Surface area and volume — Paper 3 · IGCSE Mathematics 0580

8 For C Examiner's Use NOT TO SCALE A B 6 cm C 4 cm NOT TO SCALE B A 8 cm The diagram above shows a cuboid and its net. (a) Calculate the total surface area of the cuboid. Answer(a) cm2 [3] (b) Calculate the volume of the cuboid. For Examiner's Use Answer(b) cm3 [2] (c) An ant walks directly from A to C on the surface of the cuboid. (i) Draw a straight line on the net to show this route. [1] (ii) Calculate the length of the ant’s journey. Answer(c)(ii) cm [3] (iii) Calculate the size of angle CAB on the net. Answer(c)(iii) Angle CAB = [3]

12 marks

Mark scheme: 8 (a) 208 3 M2 for 2(24 + 32 + 48) or 48 + 64 + 96 or 160 + 24 + 24 o.e. or M1 for 24 or 32 or 48 or 160 seen (b) 192 2 M1 for 6 x 8 x 4 (c) (i) straight line AC 1 (ii) 12.8 3 M2 for 10 + 8 or 100 + 64 or 164 or M1 for 10 + 8 or 100 + 64 or 164 or SC1 for complete correct use of Pythagoras (iii) 51.3 or 51.4 3 M1 for 10/8 and tan seen o.e. and M1 for tan 10/8 seen o.e. [the o.e include sin or cos with their (c)(ii)] or SC1 for complete correct use of a trig. ratio 12 104

This question in 0580/31 May/June 2005

6 The diagram shows a swimming pool with cross-section ABCDE. For The pool is 6 metres long and 3 metres wide. Examiner's AB = 2 m, ED = 1 m and BC = 3.6 m. Use 6 m 3 m NOT TO 1 m SCALE E A 2 m D B C 3.6 m (a) (i) Calculate the area of the cross-section ABCDE. Show your working. Answer(a)(i) m2 [4] (ii) Calculate the volume of the water in the pool when it is full. Give your answer in litres. [1 cubic metre is 1000 litres.] Answer(a)(ii) litres [2] (iii) One litre of water evaporates every hour for each square metre of the water surface. How many litres of water will evaporate in 2 hours? Answer(a)(iii) litres [2] For (b) Another pool holds 61 500 litres of water. Examiner's Jon uses a hosepipe to fill this pool. Use Water flows through the hosepipe at 1000 litres per hour. (i) Calculate how long it takes to fill the pool. Give your answer in hours and minutes. Answer(b)(i) hours minutes [2] (ii) Change 61 500 litres to gallons. [4.55 litres = 1 gallon.] Answer(b)(ii) gallons [1] (iii) Every 10 000 gallons of water needs 2.5 litres of purifier. How many litres of purifier does Jon use for this pool? Answer(b)(iii) litres [2] (iv) The purifier is sold in 1 litre bottles. How many bottles of purifier must Jon buy for this pool? Answer(b)(iv) [1]

14 marks

Mark scheme: 6 (a) (i) 10.8 www 4 M1 for evidence of shape being broken down (or 6 by 2 rectangle – triangle) +M1 for one correct rectangular area. +M1 for evidence of triangle calculation (ii) 32400 2√ SC1 for figs 322 to 323 or M1 for (a)(i) x 3 x 1000 (iii) 36 2 M1 for 6 x 3 x 2 (b) (i) 61 hours and 30 min 2 M1 for 61.5 (ii) art 13500 1 (iii) 3.38 2 M1 for their (b)(ii) x 2.5/10000 (iv) 4 1 √ rounding up [14]

This question in 0580/31 Oct/Nov 2005

5 (a) (i) Calculate the area of a circle with radius 3.7 centimetres. For Examiner's Use Answer(a)(i) cm2 [2] (ii) A can of tomatoes is a cylinder with radius 3.7 centimetres and height h centimetres. The volume of the cylinder is 430 cubic centimetres. Calculate h. Answer(a)(ii) h = [2] 2 cans NOT TO SCALE 3 cans 2 cans (b) Twelve cans fit exactly inside a box 3 cans long, 2 cans wide and 2 cans high. (i) Write down the length, width and height of the box. Answer(b)(i) length = cm width = cm height = cm [3] (ii) Calculate the volume of the box. Answer(b)(ii) cm3 [2] (iii) Calculate the percentage of the volume of the box occupied by the cans. Answer(b)(iii) % [3]

