Area and perimeter — Paper 1 · IGCSE Mathematics 0580

18 A 400 metre running track has two straight sections, each of length 120 metres, and two semicircular For ends. Examiner's Use 120 m NOT TO d SCALE (a) Calculate the total length of the curved sections of the track. Answer(a) m [1] (b) Calculate d, the distance between the parallel straight sections of the track. Answer(b) d = m [2]

3 marks

Mark scheme: 18 (a) 160 1 (b) Their (a) ÷π M1 50.9(…..) or 51 A1

This question in 0580/11 Oct/Nov 2005

14 (a) Calculate the circumference of a circle of diameter 8 cm. For Examiner's Use Answer(a) cm [2] (b) Q NOT TO SCALE 29º A B AQB is a semi-circle. Angle QAB = 29°. Work out the size of angle ABQ. Answer(b) Angle ABQ = [2]

4 marks

Mark scheme: 14 (a) art 25.1 www 2 M1 for π × 8 or 2π × 8 ÷ 2 implied by answer of 25 (b) 61 (Can be on 2 M1 for 90 – 29 or 180 – 90 – 29 diagram) SC1 for angle Q = 90° soi

This question in 0580/11 Oct/Nov 2007

4 The area of a square is 42.25 cm2. Work out the length of one side of the square. Answer cm [1]

1 marks

Mark scheme: 4 6.5 1

This question in 0580/11 Oct/Nov 2008

18 (a) Calculate the volume of a cylinder of radius 50 cm and height 138 cm. For Examiner's Use Answer(a) cm3 [2] (b) Write your answer to part (a) in cubic metres. Answer(b) m3 [1]

3 marks

Mark scheme: 18 (a) 1083300 to 1084000 or 2 M1 for π × 50 2 × 138 or π × 0.52 × 1.38 1080000 or 1083000 Final answer (b) Their (a) ÷ 10 6 evaluated 1ft

This question in 0580/11 Oct/Nov 2008

19 14 cm NOT TO SCALE 6 cm 10 cm 22 cm For the shape above, work out (a) the perimeter, Answer(a) cm [2] (b) the area. Answer(b) cm2 [2]

4 marks

Mark scheme: 19 (a) 64 2 M1 for 2 × (10 + 22) or 22 + 10 + 14 + 6 + (22 – 14) + (10 – 6) (b) 172 2ft M1 for (22 × 10) − 6 × ‘8’ or (140 × 10) + ‘8’ × ‘4’ or 14 × 6 + 22 × ‘4’

This question in 0580/11 Oct/Nov 2008

9 The area of a circle is 19.7 cm2. Calculate the radius of the circle. Answer cm [3]

3 marks

Mark scheme: 9 2.5(0) or 2.503…. to 2.504 3 M1 for πr2 = 19.7 soi M1 dep for 19.7 ÷ π

This question in 0580/11 May/June 2010

15 The diagram shows a prism. Examiner's The lengths are in centimetres. Use 2.5 NOT TO SCALE 1 3 8 2 4 Part of an accurate net of the prism is drawn below. Complete the net. [3]

3 marks

Mark scheme: 15 Rectangle width 1.5 cm. 1 in a correct place Rectangle width 1 cm. 1 in a correct place Accurately drawn cross-section piece 1 in a correct place

This question in 0580/12 May/June 2010

19 The diagram shows a door, AEBCD, from a model of a house. Examiner's Use ABCD is a rectangle and AEB is a semi-circle. AD = 14 cm and DC = 6 cm. E A B NOT TO SCALE 14 cm D 6 cm C (a) Calculate the area of the door. Answer(a) cm2 [3] (b) The door is 2 millimetres thick. Calculate, in cubic centimetres, the volume of the door. Answer(b) cm3 [2] Question 20 is printed on the next page.

5 marks

Mark scheme: 19 (a) 98.1 or 3 M1 for 14 × 6 (+……) 98.13 to 98.14 M1 ind for π × 32 ÷ 2 (b) 19.6 or 2ft M1 for their (a) × figs 2 19.62 to 19.63 Figs 196…. implies M1

This question in 0580/12 May/June 2010

16 Examiner's Use NOT TO SCALE 11 cm 4 cm A cylindrical can of beans has height 11 cm and radius 4 cm. A label covers the curved surface of the can completely. Calculate the area of the label. Answer cm2 [3]

3 marks

Mark scheme: 16 276 3 M2 for 2π × 4 × 11, or better, seen or 276.3 to 276.5 or M1 for 2π × 4 SC1 for 4 × π × 11 or 138…., seen

This question in 0580/13 May/June 2010

18 For Examiner's Use NOT TO SCALE 44 cm 35 cm A cylindrical tank, with radius 35 cm, is filled with water to a depth of 44 cm. (a) Calculate the area of the base of the tank. Answer(a) cm2 [2] (b) Calculate the volume of water in the tank. Answer(b) cm3 [1] (c) Change your answer to part (b) into litres. Answer(c) litres [1]

