid. A 2 1 for a square square with 4 equal 1 for all 4 triangles, isosceles or isosceles triangles equilateral. correctly positioned. Reasonable accuracy by eye. Ignore any tabs shown.

This question in 0580/11 Oct/Nov 2004

18 For Examiner's Use NOT TO 3 cm SCALE 2 cm 4 cm The solid shown is a cuboid with length 4 cm, width 2 cm and height 3 cm. (a) Draw an accurate net of the cuboid on the grid below. [2] (b) Using your net, calculate the total surface area of the cuboid. Answer(b) cm2 [2]

4 marks

Mark scheme: 18 (a) Net of the cuboid 2 M1 for a net with 6 correct size rectangles. A1 for a fully correct net. (b) 52 2ft M1 for 5 or 6 areas calculated and added or SC1 for answer of 26. ft only if 5 or 6 rectangles are shown in part (a). 8

This question in 0580/11 May/June 2006

16 The diagram shows a square tile of side 10 centimetres with 4 identical quarter circles shaded. For Examiner's Use 10 cm 10 cm Calculate the area of the unshaded region. Answer cm2 [4]

4 marks

Mark scheme: 16 21.45 to 21.6 www 4 M1 10 × 10 or 100 M1 indep π × r2 where r is 5, 4.4 or 4.5 M1 dep Subtraction of the two areas. Dependent on both first two M1’s or Alternative method Alt. M1 r × r where r is 5, 4.4 or 4.5 M1 ind 14 π × r2 where r is 5, 4.4 or 4.5 M1 dep 4 × subtraction of the two areas. Dependent on both first two M1’s Follow one method only. or W3 art 36.4 or art 39.2 www IGCSE – May/June 2009 0580, 0581 11

This question in 0580/11 May/June 2009

12 For Examiner's Use NOT TO SCALE 4 cm 7 cm The diagram shows a triangular prism of length 7 cm. The cross-section is an equilateral triangle of side 4 cm. Complete an accurate net of the prism. One rectangular face has been drawn for you. [3]

3 marks

Mark scheme: 12 Correct net layout 1 2 rectangles and 2 equilateral triangles (one on each side) in correct position to make a net. 2 accurate, 7 cm by 4 cm, rectangles on 1 top and bottom. 2 accurate equilateral triangles at the 1 within 2 mm of central grid line sides (height 3.3 cm to 3.7 cm)

This question in 0580/11 Oct/Nov 2009

3 The diagram is an accurate net for a solid shape. Write down the geometrical name for this solid shape. Answer [1]

1 marks

Mark scheme: 3 (Triangular) prism 1

This question in 0580/11 Oct/Nov 2010

5 For Examiner′s Use The diagram shows the net of a solid. Write down the mathematical name of this solid. Answer … [1] _____________________________________________________________________________________

1 marks

Mark scheme: 5 cuboid 1 Accept [rectangular] prism.

This question in 0580/12 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

17 12 cm NOT TO SCALE 12 cm The diagram shows a circle inside a square of side 12 cm. The circle touches each side of the square. Calculate the area of the shaded part of the diagram. Answer … cm2 [3] _____________________________________________________________________________________

3 marks

Mark scheme: 17 30.9 or 30.88 to 30.91 3 M2 for 12 × 12 − π × 6 × 6 or 4( 6 × 6 − 14 π × 6 × 6) M1 for 12 × 12 or π × 6 × 6 or ( 6 × 6 − 14 π × 6 × 6)

This question in 0580/13 Oct/Nov 2013

7 Four faces of a cube are drawn on the grid. Complete the net of this cube. [1] __________________________________________________________________________________________

1 marks

Mark scheme: 7 Cube net drawn correctly 1

This question in 0580/13 May/June 2014

19 The shaded shape is made by joining a square and a rhombus. NOT TO SCALE 4.5 cm 5 cm Work out (a) the perimeter of the shaded shape, … cm [1] (b) the area of the shaded shape. … cm2 [2]

3 marks

Mark scheme: 19 (a) 30 1 (b) 47.5 2 M1 for 4.5 × 5 oe

This question in 0580/13 Oct/Nov 2016

21 A cuboid has length 6 cm, width 5 cm and height 3 cm. On the 1 cm2 grid, complete the net of the cuboid. The base is drawn for you. [3]

3 marks

Mark scheme: 21 Complete correct ruled net 3 B2 for 4 correct rectangles in correct places or B1 for 2 correct side rectangles in correct places

This question in 0580/11 May/June 2017

24 The diagram shows a notice board. NOT TO SCALE 74 cm The board is in the shape of a semicircle joined to a square with side 74 cm. (a) Calculate (i) the perimeter of the board, … cm [3] (ii) the area of the board. … cm2 [3] (b) The board is a prism that is 5 cm thick. Calculate the volume of the board. … cm3 [1]

7 marks

Mark scheme: 24(a)(i) 338 or 338.3 nfww 3 M1 for 3 × 74 or 338.2 to 338.26 and M1 for 74 × π ÷ 2 24(a)(ii) 7630 nfww 3 M1 for 742 or 7626 to 7627 π× 37 2 and M1 for 2 24(b) 38100 nfww 1FT FT their (a)(ii) × 5 or 38200 or 38150 or 38130 to 38140

This question in 0580/11 May/June 2017

19 A cuboid measures 5 cm by 4 cm by 3 cm. On the 1 cm2 grid, draw an accurate net of this cuboid. One face has been drawn for you. [3]