12 marks

Mark scheme: 5 (a) (i) 43.0 art or 43 B2 M1 for π x 3.7² (ii) 10.0 art or 10 B2ft M1 for 430 ÷ their (a)(i) ft (b) (i) (length) = 22.2 B1 accept length and width interchanged (width) = 14.8 B1 (height) = 20 B1ft ft is 2 x their (a)(ii) (ii) 6570 art B2 ft ft is their L x W x H from (b)(i) M1 for L x W x H ft (substituted) (iii) 78.5 (%) art B3 ft ft is 5160 ÷ their (b)(ii) x 100 but only if answer < 100 B1 for 12 x 430 or 5160 M1 for 5160 ÷ their (b)(ii) x 100 [12]

This question in 0580/31 May/June 2008

6 (a) Write down the name of a polygon with 8 sides. For Examiner's Use Answer(a) [1] (b) Find the size of the interior angle of a regular polygon with 8 sides. Answer(b) [2] (c) A regular 8-sided polygon, centre O, and side 8 cm, is shown below. M is the mid-point of the side AB. F E NOT TO SCALE G D O H C A M B 8 cm (i) Show that OM = 9.66 cm correct to 3 significant figures. Answer (c)(i) [3] (ii) Calculate the area of the triangle AOB. For Examiner's Use Answer(c)(ii) cm2 [2] (iii) Calculate the area of the polygon. Answer(c)(iii) cm2 [1] (d) The polygon forms the cross-section of a box. The box is a prism of height 12 cm. Calculate the volume of the box. Answer(d) cm3 [1] (e) The box contains 200 toffees in the shape of cuboids, 3 cm by 2 cm by 2 cm. Calculate (i) the total volume of the 200 toffees, Answer(e)(i) cm3 [2] (ii) the percentage of the volume of the box not filled by the toffees. Answer(e)(ii) % [3]

15 marks

Mark scheme: 6 (a) Octagon 1 (b) 135 2 M1 for 180 − (360 ÷ 8) oe (c) (i) Angle OAB = their (b)/2 or W1ft 67.5 or 22.5 correct values, angle AOM = 90 − their (b)/2 4 × tan ‘67.5’ or 4 ÷ tan ‘22.5’ M1 9.656… or 9.66 A1cao Dep on W1 and M1 (ii) 38.6 to 38.64 2 M1 for 0.5 × 8 × 9.66 (iii) 308.8 to 309.12 1ft Their (c) (ii) × 8 (d) 3705.6 to 3709.44 or 3710 1ft Their (c) (iii) × 12 (e) (i) 2400 2cao M1 for 3 × 2 × 2 × 200 (ii) 35.2(3…) to 35.3(0…) 3cao M1 for their ((d) − (e) (i)) soi. (d)− (e)(i) M1 for (d) × 100 (e)(i) Or M2 for (1 (d) ) × 100 SC1 for Answer 64.7 to 64.77

This question in 0580/31 May/June 2009

7 For C Examiner's Use NOT TO D SCALE 85 cm 65 cm A 50 cm B The diagram represents the cross-section of a storage box. AB = 50 cm, AD = 65 cm and BC = 85 cm. AD is parallel to BC. (a) Write down the geometrical name of the quadrilateral ABCD. Answer(a) [1] (b) Calculate angle DCB. Answer(b) Angle DCB = [3] (c) Calculate the area of the cross-section ABCD. Answer(c) cm2 [2] (d) The storage box is 96 cm long. Calculate the volume of the box. Write down the units of your answer. 96 cm Answer(d) [2]

8 marks

Mark scheme: 7 (a) Trapezium 1 (b) 68.2 3 M2 for tan = 50 ÷ (85–65) or better B1 for 85 – 65 (= 20) seen in working area (c) 3750 2 M1 for 0.5(65 + 85) × 50 (d) 360 000 1ft ft their (c) × 96, correct to a minimum of 3sf cm3 1 units mark independent

This question in 0580/32 Oct/Nov 2010

6 For Examiner's Use NOT TO SCALE 8 cm D C 6 cm 20 cm A 12 cm B The diagram shows a prism of length 20 cm. The cross-section of the prism is a trapezium, ABCD, with AB parallel to DC. AB = 12 cm, DC = 8 cm and the perpendicular distance between AB and DC is 6 cm. (a) Calculate (i) the area of the trapezium ABCD, Answer(a)(i) cm2 [2] (ii) the volume of the prism. Answer(a)(ii) cm3 [1] (b) The prism is solid and made of brass. For Examiner's (i) One cubic centimetre of brass has a mass of 8.5 grams. Use Calculate the mass of the prism. Give your answer in kilograms. Answer(b)(i) kg [2] (ii) Brass costs $2.26 for one kilogram. How much will the brass cost to make this prism? Give your answer correct to 2 decimal places. Answer(b)(ii) $ [2]