4 marks

Mark scheme: 18 (a) 3846 to 3849 or 3850 2 M1 for π × 352 or SC1 correct volume answer (b) 169224 to 169356 1ft ft their (a) × 44 or 169400 or 169000 (c) 169.2 to 169.4 or 169 1ft ft their (b) ÷ 1000 IGCSE – October/November 2010 0580 11 4 5 4 14

This question in 0580/11 Oct/Nov 2010

18 For Examiner's D C Use NOT TO SCALE 18 cm A B The diagram shows a square ABCD. The length of the diagonal AC is 18 cm. (a) Calculate (i) the length of the side of the square, Answer(a)(i) cm [2] (ii) the area of the square. Answer(a)(ii) cm2 [2] (b) A, B, C and D lie on a circle with diameter AC. Calculate the area of this circle. Answer(b) cm2 [2]

6 marks

Mark scheme: x x 18 (a) (i) 12.7 to 12.73 2 M1 for = sin45 or = cos45 or better 18 18 (ii) 161 to 162.1 2ft M1 for method for squaring their (a)(i). (b) 254 to 255 2 M1 for π × 92

This question in 0580/12 Oct/Nov 2010

6 Calculate the area of a circle with radius 6.28 centimetres. Answer cm2 [2]

2 marks

Mark scheme: 6 124 or 123.8 2 M1 for π × 6.28 2 or 123.83 to 123.92 7.2 × 20000

This question in 0580/11 May/June 2011

20 NOT TO SCALE 8 m 2.5 m 8 m The diagram shows a circular pool of radius 2.5 m. A square piece of land surrounds the pool. Each side of the square is 8 m long. Calculate the shaded area of the land that surrounds the pool. Answer m2 [3]

3 marks

Mark scheme: 20 44.4 (44.36 to 44.38) 3 M2 for 8 × 8 − π × 2.52 or www M1 for π × 2.52

This question in 0580/13 Oct/Nov 2011

17 For 12 cm Examiner's Use 4 cm NOT TO 12 cm 18 cm 18 cm SCALE 34 cm For the shape above, work out (a) the perimeter, Answer(a) cm [2] (b) the area. Answer(b) cm2 [2]

4 marks

Mark scheme: 17 (a) 112 2 M1 Attempt to add 6 given and their 2 sides (b) 564 2 M1 for 18 × 34 – 12 × 4 : (612 – 48) or (18 × 12) + (14 × 12) + (10 × 18) or (4 × 12) + (10 × 4) + (34 × 14)

This question in 0580/13 May/June 2012

14 (a) The perimeter of a square is 28 mm. Work out the length of one side of the square. Answer(a) … mm [1] (b) Calculate the volume of a cylinder with radius 5.2 cm and height 15 cm. Answer(b) … cm3 [2] _____________________________________________________________________________________

3 marks

Mark scheme: 14 (a) 7 1 (b) 1270 or 1274 2 M1 for π × 5.22 × 15 or 1274.2 to 1274.4 4 2 M1 f 420  1 

This question in 0580/11 May/June 2013

11 For Examiner′s A Use NOT TO SCALE 8 cm B C Triangle ABC has a height of 8 cm and an area of 42 cm². Calculate the length of BC. Answer BC = … cm [2] _____________________________________________________________________________________

2 marks

Mark scheme: 11 10.5 www 2 M1 for 42 = 1 2 × BC × 8 or better

This question in 0580/12 May/June 2013

14 For Examiner′s 4 cm Use NOT TO SCALE 5 cm 10 cm 18 cm The shaded shape has rotational symmetry of order 2. Work out the shaded area. Answer … cm2 [3] _____________________________________________________________________________________

3 marks

Mark scheme: 14 260 3 M2 for [2 × ] (4 × 10 + 18 × 5) oe or M1 for a correct area statement

This question in 0580/13 May/June 2013

16 NOT TO SCALE 10 cm 6 cm This shape is made from a rectangle and a semicircle. The rectangle measures 10 cm by 6 cm. Work out the area of the shape. Answer … cm2 [3] _____________________________________________________________________________________

3 marks

Mark scheme: 16 74.1 or 74.137 to 74.140 3 M1 for 10 × 6 and M1 for 0.5 × π × 32

This question in 0580/12 Oct/Nov 2013

21 B NOT TO SCALE O 63° A C The diagram shows a circle, centre O with diameter AB = 15 cm. AC is a tangent to the circle at A and angle AOC = 63°. (a) Calculate the area of the circle. Answer(a) … cm2 [2] (b) (i) Work out the size of angle ACO. Answer(b)(i) Angle ACO = … [2] (ii) Give one geometrical reason for your answer to part (b)(i). Answer(b)(ii) … … [1] __________________________________________________________________________________________

