Compound shapes and parts of shapes — Paper 3 · IGCSE Mathematics 0580

5 For A X B Examiner's Use NOT TO 10 cm SCALE 55º D 18 cm C The diagram shows a rectangular tile ABCD which has a shaded triangle DXB. DC = 18 centimetres, BC = 10 centimetres and angle ADX = 55°. (a) Calculate the area of triangle BDC. Answer(a) cm2 [2] (b) Calculate the length of AX. Answer(b) cm [2] (c) Calculate the shaded area. Answer(c) cm2 [3] (d) Calculate the length of BD. Answer(d) cm [2]

9 marks

Mark scheme: 5 (a) 90 2 M1 for 0.5 × 18 × 10 (b) 14.3 art 2 M1 for 10 × tan 55oe (c) 18.5 to 18.6 3 M1 for 0.5 × 10 × their (b) or M1 18 – their (b) 1 M1 x 10 x their BX 2 M1 for Their (a) – (0.5 × 10 × their (b)) (d) 20.6 art 2 M1 for √( 182 + 102) oe 9

This question in 0580/31 Oct/Nov 2006

10 For Examiner's Use Diagram 1 Diagram 2 Diagram 3 Diagram 4 Diagram 5 Each of the diagrams above shows one small shaded square and a number of small unshaded squares. The diagrams form a sequence. (a) Complete Diagram 5. [1] (b) Complete the table. Diagram 1 2 3 4 5 50 n Total number of 1 4 9 16 small squares Number of small 1 1 1 1 shaded squares Number of small 0 3 8 15 unshaded squares [7] (c) Diagram p has 9999 small unshaded squares. Find p. Answer(c) p = [1]

9 marks

Mark scheme: 10 (a) 5 by 5 shape 1 (b) First row 25 2500 n² 1, 1, 1 Independent Second row 1 1 1 1 All three Third row 24 2499 n² – 1 1, 1, 1 Independent (c) 100 1

This question in 0580/31 Oct/Nov 2010

2 For Examiner's Use The shape above is the net of a solid drawn on a 1 cm square grid. (a) Write down the geometrical name of the solid. Answer(a) [1] (b) Find the perimeter of the net. Answer(b) cm [1] (c) Work out For Examiner's (i) the area of one of the triangles, Use Answer(c)(i) cm2 [2] (ii) the volume of the solid. Answer(c)(ii) cm3 [2] (d) A cuboid of length 4 cm and width 3 cm has the same volume as the solid. Calculate the height of the cuboid. Answer(d) cm [2]

8 marks

Mark scheme: 2 (a) (triangular) prism 1 (b) 49.6 to 50.4 1 (c) (i) 6 2 M1 for ½ × 4 × 3 oe (ii) 42 2ft M1 for their (c)(i) × 7 (d) 3.5 2ft M1 for their (c)(ii) ÷ (3 × 4) oe

This question in 0580/31 May/June 2011

9 The diagram shows a regular hexagon inside a circle, centre O and radius 8 cm. For Each vertex of the hexagon is on the circumference of the circle. Examiner's A and B are two vertices of the hexagon and M is the midpoint of AB. Use NOT TO SCALE O 8 cm A M B (a) Calculate (i) angle AOB, Answer(a)(i) Angle AOB = [1] (ii) angle AOM. Answer(a)(ii) Angle AOM = [1] (b) Write down the length AB. Answer(b) AB = cm [1] (c) Show that the length of OM = 6.93 cm, correct to 3 significant figures. Answer(c) [2] (d) Calculate the area of triangle AOB. For Examiner's Use Answer(d) cm2 [2] (e) Calculate the shaded area. Answer(e) cm2 [4] Question 10 is printed on the next page.