7 marks

Mark scheme: 6 (a) (i) 60 2 M1 for full method for area with correct values (ii) 1200 1ft ft their (i) × 20 (b) (i) 10.2 2ft SC1 for figs 102 or M1 for (a)(ii) × 8.5 ÷ 1000 ft their (a)(ii) × 8.5 ÷ 1000 and SC in same way (ii) 23.05 2ft ft their (b)(i) × 2.26 M1 for 23.052 or 23.1 or (b)(i) × 2.26 or B1ind for correctly rounding to 2 dp an answer with more than 2 dp

This question in 0580/33 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

10 For Examiner's Use x m 2 m 10 m NOT TO SCALE 5 m The diagram shows a ramp in the form of a triangular prism. The cross-section is a right-angled triangle of length 5 m and height 2 m. (a) Find the value of x. Give your answer correct to 1 decimal place. Answer(a) x = [3] (b) Find the area of the cross-section. Answer(b) m2 [2] (c) The ramp is 10 m long. Calculate the volume of the ramp. Answer(c) m3 [1] (d) Calculate the total surface area of all five faces of the ramp. For Examiner's Use Answer(d) m2 [3] (e) Each face of the ramp is painted. Paint costs $2.25 per square metre. Calculate the total cost of the paint. Answer(e) $ [1] Question 11 is printed on the next page.

10 marks

Mark scheme: 10 (a) 5.4 cao 3 M1 for 22 + 52 (= x2) implied by 29 A1 5.38(51..) or 29 or 5.39 B1 indep for rounding their answer to 1 decimal place (b) 5 2 M1 for 0.5 × 5 × 2 oe (c) 50 1ft 10 × their (b) (d) 134 3ft M2 for 2 × their (b) + 10 × their (a) + 2 × 10 + 5 × 10 or better M1 for any 3 faces correct (e) 301.5(0) 1ft Their (d) × 2.25

This question in 0580/31 Oct/Nov 2011

6 For E NOT TO Examiner's SCALE Use F 16 cm D C 24 cm A 30 cm B The diagram shows a wedge in the shape of a triangular prism. AB = 30 cm, AF = 16 cm and BC = 24 cm. Angle BAF = 90°. (a) Calculate (i) the area of triangle ABF, Answer(a)(i) cm2 [2] (ii) the volume of the wedge. Answer(a)(ii) cm3 [1] (b) (i) Calculate BF. Answer(b)(i) cm [2] (ii) 1.6 cm NOT TO SCALE A coin with diameter 1.6 cm is rolled down the sloping surface of the wedge. It travels in a straight line parallel to BF, starting on FE and ending on BC. Calculate the number of complete turns it makes. Answer(b)(ii) [3] (c) On the grid, complete the net of the wedge. For The base and one of the triangles have been drawn for you. Examiner's Use Each square on the grid represents a square of side 4 centimetres. [3] (d) Calculate the surface area of the wedge. Answer(d) cm2 [3]

14 marks

Mark scheme: 6 (a) (i) 240 2 M1 for 0.5 × 30 × 16 (ii) 5760 1ft ft is (a)(i) × 24 (b) (i) 34 2 M1 for (FB 2) = 16 2 + 30 2 (ii) 6 3 M1 for (circumference) = 1.6 × π M1 dep their (b)(i) ÷ their 1.6π (6.76 implies M1, M1) If 0 scored either SC1 for their (b)(i) ÷ 3.2 × π and then SC1 for truncating correctly If M1 or still 0 scored then SC1 for truncating correctly any number with at least 1 decimal place (c) 6 by 4 rectangle above 1 6 by their 8.5 rectangle below 1ft ft (b)(i) ÷ 4 Correct triangle on AB 1 1 1 (d) 2400 3cao M2 for × 30 × 16 + × 30 × 16 + 16 × 24 + 2 2 30 × 24 + their 34 × 24 (M1 for any 3 areas) If 0, SC2 for 150 or SC1 for 120 (3 rectangles) or SC1 for 30 (2 triangles)