5 marks

Mark scheme: 21 (a) 177 or 176.7 to 176.74 2 M1 for π × 7.52 oe (b) (i) 27 2 B1 for angle CAO marked, or clearly used, as a right-angle (or 90°) or M1 for 180 – 90 – 63 oe (ii) one correct geometrical reason 1 [angle between a] radius [and a] tangent [is a] right-angle or [angles in a] triangle [add up to] 180° or [the] angles [have to] add to 180°

This question in 0580/12 May/June 2014

12 The area of a square is 36 cm2. Calculate the perimeter of this square. Answer … cm [2] __________________________________________________________________________________________

2 marks

Mark scheme: 12 24 2 M1 for √36 × 4 oe or B1 for 6 seen

This question in 0580/13 May/June 2014

19 NOT TO SCALE 7 cm 4 cm The diagram shows a prism. The cross section is an equilateral triangle. On the grid, draw an accurate net of the prism. The base is drawn for you. [3] __________________________________________________________________________________________

3 marks

Mark scheme: 19 Correct ruled net drawn 3 B1 for rectangles, even if incorrect or not joined, drawn one on each side of the given one and two triangles opposite sides and B1 for 2 correct ruled rectangles and B1 for 2 correct ruled equilateral triangles

This question in 0580/11 Oct/Nov 2014

15 (a) A parcel is in the shape of a cuboid of length 18 cm, width 10 cm and height 8 cm. Calculate the volume of the parcel. Answer(a) … cm3 [2] (b) The mass of the parcel is 1.7 kilograms. Change 1.7 kilograms to grams. Answer(b) … g [1] __________________________________________________________________________________________

3 marks

Mark scheme: 15 (a) 1440 2 M1 for 18 × 10 × 8 (b) 1700 1

This question in 0580/13 Oct/Nov 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

11 The volume, V, of a cylinder with radius r and height h is V = πr2h. Calculate the volume of a cylinder with radius 7 cm and height 8 cm. Answer … cm3 [2] __________________________________________________________________________________________

2 marks

Mark scheme: 11 1230 or 1231 to 1232 2 M1 for π × 7 × 7 × 8 or better 4 5

This question in 0580/12 Feb/March 2015

12 6 m NOT TO 0.8 m SCALE 3 m 0.8 m Leah is making a path in her garden using gravel. The diagram shows the path. A bag of gravel covers an area of 0.5 m2. Work out the number of bags of gravel Leah must buy to make the path. Answer … [3] __________________________________________________________________________________________

3 marks

Mark scheme: 12 14 nfww 3 M2 for (0.8 × 6 + 2.2 × 0.8) oe ÷ 0.5 oe or M1 for 0.8 × 6 + 2.2 × 0.8 oe If zero scored, SC1 for their attempt at area ÷ 0.5 and SC1 for any non-integer answer for their value ÷ 0.5 rounded up

This question in 0580/11 Oct/Nov 2015

18 NOT TO SCALE 6.1 cm A protractor is a semi-circle of radius 6.1 cm. Calculate the perimeter of the protractor. Answer … cm [3] __________________________________________________________________________________________

3 marks

Mark scheme:  2 18 31.4 or 31.36 to 31.37 3 M2 for × 1.6 × π + 2 × 1.6 oe  2  or B2 for 19.16 to 19.17 or 19.2 or M1 for 6.1 × π or for 12.2 × π

This question in 0580/11 Oct/Nov 2015

22 7 cm NOT TO SCALE 6 cm 10 cm (a) Calculate the area of the trapezium. … cm2 [2] (b) The trapezium is the cross section of a prism. The length of the prism is 12 cm. Calculate the volume of the prism. Give the units of your answer. … … [2] Question 23 is printed on the next page.

4 marks

Mark scheme: 1 22 (a) 51 2 M1 for × (10 + 7) × 6 oe 2 (b) 612 1FT FT 12 × their (a) cm3 1

This question in 0580/12 May/June 2016

9 NOT TO SCALE 6 cm 5 cm x cm The area of this parallelogram is 51.5 cm2. Work out the value of x. x = … [2]

2 marks

Mark scheme: 9 10.3 oe 2 M1 for 5x = 51.5 oe

This question in 0580/13 May/June 2016

9 A circular pool has radius 8 m. Calculate the circumference of the pool. … m [2]

2 marks

Mark scheme: 9 50.3 or 50.26 to 50.272 2 M1 for 2 × π × 8 oe

This question in 0580/11 Oct/Nov 2016

12 13 cm NOT TO 5 cm SCALE 4 cm 16 cm Calculate the area of this trapezium. … cm2 [2]

2 marks

Mark scheme: (13 + 16 ) × 412 58 2 M1 for or 4 × 13 + 12 × 4 × 3 oe 2 x

This question in 0580/12 Oct/Nov 2016

19 (a) Work out the perimeter of a regular octagon with side length 4 cm. … cm [1] (b) Work out the interior angle of a regular 12-sided shape. … [3]