11 marks

Mark scheme: 9 (a) (i) 60 1 (ii) 30 1ft ft their (i) ÷ 2 (b) 8 (cm) 1 x (c) cos 30 = or 82 = x2 + 42 M1ft ft their angle AOM or AB 8 6.928 … A1 (d) 27.7(2) cao 2 1 M1 × their (b) × 6.93 soi 2 (e) 34.7–34.9 4 M1 (circle) = π × 82 soi M1 (hexagon) = 6 × their (d) soi M1dep their circle – their hexagon

This question in 0580/33 May/June 2012

8 For D Examiner's Use NOT TO SCALE 42° E C F H 8.5 m 6 m G 2 m A 12 m B The diagram shows a house, built on level ground. ABCE is a rectangle with AB = 12 m and BC = 8.5 m. CDE is an isosceles triangle. (a) Use trigonometry to calculate DF. Answer(a) DF = m [2] (b) Calculate the area of triangle CDE. Answer(b) m2 [2] (c) A ladder, GH, of length 6 m, leans against the house wall. The foot of the ladder is 2 m from this wall. Calculate AH. Answer(c) AH = m [3] (d) This diagram shows the plan of the driveway to the house. For Examiner's Use HOUSE 12 m NOT TO SCALE 18 m 3 m 14 m Work out the perimeter of the driveway. Answer(d) m [2] (e) The driveway is made from concrete. The concrete is 15 cm thick. Calculate the volume of concrete used for the driveway. Give your answer in cubic metres. Answer(e) m3 [4]

13 marks

Mark scheme: 8 (a) 5.4(0) 2 M1 tan 42 = DF/6 or better (b) 32.4 2ft M1 12 × their 5.4 ft 2 (c) 5.66 3 M2 6 2 − 2 2 or better (accept √32 or 5.65) or M1 62 − 22 or better (accept 32 ) (d) 64 2 M1 12 + 18 + 14 + 3 + 2 + 15 (e) 33.3 cao 4 M1 (12 × 18) + (their (2) × 3) oe and A1 222 and M1 their 222 ft × 0.15

This question in 0580/33 Oct/Nov 2012

11 (a) Calculate the area of a circle of radius 6 cm. For Examiner′s Use Answer(a) … cm2 [2] (b) 6 cm NOT TO SCALE Each circle in this rectangle has a radius of 6 cm. The circles fi t exactly in the rectangle. Calculate the shaded area. Answer(b) … cm2 [4]

6 marks

Mark scheme: 11 (a) 113 or 113.09 to 113.112 2 M1 for π × 62 or better (b) 185 or 186 or 185.76 4 or 185.328 to 185.42 M1 for their (a) × 6 M1 for 24 × 36 soi, imp by 864 M1 for their (24 × 36) – their (their (a) × 6) ft their (a) for M3

This question in 0580/31 May/June 2013

5 (a) (i) Write down the name of a solid which is not a prism. Answer(a)(i) … [1] (ii) A prism has a cross-sectional area, A, and height, h. Write down an expression, in terms of A and h, for the volume of the prism. Answer(a)(ii) … [1] (b) The volume, V, of a cylinder with radius r and height h is V = πr2h . (i) Calculate the volume of a cylinder with radius 3 cm and height 12 cm. Answer(b)(i) … cm3 [2] (ii) Ravi puts 150 identical marbles in the cylinder. He fi lls the cylinder to the top with 160 cm3 of water. Find the volume of one marble. Give your answer correct to 2 signifi cant fi gures. Answer(b)(ii) … cm3 [4] (iii) Make r the subject of the formula V = πr2h . Answer(b)(iii) r = … [2] __________________________________________________________________________________________

10 marks

Mark scheme: 5 (a) (i) one of e.g. cone, sphere, pyramid 1 (ii) Ah 1 (b) (i) 339 2 M1 π × 32 × 12 their 339 - 160 (ii) 1.2 cao 4 M2 FT for soi 150 or M1 FT for their 339 – 160 soi A1 for 1.19... If A0 scored then B1 for correct rounding of their 3 sig fig or more answer. v v (iii) r = 2 M1 for r2 = πh πh

This question in 0580/33 May/June 2014

3 (a) The diagram shows part of a net for a cuboid drawn on a 1 cm2 grid. (i) Complete the diagram for the net of the cuboid. [1] (ii) Calculate the surface area of the cuboid. Answer(a)(ii) … cm2 [2] (iii) Calculate the volume of the cuboid. Give the units of your answer. Answer(a)(iii) … … [3] (b) A different cuboid has volume 60 cm3. Its sides are all integer lengths. All of its sides have length greater than 1cm. The length of one of its sides is a square number. Write down the dimensions of the cuboid. Answer(b) … cm by … cm by … cm [2]