This question in 0580/32 Oct/Nov 2011

1 (a) Indira buys 1250 square metres of land to build a hotel. For Each square metre of land costs $12 . Examiner's Use Calculate the cost of the land. Answer(a) $ [1] (b) The cost of the land is 3% of the cost of the hotel. Calculate the cost of the hotel. Answer(b) $ [2] (c) The hotel has 84 rooms. The types of room are in the ratio family : double : single = 3 : 5 : 4 . Calculate the number of double rooms. Answer(c) [2] (d) Each single room is a cuboid, 4.5 m long, 3.2 m wide and 2.8 m high. Calculate the volume of a single room. Answer(d) m3 [2] (e) The total hotel income for the first year was $992 000 . For 3 Examiner's (i) The hotel spent of the total hotel income on staff wages. Use 8 Calculate the staff wages. Answer(e)(i) $ [1] (ii) The hotel also spent $420 000 on food. Calculate how much of the total hotel income was left. Answer(e)(ii) $ [2] (iii) Calculate $420 000 as a percentage of $992 000 . Give your answer correct to 1 decimal place. Answer(e)(iii) % [2] (f) To make improvements, Indira borrows $3 500 at a rate of 6% per year simple interest. She pays back all the amount at the end of 3 years. Calculate the total amount she needs to repay. Answer(f) $ [3]

15 marks

Mark scheme: Qu. Answers Mark Part Mark 1 (a) ($) 15 000 1 (b) ($) 500 000 2ft M1 for their 15 000 ÷ 3 × 100 (c) 35 2 M1 for 84 ÷ ( 3 + 5 + 4) or 84 ÷ 12 (d) 40.32 or 40.3 2 M1 for 4.5 × 3.2 × 2.8 (e) (i) ($) 372 000 1 (ii) ($) 200 000 2ft M1 for 992 000 − (their (e)(i) + 420 000) (iii) 42.3 cao 2 M1 for 420 000 ÷ 992 000 × 100 or better (f) ($) 4130 3 M1 for 3500 × 3 × 6 ÷ 100 oe A1 for 630 soi After M1A0 then SCB1 for their 630 + 3500

This question in 0580/32 May/June 2012

3 Here is a scale drawing of a shop floor, EFGH. For The scale is 1 centimetre represents 2 metres. Examiner's Use F G H Scale: 1 cm to 2 m E (a) What is the mathematical name of the shape EFGH? Answer(a) [1] (b) What type of angle is angle EFG? Answer(b) [1] (c) Find the actual length, in metres, of the side EH. Answer(c) m [2] (d) Measure angle FEH. Answer(d) Angle FEH = [1] (e) Complete this part using ruler and compasses only. All construction arcs must be clearly shown. A table is placed • nearer to E than to H and • less than 14 m from H. By constructing two loci on the scale drawing, find and label the region R, where the table is placed. [5] (f) The shop sells shoes which are packed in boxes. Each box is a cuboid 33.2 cm long, 16.8 cm wide and 11 cm high. Calculate the volume of one of these shoe boxes. Answer(f) cm3 [2]

12 marks

Mark scheme: 3 (a) quadrilateral 1 (b) obtuse 1 (c) 23.6–24.4 2 M1 for 11.8 – 12.2 (d) 31–35 1 (e) construction of perpendicular 5 B1 for two pairs of arcs, same radius, centres E bisector of EH and H part circle centre H radius 7 cm B1 for bisector within 2mm of correct one, ± 2° of indication of region correct angle B1 for part circle centre H B1 for radius 7 cm B1ft for an indication of the region, ft dependent on at least B2 from above (f) 6135.36 or 6135.4 or 6135 or 6140 2 M1 for 33.2 × 16.8 × 11

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

6 Finn is going camping. For Examiner′s The diagram shows his tent. Use 2.5 m B NOT TO SCALE 1.5 m 1.2 m A M C ABC is an isosceles triangle. M is the midpoint of AC. AB = 1.5 m and BM = 1.2 m. (a) Show that AM = 0.9 m. Answer(a) [2] (b) Use trigonometry to calculate angle ABM. Answer(b) Angle ABM = … [2] (c) The tent is a prism of length 2.5 m. For Examiner′s The area of triangle ABC is 1.08 m2. Use Calculate the volume of the tent. Give the units of your answer. Answer(c) … … [2] (d) Calculate the surface area of the tent, including the base. Answer(d) … m2 [3] _____________________________________________________________________________________