4 marks

Mark scheme: 19 (a) 32 1 360 180 × (12 − 2) (b) 150 3 M2 for 180 − or 12 12 ( 2 × 12 − 4 ) × 90 or 12 360 or M1 for or 180 × (12 – 2) or 12 (2 × 12 – 4) × 90 soi

This question in 0580/12 Oct/Nov 2016

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

7 A circular plate has diameter 27 cm. Calculate the circumference of the plate. … cm [2]

2 marks

Mark scheme: 7 84.8 or 84.82 to 84.83[…] 2 M1 for 27 × π 10 × 20

This question in 0580/12 Feb/March 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

24 (a) Work out the area of a circle with radius 6 cm. … cm2 [2] (b) A solid cylinder has length 15 cm and radius 6 cm. NOT TO SCALE 6 cm 15 cm Calculate the total surface area of the cylinder. … cm2 [4]

6 marks

Mark scheme: 24(a) 113 or 113 to 113.12 2 M1 for π × 62 24(b) 792 or 791 or 791.4 to 791.8 4 M2 for 2 × π × 6 ×15 and M1FT for 2 × their (a) or 2 × π × 62

This question in 0580/12 May/June 2017

9 Calculate the area of a circle with diameter 9 cm. … cm2 [2]

2 marks

Mark scheme: 9 63.6 or 63.61 to 63.63 2 M1 for π × 4.52

This question in 0580/11 Oct/Nov 2017

20 (a) NOT TO SCALE 6.7 cm 10.4 cm 9.2 cm 12.8 cm The diagram shows a small rectangle inside a large rectangle. Work out the shaded area. … cm2 [2] (b) NOT TO 5 cm SCALE 2 cm 8 cm Work out the surface area of this cuboid. … cm2 [3]

5 marks

Mark scheme: 20(a) 71.48 2 M1 for 12.8 × 10.4 or 9.2 × 6.7 or for an area of a suitable rectangle from shaded area 20(b) 132 3 M2 for 2 × (8 × 2 + 2 × 5 + 8 × 5) oe or M1 for at least two of 8 × 2, 8 × 5 and 2 × 5

This question in 0580/11 Oct/Nov 2017

11 The area of a triangle is 528 cm2. The length of its base is 33 cm. Calculate the perpendicular height of the triangle. … cm [2]

2 marks

Mark scheme: 11 32 2 1 M1 for × 33 × h = 528 oe 2

This question in 0580/12 Oct/Nov 2017

15 Calculate the size of one interior angle of a regular 12-sided polygon. … [3]

3 marks

Mark scheme: 15 150 3 M2 for (12 – 2) × 180 ÷ 12 or 180 – 360 ÷ 12 or M1 for (12 – 2) × 180 or 360 ÷ 12 soi 30

This question in 0580/13 Oct/Nov 2017

22 NOT TO SCALE 10 cm The diagram shows a shape made from a square and a semi-circle. Calculate the area of the shape. Give the units of your answer. … … [5]

5 marks

Mark scheme: 22 139 or 139.2 to 139.3 4 2 1 2 M3 for 10 + × π × 5 2 1 2 or M2 for × π × 5 2 or M1 for radius = 5 or [area of square]102 cm2 1

This question in 0580/13 Oct/Nov 2017

17 The diagram shows a cuboid. NOT TO 8 cm SCALE 4 cm 10 cm Work out the surface area of this cuboid. … cm2 [3]

3 marks

Mark scheme: 17 304 3 M2 for [2 ×]( (10 × 4) + (10 × 8) + (4 × 8)) or M1 for one of 10 × 4 or 10 × 8 or 4 × 8

This question in 0580/13 May/June 2018

22 Work out the area of each shape. (a) 8.4 cm NOT TO SCALE 3.5 cm … cm2 [2] (b) 18 cm NOT TO SCALE 12 cm 10 cm … cm2 [2]

4 marks

Mark scheme: 22(a) 29.4 2 M1 for 8.4 × 3.5 22(b) 168 2 M1 for 12 × (10 +18) ÷ 2 oe

This question in 0580/13 May/June 2018

13 Calculate the size of one exterior angle of a regular 15-sided polygon. … [2]

2 marks

Mark scheme: 13 24 nfww 2 M1 for 360 ÷ 15 If zero scored, SC1 for answer of 156

This question in 0580/11 Oct/Nov 2018

15 The diagram shows the top of a table. 1.2 m NOT TO 0.4 m SCALE 0.9 m 0.7 m (a) Calculate the perimeter. … m [1] (b) Calculate the area. … m2 [2]

3 marks

Mark scheme: 15(a) 4.2 1 15(b) 0.83 [m2] or 8300 cm2 2 M1 for 0.4 × 1.2 + (0.9 – 0.4) × 0.7 or 0.7 × 0.9 + (1.2 – 0.7) × 0.4 or 1.2 × 0.9 – (0.9 – 0.4) × (1.2 – 0.7) or for one of the above, consistently using cm e.g. 40 × 120 + (90 – 40) × 70