8 marks

Mark scheme: 3 (a) (i) Correct net 1 (ii) 132 2 M1 for ( 2 × 5 + 2 × 8 + 5 × 8) × 2 oe or SC1 for correct area of their net, if it has 6 rectangles (iii) 80 2 M1 for 8 × 5 × 2 cm3 1 (b) 3, 4, 5 2 M1 for any 3 integers with a product of 60 or M1 for any 3 numbers with a product of 60, satisfying 2 of the conditions

This question in 0580/32 Oct/Nov 2015

8 The grid shows the first three diagrams in a sequence. Each diagram is made using small squares that are white or grey. Diagram 1 Diagram 2 Diagram 3 Diagram 4 (a) On the grid, draw Diagram 4. [1] (b) Write down the term to term rule for the number of grey squares. … [1] (c) Diagram number 1 2 3 4 n Number of small white squares 1 4 9 Number of small grey squares 3 5 7 Total number of small squares 4 9 16 Complete the table. [6] (d) Work out the number of small white squares in Diagram 18. … [1] (e) One of the diagrams has a total of 900 small squares. Work out its Diagram number. Diagram … [2] (f) Another diagram has 43 small grey squares. Work out the total number of small squares in this diagram. … [3]

14 marks

Mark scheme: 8(a) Correct diagram 1 8(b) Add 2 oe 1 8(c) 16 n2 oe 6 B2 for 16, 9 and 25 9 2n + 1 oe or B1 for 2 correct 25 (n + 1)2 oe B1 for n2 oe B2 for 2n + 1 oe or B1 for 2n + c or kn + 1 (k ≠ 0) B1 for (n + 1)2 oe 8(d) 324 1 8(e) 29 2 M1 for their (n + 1)2 = 900 or B1 for 900 or 30 8(f) 484 3 M1 for their ( 2 n + 1) = 43 M1dep on M1 scored for 43 + their n 2 2 or for their( n + 1)

This question in 0580/32 Feb/March 2020

6 NOT TO SCALE 3 cm 6 cm 4 cm The diagram shows a right-angled triangular prism. (a) On the 1 cm2 grid, complete the net of the prism. One face has been drawn for you. [3] (b) Work out the surface area of the prism. … cm2 [3] (c) Work out the volume of the prism. … cm3 [2]

8 marks

Mark scheme: 6(a) Correct net 3 B2 for 2 or 3 correct faces in the correct place or B1 for 1 correct face in the correct place 6(b) 84 3 M2 for 5 × 6 + 6 × 4 + 6 × 3 oe or better or 6 × (5 + 4 + 3) oe or better or 2( 12 × 3 × 4) oe or better or M1 for one correct area × 3 × 4 × 6 oe6(c) 36 2 M1 for 12

This question in 0580/31 Oct/Nov 2020

4 (a) The diagram shows the plan of part of Rachel’s garden. 14.6 m 3.2 m NOT TO SCALE 10.9 m 8.5 m Calculate the area. … m2 [3] (b) Rachel has a pond in her garden in the shape of a circle. The circumference of the pond is 4.25 m. Calculate the diameter of the pond. Give your answer in centimetres. … cm [3] (c) A plant pot is a cylinder with radius 15 cm and height 24 cm. Calculate the volume of the pot. … cm3 [2] (d) The diagram shows two mathematically similar plant pots. h NOT TO 21.6 cm SCALE 27 cm 33 cm The smaller pot has height 21.6 cm and diameter 27 cm. The larger pot has diameter 33 cm. Find the height, h, of the larger pot. h = … cm [2] (e) A shop sells bags of compost in three different sizes. Small Medium Large 30 litres 50 litres 75 litres $5.82 $9.45 $14.50 Work out which size of bag gives the best value. Show how you decide. … [3]