9 marks

Mark scheme: 6 (a) AM2 + 1.22 = 1.52 or [AM2] = 1.52 – 1.22 M1 [AM=] √ (1.52 – 1.22) or √( 2.25 – 1.44) or √0.81 M1dep 2.1 (b) 36.9 or 36.87 or 36.8[6 … ] 2 M1 for cos[ABM] = oe or better 5.1 (c) 2.7 1 m3 1 indep (d) 14.2 or 14.16 3 M2 for 2 × 0.5 × 2 × 0.9 × 1.2 + 2.5 × 2 × 0.9 + 2 × 2.5 × 1.5 or better or M1 for 2.5 × 2 × 0.9 or 2 × 2.5 × 1.5 or better if M0 then SC1 for 13.41 IGCSE – May/June 2013 0580 32

This question in 0580/32 May/June 2013

7 For Examiner′s D Use E C NOT TO SCALE 2.25 m 1.5 m A B 1.0 m The diagram shows a trapezium ABCD. AB = 1.0 m, AD = 2.25 m, BC = 1.5 m and angle DEC = 90°. (a) Using trigonometry, calculate angle DCE. Answer(a) Angle DCE = … [3] (b) Calculate the area of the trapezium ABCD. Answer(b) … m2 [2] (c) ABCD is the cross-section of a box. The box is 2 m long. Calculate the volume of the box. D C 2 m B A Answer(c) … m3 [1] (d) On the grid, complete the net of the box. For Examiner′s The base and one face of the box have been drawn for you. Use The scale is 2 cm to 1 m. [4] _____________________________________________________________________________________

10 marks

Mark scheme: 7 (a) [Angle DCE =] 36.9 or 36.8699 to 36.9 3 B1 for [DE =] 0.75 soi their DE M1 for than DCE = 0.1 (b) 1.875 or 1.88 2 M1 for 0.5 × (1.5 + 2.25) × 1.0 oe (c) 3.75 1FT their (b) × 2 IGCSE – October/November 2013 0580 33 (d) 3 rectangles and 1 trapezium correctly 4 B1 for rectangle to right 6 by 8 squares placed on the grid with correct scale and B1 for an accurate and correctly placed size. trapezium B1 for a rectangle to left 9 by 8 squares B1 for rectangle 5 by 8 squares and further to the left

This question in 0580/33 Oct/Nov 2013

5 E F D A NOT TO 7 cm SCALE 5 cm B 4 cm C The diagram shows a solid in the shape of a triangular prism. AC = 5 cm, BC = 4 cm and CD = 7 cm. Angle ABC = 90°. (a) What does the word prism tell you about the solid in the diagram? … [1] (b) Show that AB = 3 cm. [2] (c) Calculate the volume of the prism. Give the units of your answer. … … [4] (d) On the 1 cm2 grid, complete the net of the prism. Two faces have been drawn for you. [3] (e) Calculate the surface area of the prism. … cm2 [2]

12 marks

Mark scheme: 5 (a) constant cross-sectional area oe 1 (b) [AB2] + 42 = 52 M1 [AB] = 5 2 − 4 2 = 9 M1 3 × 4 (c) 42 3 M2 for × 7 2 3 × 4 or M1 for 2 If zero scored SC1 for answer 84 cm3 1 B1 independent (d) correct net drawn 3 M1 for 7 × 4 rectangle drawn in correct place M1 for one 3,4,5 triangle drawn correctly

This question in 0580/32 Feb/March 2016

4 (a) A cuboid has length 4 cm, width 3 cm and height 1.5 cm. (i) Calculate the volume of the cuboid. … cm3 [2] (ii) On the grid, draw an accurate net of the cuboid. One face has been drawn for you. [3] (b) 5x + 4 NOT TO x + 1 SCALE 3x 2x In the diagram, all lengths are in centimetres. (i) Find an expression, in terms of x, for the perimeter of the shape. Give your answer in its simplest form. … [2] (ii) The perimeter of the shape is 72 cm. Work out the value of x. x = … [2] (iii) Calculate the total area of the shape. … cm2 [3]

12 marks

Mark scheme: 4 (a) (i) 18 2 M1 for 4 × 3 × 1.5 (ii) Correct net 3 B2 for 6 rectangles correctly positioned to form net of cuboid or B1 for two 4 cm by 3 cm rectangles, two 4 cm by 1.5 cm rectangles and two 3 cm by 1.5 cm rectangles seen (b) (i) 16x + 8 or 8(2x + 1) 2 M1 for 2(5x + 4 + 3x) oe or 16x + k as answer or for 3x + 4 or 2x – 1 seen

