Compound shapes and parts of shapes — Paper 2 · IGCSE Mathematics 0580

22 For A Examiner's B Use 4.40 cm 3.84 cm X NOT TO SCALE C 9.40 cm D A, B, C and D lie on a circle. AC and BD intersect at X. (a) Give a reason why angle BAX is equal to angle CDX. Answer(a) [1] (b) AB = 4.40 cm, CD = 9.40 cm and BX = 3.84 cm. (i) Calculate the length of CX. Answer(b)(i) CX = cm [2] (ii) The area of triangle ABX is 5.41 cm2. Calculate the area of triangle CDX. Answer(b)(ii) cm2 [2] Question 23 is printed on the next page.

5 marks

Mark scheme: 22 (a) Angles in same segment 1 CX 4.9 (b) (i) 8.2(0) 2 M1 for = (= 2.136) oe .384 4.4 2 ∆  4.9  (ii) 24.7 2 M1 for =   (= 4.564) oe .541  4.4  2

This question in 0580/23 Oct/Nov 2011

6 The volumes of two similar cones are 36π cm3 and 288π cm3. The base radius of the smaller cone is 3 cm. Calculate the base radius of the larger cone. Answer … cm [3] _____________________________________________________________________________________

3 marks

Mark scheme: 288π 6 6 3 M2 for 3 × 3 36π 288π 36π or M1 for 3 × 3 or 3 × 3 36π 288π

This question in 0580/23 May/June 2013

18 NOT TO SCALE The two containers are mathematically similar in shape. The larger container has a volume of 3456 cm3 and a surface area of 1024 cm2. The smaller container has a volume of 1458 cm3. Calculate the surface area of the smaller container. Answer … cm2 [4] __________________________________________________________________________________________

4 marks

Mark scheme: 18 576 4 M1 for 14583456 or 14583456 M1 dep for 3 their fraction M1 for (their cube root )2

This question in 0580/22 May/June 2014

18 NOT TO SCALE 8 m 5 m 5 m 12 m The diagram shows the front face of a barn. The width of the barn is 12 m. The height of the barn is 8 m. The sides of the barn are both of height 5 m. (a) Work out the area of the front face of the barn. Answer(a) … m2 [3] (b) The length of the barn is 15 m. NOT TO Work out the volume of the barn. SCALE 15 m Answer(b) … m3 [1] __________________________________________________________________________________________

4 marks

Mark scheme: 1 18 (a) 78 3 M2 for 5 × 12 + × 12 × (8 – 5) or 2 1 × 6 × (5 + 8) × 2 oe 2 1 or M1 for 5 × 12, × 12 × (8 – 5) , 2 1 × 6 × (5 + 8) or 12 × 8 – (…) 2 (b) 1170 1FT 15 × their (a)

This question in 0580/22 May/June 2015

17 8 cm 32 cm 40 cm 125° NOT TO SCALE 48 cm The diagram shows the cross section of part of a park bench. It is made from a rectangle of length 32 cm and width 8 cm and a curved section. The curved section is made from two concentric arcs with sector angle 125°. The inner arc has radius 40 cm and the outer arc has radius 48 cm. Calculate the area of the cross section correct to the nearest square centimetre. … cm2 [5]

5 marks

Mark scheme: 17 1024 cao 5 B4 for 1023 to 1024.0… or 1020 or 125 2 125 2 M3 for × π × 48 − × π × 40 + 32 × 8 360 360 or 125 2 125 2 M1 for × π × 48 or × π × 40 360 360 and M1 for 32 × 8 + k π If B0 scored B1 for their more accurate decimal answer rounded correctly to an integer

This question in 0580/22 Oct/Nov 2016

14 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: 14 (a) 30 1 (b) 47.5 2 M1 for 4.5 × 5 oe

This question in 0580/23 Oct/Nov 2016

19 The diagram shows a pentagon ABCDE. A E B D C (a) Using a straight edge and compasses only, construct the bisector of angle BCD. [2] (b) Draw the locus of the points inside the pentagon that are 3 cm from E. [1] (c) Shade the region inside the pentagon that is • less than 3 cm from E and • nearer to DC than to BC. [1]

4 marks

Mark scheme: 19(a) Correct rulled bisector withw two 2 B1B for correcct ruled bisecctor with no//wrong arcs pairs of arccs 19(b) Correct arcc centre E raadius 3 cm 1 inside penttagon 19(c) Correct reggion shaded 1 DependentD ono at least B11 in part (a) anda 1 mark in partp (b) and a closed regiion

This question in 0580/22 Oct/Nov 2018

18 7 cm NOT TO SCALE 12 cm The diagram shows a solid made from a cylinder and a hemisphere, both of radius 7 cm. The cylinder has length 12 cm. Work out the total surface area of the solid. [The surface area, A, of a sphere with radius r is A = 4rr 2 .] … cm2 [4]