This question in 0580/11 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

12 NOT TO SCALE 3.5 cm 8.4 cm Calculate the area of this triangle. … cm2 [2]

2 marks

Mark scheme: 12 14.7 2 1 M1 for × 8.4 × 3.5 oe 2

This question in 0580/12 May/June 2019

21 NOT TO SCALE 9 cm The diagram shows a semicircle with diameter 9 cm. Calculate the total perimeter of this semicircle. … cm [3]

3 marks

Mark scheme: 21 23.1 or 23.137 to 23.139 or 23.14 3 9π M2 for oe 2 or M1 for 9π oe

This question in 0580/12 May/June 2019

16 NOT TO SCALE 4 cm 12 cm 15 cm The diagram shows a cuboid measuring 15 cm by 12 cm by 4 cm. Calculate the surface area of the cuboid. … cm2 [3]

3 marks

Mark scheme: 16 576 3 M2 for [2 ×] (15 × 4 + 12 × 4 + 12 × 15) oe or M1 for one correct area, 15 × 4 or 12 × 4 or 12 × 15

This question in 0580/12 Oct/Nov 2019

16 A cuboid measures 5 cm by 7 cm by 9.5 cm. NOT TO SCALE 7 cm 5 cm 9.5 cm Work out the surface area of this cuboid. … cm2 [3]

3 marks

Mark scheme: 16 298 3 M2 for [2×] (5×7 + 5× 9.5 + 7 × 9.5) oe or M1 for one correct area, 5 × 7 or 5 × 9.5 or 7 × 9.5

This question in 0580/13 Oct/Nov 2019

14 NOT TO 8.5 cm SCALE 10.8 cm The diagram shows a right-angled triangle. (a) Calculate the area. … cm2 [2] (b) Calculate the perimeter. … cm [3]

5 marks

Mark scheme: 14(a) 45.9 2 M1 for 0.5 × 8.5 × 10.8 oe 14(b) 33[.0] or 33.04… 3 2 2 M2 for 8.5 + 10.8 + 8.5 + 10.8 oe or M1 for 8.52 + 10.82 oe

This question in 0580/12 Feb/March 2020

7 Rectangle A measures 3 cm by 8 cm. 8 cm NOT TO 3 cm A SCALE Five rectangles congruent to A are joined to make a shape. NOT TO SCALE Work out the perimeter of this shape. … cm [2]

2 marks

Mark scheme: 7 86 2 M1 for correct method to find the perimeter e.g. (8 + 3) × 2 × 5 – 3 × 8 If 0 scored, SC1 for answer 98

This question in 0580/11 May/June 2020

15 11 cm NOT TO SCALE 5 cm 7 cm Calculate the area of the trapezium. … cm2 [2]

2 marks

Mark scheme: 15 45 2 11 + 7 M1 for × 5 oe 2

This question in 0580/12 May/June 2020

21 A solid cylinder has radius 3 cm and height 4.5 cm. Calculate the total surface area of the cylinder. … cm2 [4]

4 marks

Mark scheme: 21 141 or 141.3 to 141.4 4 M1 for [2 ×] π × 32 M2 for 2 × π × 3 × 4.5 or M1 for 2 × π × 3 [× 4.5]

This question in 0580/13 May/June 2020

6 24 m NOT TO SCALE x m 17 m 19 m 7 m The diagram shows a shape made from rectangles. The shape has a total area of 517 m2. Find the value of x. x = … [4]

4 marks

Mark scheme: 6 16 4 Accept any correct method e.g. M1 for 19 × 7 M1 for 517 – their 133 M1 for their 384 ÷ 24

This question in 0580/11 Oct/Nov 2020

15 C NOT TO SCALE h cm A 6 cm B The area of triangle ABC is 27 cm2 and AB = 6 cm. Calculate the value of h. h = … [2]

2 marks

Mark scheme: 15 9 2 1 M1 for × 6 × h = 27 oe 2

This question in 0580/12 Oct/Nov 2020

13 7 cm NOT TO x cm SCALE 6 cm 12 cm 11 cm The area of the parallelogram is the same as the area of the trapezium. Work out the value of x. x = … [3]

3 marks

Mark scheme: 13 8 3 M2 for 12 × (7 + 11) × x = 12 × 6 or better or M1 for 12 × 6 or 12 × (7 + 11) × x

This question in 0580/13 Oct/Nov 2020

21 C NOT TO 6 cm SCALE O B 5 cm A The diagram shows a shape made from a quarter-circle, OAB, and a right-angled triangle OBC. The radius of the circle is 5 cm and OC = 6 cm. Calculate the area of the shape. … cm2 [3]

3 marks

Mark scheme: 21 34.6 or 34.63 to 34.64 3 1 2 1 M2 for × π × 5 + 5 × 6 oe 4 2× 1 2 1 or M1 for × π × 5 oe or 5 × 6 oe 4 2×