13 marks

Mark scheme: 4(a) 112.17 3 M2 for 14.6 × 10.9 – (14.6 – 8.5) × (10.9 – 3.2) oe or M1 for a correct method to find one of the six areas or B1 for 7.7 or 6.1 soi 4(b) 135 or 135.26 to 135.3 3 4.25 M1 for oe π B1 for their answer in metres seen correctly converted to cm or 425 [cm] seen 4(c) 17 000 or 16 960 to 16 970 2 M1 for π × 152 × 24 oe 4(d) 26.4 2 21.6 27 M1 for = oe or better h 33 4(e) Medium 3 M2 for 3 correct consistent divisions shown With correct comparisons made of the but either not evaluated to enough accuracy 3 bags with suitable accuracy shown or wrong bag selected or M1 for 2 correct consistent divisions shown for 2 bags

This question in 0580/33 Oct/Nov 2020

6 The diagram shows a point P, a shape S and lines A and B on a 1cm2 grid. y 9 P 8 7 6 A S 5 4 3 2 1 B x – 2 – 1 0 1 2 3 4 5 6 7 8 9 10 (a) Line A is parallel to line B. Explain what parallel means. … [1] (b) Write down the coordinates of point P. ( … , … ) [1] (c) (i) Write down the mathematical name for shape S. … [1] (ii) Work out the area of shape S. … cm2 [1] (d) (i) Find the gradient of line A. … [1] (ii) Write down the equation of line A. … [2]

7 marks

Mark scheme: 6(a) Correct explanation 1 6(b) (5,8) 1 6(c)(i) Parallelogram 1 6(c)(ii) 15 1 6(d)(i) 2 1 oe 5 6(d)(ii) 2 2 2 y = their x + 6 oe B1 for their x + 6 5 5 final answer 2 or y = their x + c , c ≠ 6 5 or y = mx + 6, m ≠ 0

This question in 0580/32 Feb/March 2021

7 (a) 15 m NOT TO 15 m SCALE 12 m 22 m The diagram shows a shape made from a quarter circle and a trapezium. Find the total area of this shape. … m2 [4] (b) h cm NOT TO 15.8 cm SCALE The diagram shows a rectangle. The area of the rectangle is 387.1 cm 2. Find the value of h. h = … [2] (c) NOT TO SCALE 15 cm 32 cm 18 cm The diagram shows a right-angled triangular prism. Find the volume of the prism. … cm3 [3]

9 marks

Mark scheme: 7(a) 399 or 398.7… 4 1 15 + 22 M3 for 152 × π × 4 + × 12 oe 2 or M2 for 152 × π × 14 oe 15 + 22 or 152 × π and × 12 oe 2 15 + 22 or M1 for 152 × π or × 12 oe 2 7(b) 24.5 2 M1 for 387.1 ÷ 15.8 7(c) 4320 3 M2 for 15 × 18 × 12 × 32 oe or M1 for 15 × 18 × 12 oe

This question in 0580/32 Oct/Nov 2021

2 (a) Write down the number of sides of a hexagon. … [1] (b) B A C In triangle ABC, AB = AC. (i) Write down the mathematical name for this type of triangle. … [1] (ii) Measure angle CAB. Angle CAB = … [1] (iii) Write down the mathematical name for angle CAB. … [1] (c) Show that the interior angle of a regular pentagon is 108°. [2] (d) B C NOT TO SCALE D A 248° ABCD is a parallelogram. The reflex angle at D is 248°. Find angle DCB. Angle DCB = … [2] (e) The angles of a triangle are in the ratio 3 : 5 : 7. Find the size of the largest angle in this triangle. … [3]

11 marks

Mark scheme: 2(a) 6 1 2(b)(i) Isosceles 1 2(b)(ii) 124 1 2(b)(iii) Obtuse 1 2(c) 360 M2 360 180 − [= 108] M1 for or (5 – 2)  180 5 5 (5  2)  180 or [= 108 ] 5 2(d) 68 2 360 2 (360  248) M1 for 248 – 180 or 2 or 180 – (360 – 248) or B1 for ADC = 112 2(e) 84 3 180 M2 for  j or better 3  5  7 where j = 1, 3, 5 or 7 7 or B1 for 180 or k 15

This question in 0580/31 May/June 2022

1 The diagram shows three quadrilaterals on a 1 cm 2 grid. y 10 9 8 7 B 6 5 A 4 3 2 1 x – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 8 – 1 – 2 – 3 – 4 – 5 C – 6 – 7 – 8 – 9 – 10 (a) Write down the mathematical name of quadrilateral A. … [1] (b) Find the area of quadrilateral A. … cm2 [1] (c) Describe fully the single transformation that maps quadrilateral A onto (i) quadrilateral B, … … [3] (ii) quadrilateral C. … … [2] (d) On the grid, draw the image of (i) quadrilateral C after a 90° anticlockwise rotation about the origin, [2] (ii) quadrilateral C after a reflection in the line x = 1. [2]