4 marks

Mark scheme: 18 990 or 989.58 to 989.73 4 M1 for 4 × π × 72 [÷2] M1 for π × 72 M1 for π × 7 × 2 × 12

This question in 0580/21 Oct/Nov 2020

19 100° NOT TO 8 cm SCALE x° 9 cm (a) Calculate the value of x. x = … [3] (b) Calculate the area of the triangle. … cm2 [3]

6 marks

Mark scheme: 19(a) 61.1 or 61.08 to 61.09... 3 8sin100 M2 for [sin x =] oe or better 9 9 8 or M1 for = oe sin100 sin x 19(b) 11.7 or 11.66 to 11.67 3 M2 for 1 × 9 × 8 × sin(180 − 100 − their (a)) oe 2 or M1 for 180 – 100 – their (a)

This question in 0580/22 Oct/Nov 2020

15 6 cm A B NOT TO SCALE X 8 cm 7 cm C D 12 cm In the diagram, AB is parallel to CD. AD and BC intersect at X. AB = 6 cm , CD = 12 cm , CX = 8 cm and DX = 7 cm . (a) Complete the statement. Triangle ABX is … to triangle DCX. [1] (b) Work out the length of BX. BX = … cm [2] (c) The area of triangle DCX is 26. 906 cm 2. Use this value to find the area of (i) triangle ABX, … cm2 [2] (ii) triangle ACX. … cm2 [1]

6 marks

Mark scheme: 15(a) Similar 1 15(b) 4 2 12 8 M1 for = oe or better 6 BX If 0 scored SC1 for answer 3.5 15(c)(i) 6.7265 or 6.73 or 6.726 to 6.727 2 2  1  M1 for scale factor 22 or   oe soi  2  15(c)(ii) 13.453 or 13.5 or 13.45 to 13.46 1 FT their (c)(i) × 2

This question in 0580/23 May/June 2021

18 Two bottles are mathematically similar. The small bottle has a capacity of 324 ml and a height of 12 cm. The large bottle has a capacity of 768 ml. Calculate the height of the large bottle. … cm [3]

3 marks

Mark scheme: 18 16 3 768 M2 for 12  3 oe 324 768 324 h 3 768 or M1 for 3 or 3 or 3 = 324 768 12 324 oe

This question in 0580/23 Oct/Nov 2022

18 Two solids are mathematically similar and have volumes 81 cm 3 and 24 cm 3. The surface area of the smaller solid is 44 cm 2. Calculate the surface area of the larger solid. … cm2 [3]

3 marks

Mark scheme: 18 99 3 2  81  3 M2 for 44   oe  24  1 1  81  3  24  3 or M1 for   oe or   oe  24   81   44 3  24  2 or = oe      Area   81 

This question in 0580/22 Feb/March 2023

22 B 41° 13.6 cm A C NOT TO SCALE D ABCD is a rhombus with side length 13.6 cm. Angle ABC = 41°. BAC is a sector of a circle with centre B. DAC is a sector of a circle with centre D. Calculate the shaded area. … cm2 [4]

4 marks

Mark scheme: 22 110 or 110.3… 4 1 41 M3 for [2 ×] (2( × 13.62 × sin 41) – ( × 2 360 π × 13.62)) oe OR  1  M1 for  13.62 × sin 41 oe    2  41 M1 for [2×] × π × 13.62 oe 360

This question in 0580/21 Oct/Nov 2023

16 NOT TO SCALE 6 cm 5 cm The diagram shows a solid made by joining a hemisphere to a cylinder. The radius of both the hemisphere and the cylinder is 6 cm. The height of the cylinder is 5 cm. Find the total surface area of the solid. Give your answer in terms of r. … cm2 [4]

4 marks

Mark scheme: 16 168 π 4 B3 for answer 168 OR M3 for 2 1 2 π  6 +  4π  6 + 2π 6 5 oe 2 OR To a maximum of 2 marks ignoring extra areas added or subtracted M1 for π × 62 1 2 M1 for 4 π 6 oe 2 M1 for 2 × π × 6 × 5

This question in 0580/22 May/June 2025

17 Solid A is mathematically similar to solid B. H cm NOT TO SCALE 7 cm Solid A Solid B The height of solid A is 7 cm and its surface area is 60 cm2. The surface area of solid B is 540 cm2. Calculate the height of solid B. … cm [3]

3 marks

Mark scheme: 17 21 3 540 60 M2 for 7 × oe or 7 ÷ oe 60 540 540 60 or M1 for oe or oe or 60 540  7 2 60 oe  =  H  540

This question in 0580/23 May/June 2025