This question in 0580/12 Feb/March 2021

7 The diagram shows a box in the shape of a cuboid. The box has an open top. NOT TO 4 cm SCALE 2 cm 5 cm (a) On the 1 cm 2 grid, draw a net of this box. [3] (b) The outside of the box is painted. Work out the total area that is painted. … cm2 [2]

5 marks

Mark scheme: 7(a) Correct net 3 B2 for 3 or 4 correct faces in the correct place provided no more than 6 faces or B1 for 1 or 2 correct faces in the correct place SC2 for correct net with internal lines missing 7(b) 66 2 M1 for 2 × (5 × 4 + 2 × 4) + 5 × 2 oe If 0 scored, SC1 for 76 surface area of closed box

This question in 0580/13 May/June 2021

2 This shape is drawn on a 1 cm 2 grid. Find the perimeter of the shape. … cm [1]

1 marks

Mark scheme: 2 24 1

This question in 0580/11 Oct/Nov 2021

16 Calculate the size of one interior angle of a regular octagon. … [2]

2 marks

Mark scheme: 16 135 2 M1 for 180 – (360 ÷ 8) oe or ( 8 – 2 ) × 180 oe 8

This question in 0580/11 Oct/Nov 2021

11 NOT TO 3 cm SCALE 2.5 cm 5 cm The diagram shows a cuboid. On the 1cm2 grid, draw an accurate net of this cuboid. One face has been drawn for you. [3]

3 marks

Mark scheme: 11 Correct ruled net 3 B2 for 3 or 4 correct faces in the correct places or B1 for 1 or 2 correct faces in the correct places

This question in 0580/12 Oct/Nov 2021

21 Work out the size of one interior angle of a regular 10-sided polygon. … [2]

2 marks

Mark scheme: 21 144 2 M1 for 180 – (360 ÷ 10) oe or (10 − 2) × 180 oe 10

This question in 0580/12 Oct/Nov 2021

17 7 cm NOT TO 12 cm SCALE y cm The area of this trapezium is 96 cm2. Find the value of y. y = … [3]

3 marks

Mark scheme: 17 9 3 M2 for 7 + y = 16 or M1 for 0.5 × 12 × (7 + y) = 96 oe

This question in 0580/13 Oct/Nov 2021

23 204 mm NOT TO SCALE 72 mm 180 mm Work out the area of this trapezium. … mm2 [5] Question 24 is printed on the next page.

5 marks

Mark scheme: 23 21 600 5 B3 for 168 OR M2 for 2042 – 1802 or better or M1 for […]2 + 1802 = 2042 oe A1 for 96 dep on M2 1 and M1 for (72 + their168) × 180 2 oe If zero scored, then SC1 for 72 × 180 alone or as part of total area calculation

This question in 0580/11 May/June 2022

11 Find the total surface area of a cuboid with length 8 cm, width 6 cm and height 3 cm. … cm2 [3]

3 marks

Mark scheme: 11 180 3 M2 for  2  8  6 8 3 3 6  oe or M1 for 8 × 6 or 8 × 3 or 3 × 6

This question in 0580/12 May/June 2022

4 Work out the area of a rectangle that is 9.5 m long and 6.8 m wide. … m2 [2]

2 marks

Mark scheme: 4 64.6 2 M1 for 9.5 × 6.8

This question in 0580/13 May/June 2022

15 8.6 cm NOT TO 7.5 cm SCALE 14.2 cm Work out the area of the trapezium. … cm2 [2]

2 marks

Mark scheme: 15 85.5 2 (8.6 + 14.2)  7.5 M1 for oe 2

This question in 0580/13 Oct/Nov 2022

18 NOT TO 14 cm SCALE h cm 10 cm The diagram shows a right-angled triangle. (a) Calculate the value of h. h = … [3] (b) Find the perimeter of this triangle. … cm [1]

4 marks

Mark scheme: 18(a) 9.8[0] or 9.797 to 9.798 3 M2 for 142 –102 oe or better or M1 for 102 + h2 = 142 oe or better 18(b) 33.8 or 33.79 to 33.80 1 FT 24 + their (a)

This question in 0580/13 Oct/Nov 2022

12 Work out the size of one interior angle of a regular 9-sided polygon. … [2]

2 marks

Mark scheme: 12 140 2 M1 for 180 − (360 ÷ 9) oe or (9 − 2)  180 oe 9

This question in 0580/12 Feb/March 2023

17 Find the size of an interior angle of a regular 15-sided polygon. … [2]

2 marks

Mark scheme: 17 156 2 M1 for 180 − (360 ÷ 15) oe or{(15 − 2)×180}÷ 15 oe

This question in 0580/12 May/June 2023

8 NOT TO 5 cm SCALE 3 cm 8 cm Find the total surface area of the cuboid. … cm2 [3]

3 marks

Mark scheme: 8 158 3 M2 for 2 8  5  8  3  5  3  or M1 for 8  5 or 8  3 or 5  3

This question in 0580/13 May/June 2023

15 Calculate the interior angle of a regular 9-sided polygon. … [2]

2 marks

Mark scheme: 15 140 2 180  ( 9 − 2 ) 360 M1 for or 180 – 9 9

This question in 0580/12 Oct/Nov 2023

12 10 cm NOT TO SCALE 4 cm 5 cm The diagram shows the net of a cuboid. (a) Work out the surface area of this cuboid. … cm2 [2] (b) Work out the volume of this cuboid. … cm3 [2]