11 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) Kite 1 1(b) 4 1 1(c)(i) Enlargement 3 B1 for each [centre] (−8, 2) [scale factor] 2 1(c)(ii) Translation 2 B1 for each  0      10  OR Reflection in y = –1 oe 1(d)(i) Correct rotation 2 B1 for a correct 90° clockwise rotation about (6, −1), (7, −4), (6, −5), (5, −4) (0, 0) or correct orientation, incorrect position 1(d)(ii) Correct reflection 2 B1 for a correct reflection in y = 1 or in (3, −6), (6, −5), (7, −6), (6, −7) x = k, k ≠ 1

This question in 0580/33 May/June 2022

1 (a) l P Draw a line through point P that is perpendicular to line l. [1] (b) Write down the mathematical names for two different quadrilaterals with • two lines of symmetry and • rotational symmetry of order two. … and … [2] (c) The diagram shows a quadrilateral on a 1 cm2 grid. Find the area of this quadrilateral. … cm2 [1] (d) H G x° F 143° 103° NOT TO SCALE 82° E y° D The diagram shows a quadrilateral DEFG and a straight line FGH. (i) Angle DEF = 82° . Write down the mathematical name for this type of angle. … [1] (ii) Work out the value of x. Give a geometrical reason for your answer. x = … because … … [2] (iii) Work out the value of y. Give a geometrical reason for your answer. y = … because … … [2]

9 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) Ruled line drawn through P, 1 perpendicular to l. 1(b) rectangle rhombus 2 B1 for each 1(c) 11 1 1(d)(i) acute 1 1(d)(ii) 37 1 Angles on a straight line add to 180 1 1(d)(iii) 32 1 Angles in a quadrilateral add to 360 1

This question in 0580/32 Feb/March 2024

8 (a) 8.2 cm NOT TO 5.4 cm SCALE 12.6 cm Find the area of this trapezium. … cm2 [2] (b) NOT TO SCALE 4.5 cm b cm The area of this triangle is 15.3 cm 2. Find the value of b. b = … [2] (c) A circle has a circumference of 58.6 cm . Find the radius of this circle. … cm [2] (d) 28 cm NOT TO SCALE 12 cm The diagram shows a rectangle with two semicircles removed. Calculate the shaded area. … cm2 [4]

10 marks

Mark scheme: 8(a) 56.2 or 56.16 2 8.2  12.6 M1 for  5.4 oe 2 8(b) 6.8 2 M1 for 12 × 4.5 × b = 15.3 or better 8(c) 9.33 or 9.325 to 9.327 2 M1 for 58.6 ÷ [2]π 8(d) 223 or 222.8 to 222.91 4 M1 for 28 × 12 or 336 M1 for π × 62 oe M1 for their 336 − their 113

This question in 0580/33 May/June 2024

29 10 cm NOT TO SCALE 9 cm 16 cm This shape is made from a rectangle and a semicircle. The diameter of the semicircle is 10 cm. Calculate the perimeter of this shape. … cm [3] Question 30 is printed on the next page.

3 marks

Mark scheme: 29 55.7 or 55.70 to 55.71 3 M2 for 16 + 9 + 9 + (16 – 10) 1 + their( ×π×10) oe 2 1 or M1 for π × 10 [× ] 2 1 or 2× π × 5 [× ] oe 2 or 16 + 9 + 9 + (16 – 10) oe

This question in 0580/31 May/June 2025

9 8 cm 7 cm NOT TO 15 cm 12 cm SCALE 5 cm 23 cm Find the area of the shape. … cm2 [2]

2 marks

Mark scheme: 9 171 2 M1 for 12 × 8 + 5 × 15 oe or 23 × 5 + 8 × 7 oe or 15 × 5 + 8 × 7 + 8 × 5 oe or 23 × 12 – 15 × 7 oe

This question in 0580/33 Oct/Nov 2025