3 marks

Mark scheme: 19 Correct ruled net 3 B2 for 4 more correct faces in correct position or B1 for 2 or 3 more correct faces in correct position

This question in 0580/12 Oct/Nov 2017

14 (a) The diagram shows a solid cuboid made of identical cubes. NOT TO SCALE Work out the number of cubes in the cuboid. … [1] (b) The diagram shows the nets of two solids. Write down, under each net, the mathematical name for the solid. … … [2]

3 marks

Mark scheme: 14(a) 160 1 14(b) Cone, [square based] pyramid 2 B1 for each

This question in 0580/12 May/June 2019

22 A closed box in the shape of a cuboid has length 5 cm, width 4 cm and height 2 cm. (a) Calculate the volume of the box. … cm3 [2] (b) On the 1 cm2 grid, complete the net of this box. [2]

4 marks

Mark scheme: 22(a) 40 2 M1 for 5 × 4 × 2 22(b) 4 correct rectangles only, added in 2 B1 for 2 correct rectangles in correct correct positions positions

This question in 0580/13 May/June 2019

7 A cuboid has length 3 cm, width 2 cm and height 1 cm. On the 1 cm2 grid, draw a net of the cuboid. [3]

3 marks

Mark scheme: 7 Correct net 3 B2 for 4 correctly connected faces drawn or B1 for 2 correct connected faces drawn or for 6 correct faces drawn

This question in 0580/12 Feb/March 2020

9 NOT TO SCALE 3 cm 4 cm The diagram shows a prism. The cross-section of the prism is an equilateral triangle. Draw a net of the prism on the 1cm2 grid. [3]

3 marks

Mark scheme: 9 Correct net 3 B1 for one correct face drawn B1 for 3 rectangles and 2 triangles drawn in correct places, but not the correct size

This question in 0580/12 Feb/March 2021

14 NOT TO SCALE 5 cm 5 cm h 4 cm (a) Calculate the height, h, of the triangle. h = … cm [3] (b) The triangle is one face of a square-based pyramid. On the 1 cm2 grid, draw a net of this pyramid. [3]

6 marks

Mark scheme: 14(a) 4.58 or 4.582 to 4.583 3 M2 for 52 − 22 or better or M1 for 52 = 22 + h2 or better 14(b) Correct ruled net of the pyramid 3 B2 for a 4 by 4 square and 4 isosceles triangles on the sides of the square or B1 for a 4 by 4 square or at least one isosceles triangle drawn on a side of a square

This question in 0580/13 May/June 2022

4 5 cm NOT TO 4 cm SCALE 2 cm Complete the net of this cuboid on the 1 cm 2 grid. One face has been drawn for you. [3]

3 marks

Mark scheme: 4 Fully correct net 3 B2 for 4 correct faces in the correct places or B1 for 2 or 3 correct faces in the correct places

This question in 0580/12 Oct/Nov 2022

10 5 cm NOT TO SCALE 4 cm 6 cm 3 cm The diagram shows a right-angled triangular prism. On the 1 cm2 grid, complete the net of this prism. One face has been drawn for you. [3]

3 marks

Mark scheme: 10 Fully correct net 3 B2 for 2 correct rectangles in the correct places but in either order or B1 for 1 correct rectangle in the correct place If B0 or B1 scored, SC1 for two 3 4 5 triangles on opposite sides of a rectangle

This question in 0580/12 May/June 2023

9 4 cm NOT TO 4 cm SCALE 2 cm 4 cm The diagram shows a triangular prism. On the 1 cm 2 grid, draw a net of the prism. [3]

3 marks

Mark scheme: 9 Correct ruled net 3 B2 for 3 rectangles of the same size and 2 triangles with at least 2 sides the same size drawn in correct places but not the correct size or B1 for one correct face drawn as part of a net

This question in 0580/13 May/June 2023

12 (a) Kat has a method for finding the difference between two square numbers, a 2 - b 2 . Her method is (the sum of a and b) # (the difference between a and b) . She shows her method for 17 2 - 13 2 . 17 2 - 13 2 = ( 17 + 13) # ( 17 - 13) = 30 # 4 = 120 Work out 29 2 - 21 2 using Kat’s method. … [2] (b) In this part, all lengths are in centimetres. 17 NOT TO SCALE 17 13 13 100 The diagram shows a prism. Work out the volume of the prism. … cm3 [2]

4 marks

Mark scheme: 12(a) ( 29 + 21)  ( 29 − 21) M1 = 50  8 400 A1 12(b) 12000 2 2 2 M1 for 17 − 13 [ ×100] oe ( )

This question in 0580/12 Feb/March 2025

14 C NOT TO SCALE 4 cm D 6 cm A 6 cm B The diagram shows a triangular prism. ABC is an isosceles triangle with AC = BC. The perpendicular height of triangle ABC is 4 cm. AB = 6 cm and BD = 6 cm. (a) Complete this statement. The prism has … faces and … edges. [2] (b) Show that the length of BC is 5 cm. [2] (c) Complete the net of the prism on the 1 cm 2grid. The base has been drawn for you. [3]

7 marks

Mark scheme: 14(a) 5 9 2 B1 for each 14(b) 2 2 2 2 2 3 + 4 [=5] M1 for 3 + 4 14(c) correct net drawn 3 B2 for 3 correct extra faces drawn in correct places or B1 for 1 correct extra face drawn in correct place

This question in 0580/12 Feb/March 2025