4 marks

Mark scheme: 12(a) 220 2 M1 for [2]( 5  4 + 4  10 + 5  10 ) 12(b) 200 2 M1 for 5 4 10

This question in 0580/12 Feb/March 2024

5 The diagram shows a shape on a 1 cm2 grid. Find the area of this shape. … cm2 [1]

1 marks

Mark scheme: 5 12 1

This question in 0580/11 May/June 2024

16 NOT TO SCALE x + 7 3x - 12 The diagram shows a rectangle with length 3x - 12 and width x + 7 . Find an expression for the perimeter of the rectangle. Give your answer in its simplest form. … [3]

3 marks

Mark scheme: 16 8 x  10 or 2  4 x  5  3 B2 for 8 x  10 seen and spoilt final answer or M2 for 2  x  7   2  3 x  12  oe or M1 for x  7  3 x  12 oe or B1 for 8 x or  10 in final answer

This question in 0580/11 May/June 2024

25 12.8 cm J L NOT TO SCALE 12.8 cm K The diagram shows a shape made from a triangle JKL and a semicircle with diameter JL. JKL is an isosceles right-angled triangle with JK = JL = 12.8 cm. (a) Calculate the area of this shape. … cm2 [3] (b) Calculate the perimeter of this shape. … cm [4]

7 marks

Mark scheme: 25(a) 146 or 3 146.2 to 146.3 1 M1 for  12.8  12.8 2  1   12.8  2 M1 for       2   2  25(b) 51[.0] or 4 1 M1 for  12.8 51.00 to 51.01… 2 2 2 12.8 M2 for 12.8  12.8 or oe Sin 45 or M1 for 12.8 2  12.8 2 oe 12.8 or sin 45 = oe KL

This question in 0580/11 May/June 2024

7 The base of a cuboid measures 10 cm by 7 cm. The volume of the cuboid is 280 cm3. Calculate the height of the cuboid. … cm [2]

2 marks

Mark scheme: 7 4 2 M1 for 10 × 7 × [...] = 280 oe

This question in 0580/13 May/June 2024

12 The diagram shows a cuboid. NOT TO 3 cm SCALE 2 cm 6 cm On the 1 cm2 grid, complete a net of this cuboid. One face has been drawn for you. [3]

3 marks

Mark scheme: 12 Fully correct net 3 B2 for 3 or 4 extra correct faces in the correct places B1 for 1 or 2 extra correct faces in the correct places

This question in 0580/13 May/June 2024

11 The circumference of a wheel is 198.55 cm. Calculate the diameter of the wheel. Give your answer in millimetres. … mm [3]

3 marks

Mark scheme: 11 632 or 631.9 to 632.0… 3 B2 for 63.2 or 63.19 to 63.20…. as diameter 198.55 1985.5 or M1 for or   If zero scored, then B1 for a correct conversion from cm to mm

This question in 0580/11 Oct/Nov 2024

16 w cm NOT TO SCALE 8 cm 12 cm The diagram shows a trapezium with parallel sides of length 12 cm and w cm. The height of the trapezium is 8 cm. The area of the trapezium is 78 cm2. Find the value of w. w = … [2]

2 marks

Mark scheme: 16 7.5 2 (12 + w )  8 M1 for = 78 oe or better 2

This question in 0580/11 Oct/Nov 2024

18 The diagram shows a rectangle and two points, P and C, on a 1 cm2 grid. y 9 P 8 7 6 C 5 4 3 2 1 0 x 1 2 3 4 5 6 7 8 (a) Write down the coordinates of point C. ( … , … ) [1] (b) The rectangle is enlarged by scale factor 2 with centre of enlargement point C. Find the coordinates of the image of point P. ( … , … ) [2] (c) Find the area of the enlarged rectangle. … cm2 [1]

4 marks

Mark scheme: 18(a) (0, 5) 1 18(b) (14, 11) 2 B1 for each 18(c) 60 1

This question in 0580/11 Oct/Nov 2024

14 The diagram shows a trapezium. NOT TO 9.5 cm SCALE x cm 6 cm The area of the trapezium is 42 cm 2. Calculate the value of x. x = … [2]

2 marks

Mark scheme: 14 4.5 oe 2 1 M1 for 6 ( x + 9.5 ) = 42 oe or better 2 2 or for 42   −9.5 oe 6

This question in 0580/12 Oct/Nov 2024

20 Points A and B lie on a circle, centre O and radius r. A r O r B The area of the circle is 120 cm 2. Find the area of the right-angled triangle AOB. … cm2 [3]

3 marks

Mark scheme: 20 19.1 or 19.09… nfww 3 1 120 M2 for × ( )2 2  OR 120 M1 for oe implied by 6.18…  1 or for × (their r)2 2

This question in 0580/12 Oct/Nov 2024

10 The surface area of a cube is 121.5 cm 2. Calculate the length of one side of the cube. … cm [2]

2 marks

Mark scheme: 10 4.5 2 M1 for 121.5 ÷ 6

This question in 0580/13 Oct/Nov 2024

10 A shape is drawn on a 1 cm 2 grid. (a) Find the area of the shape. … cm2 [1] (b) On the grid, shade 50% of the shape. [1]

2 marks

Mark scheme: 10(a) 20 1 10(b) 10 squares shaded 1

This question in 0580/12 Feb/March 2025

24 A circle has radius 7 cm. A square has side x cm. The circumference of the circle is the same length as the perimeter of the square. Find the value of x. Give your answer in terms of r. x = … [3]

3 marks

Mark scheme: 24 7π 3 M2 for 2π×7=4x oe or 3.5π 2 or M1 for 2π  7 or14π or 4x

This question in 0580/12 Feb/March 2025

10 A cuboid has length 5 cm, width 2 cm and height 3 cm. (a) Draw a net of the cuboid on the 1 cm2 grid. [3] (b) Work out the volume of the cuboid. Give the units of your answer. … … [2]

5 marks

Mark scheme: 10(a) Fully correct net 3 B2 for 4 correct faces in correct places or B1 for 2 correct faces in correct places 10(b) 30 cm3 2 B1 for 30 B1 for cm3

This question in 0580/12 May/June 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

16 The diagram shows a point P and three triangles, A, B and C, on a 1 cm2 grid. y 7 6 5 4 C 3 B 2 1 A x - 4 -3 -2 -1 0 1 2 3 4 5 6 -1 -2 P -3 - 4 - 5 - 6 (a) Find the area of triangle B. … cm2 [1] (b) (i) Write down the coordinates of point P. ( … , … ) [1] - 20 (ii) Work out the coordinates of point P after a translation by the vector e o. 12 ( … , … ) [1] (c) Draw the image of triangle A after a reflection in the line y =-1. [2] (d) Describe fully the single transformation that maps (i) triangle A onto triangle B … … [3] (ii) triangle A onto triangle C. … … [3]

11 marks

Mark scheme: 16(a) 6 1 16(b)(i) 4, –3 1 16(b)(ii) –16, 9 1 FT their (b)(i) 16(c) Triangle drawn with coordinates 2 B1 for reflection in y = k or in x = −1 (1, −2 ) , ( 2, −2 ) and ( 2, −5 ) 16(d)(i) Enlargement 3 B1 for each [scale factor] 2 [centre] ( −1,0 ) 16(d)(ii) Rotation 3 B1 for each 90˚ clockwise [centre] (2,3 )

This question in 0580/12 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

14 4 cm NOT TO SCALE h cm 10 cm The diagram shows a trapezium. The area of the trapezium is 42 cm 2. Work out the value of h. h = … [2]

2 marks

Mark scheme: 14 6 nfww 2 1 M1 for (4 + 10) h = 42 oe or better 2

This question in 0580/13 May/June 2025

12 NOT TO SCALE 4 cm 3 cm 5 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: 12 Fully correct net 3 B2 for 3 correct extra faces in correct places or B1 for 1 correct extra face in correct place

This question in 0580/11 Oct/Nov 2025

27 NOT TO SCALE 8 cm The diagram shows a semicircle. The radius of the semicircle is 8 cm. Find the perimeter of the semicircle. Give your answer in terms of r in its simplest form. … cm [3]

3 marks

Mark scheme: 27 8π + 16 or 8(π + 2) 3 8 + 8 M2 for [perimeter =] × π + 8 + 8 oe 2 final answer or 8π + 16 oe seen and then spoilt 8 + 8 or M1 for [arc = ] × π oe 2

This question in 0580/11 Oct/Nov 2025

13 5 cm NOT TO 3 cm SCALE 4 cm 4 cm The diagram shows a right-angled triangular prism. Complete the net of this prism on the 1 cm2 grid. One face has been drawn for you. [3]

3 marks

Mark scheme: 13 Fully correct net 3 B2 for the two correct rectangles, in either order below the given face and two 3,4,5 triangles, one on each side or B1 for 1 correct rectangle in either place below the given face or for two 3, 4, 5 triangles, one each side

This question in 0580/12 Oct/Nov 2025

17 8 cm NOT TO SCALE 6 cm 14 cm Calculate the area of this trapezium. … cm2 [2]

2 marks

Mark scheme: 17 66 2 8 + 14 M1 for  6 oe 2

This question in 0580/12 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