This question in 0580/32 May/June 2016

8 (a) A cuboid measures 6 cm by 3 cm by 2 cm. (i) On this 1 cm2 grid, complete the net of the cuboid. [3] (ii) Calculate the volume of the cuboid. … cm3 [2] (b) Write down the mathematical name of this shape. … [1] (c) Mark an obtuse angle on this trapezium. [1] (d) A regular polygon has an exterior angle of 22.5°. Work out how many sides this polygon has. … [2] (e) NOT TO SCALE 20 cm 6 cm x cm The diagram shows a shape made from a semi-circle, radius 6 cm, and a right-angled triangle. (i) Show that x = 16. [2] (ii) Calculate the area of the shape. … cm2 [5]

16 marks

Mark scheme: 8 (a) (i) Correct net 3 B2 for 3 or 4 correct faces in correct position or B1 for 1 or 2 correct faces in correct position (ii) 36 2 M1 for 6 × 3 × 2 oe (b) Hexagon 1 (c) Obtuse angle indicated 1 360 360 (d) 16 2 M1 for or = 22.5 22.5 n 180 ( n − 2 ) or = 157.5 oe n (e) (i) 20 2 − 12 2 M2 M1 for 202 = 122 + x2 or [x2 =] 202 – 122 π6 2 (ii) 153 or 152.5 to 152.6 5 M2 for soi by 56.5… . or 18 π 2 or M1 for π62 soi by 113 or 113.0…. or 113.1…. or 36 π M1 for 0.5 × 12 × 16 soi by 96 M1dep for their 56.5... + their 96 dep on at least M1 earned soi

This question in 0580/31 Oct/Nov 2016

3 (a) Tariq wants to buy some orange juice. He sees these offers in a shop. Offer A Offer B Offer C 1-litre carton 2-litre carton Pack of 4 1-litre cartons $0.65 $1.25 $2.56 Work out the lowest amount Tariq could pay for 5 litres of orange juice. Show how you decide. Tariq buys … cartons. The lowest amount is $ … [3] (b) Bottle P contains 1.5 litres of lemonade. 1 Bottle Q contains 3 more lemonade than bottle P. Work out how much lemonade is in bottle Q. … litres [2] (c) Tariq makes a fruit drink. He mixes 500 ml of orange juice, 200 ml of pineapple juice and 1 litre of lemonade. (i) Write the ratio orange juice : pineapple juice : lemonade in its simplest form. … : … : … [2] (ii) Tariq makes more of this fruit drink. Work out the total amount of fruit drink he makes when he uses 2 litres of orange juice. Give your answer in litres. … litres [3] (d) Tariq pours 300 cm3 of fruit drink into a glass. The glass is in the shape of a cylinder with radius 3.5 cm. The height of the drink in the glass is h cm. NOT TO SCALE h cm 3.5 cm Work out the value of h. h = … [2] (e) The capacity of a jug is 750 ml correct to the nearest 10 ml. Write down the upper and lower bounds of the capacity of the jug. Upper bound = … ml Lower bound = … ml [2]

14 marks

Mark scheme: 3 (a) 2 B and 1 A selected, with 2 M1 for one correct cost for 5 litres at least one other or B1 for 0.625 or 0.64 combination and its value seen or 2 B and 1 A selected, with 1 Independent 0.625 and 0.64 seen 3.15 selected 1 (b) 2 2 M1 for [1.5 + ] × 1.5 oe soi by 0.5 3 (c) (i) 5 : 2 : 10 2 M1 for 500 : 200 : 1000 oe (ii) 6.8 3 B2 for answer 6800 or 2 M2 for × 17 oe or for 4 × (0.5 + 0.2 + 1) 5 or for 4 × (500 + 200 + 1000) oe 5 2000 or M1 for soi or for oe soi by 4 17 500 (d) 7.79 or 7.80 or 7.794 to 2 M1 for 300 = π × 3.52 × h or better implied by 7.795 300 (38.4to38.5) (e) 755 2 B1 for one correct or both values reversed 745

This question in 0580/32 Oct/Nov 2016

6 (a) A bag contains 5 white and 6 black marbles. (i) A marble is chosen at random from the bag and then replaced. Write down the probability that the marble is black. … [1] (ii) Delilah adds some more black marbles to the bag. The probability of choosing a black marble is now 23 . How many black marbles did she add to the bag? … [2] (b) A white marble costs w cents and a black marble costs b cents. (i) 2 white marbles and 5 black marbles cost 155 cents. Complete the equation. 2w + 5b = … [1] (ii) 3 white marbles and 10 black marbles cost 290 cents. Write down an equation to show this information. … [1] (iii) Solve your two equations to find the value of w and the value of b. You must show all your working. w = … b = … [3] (c) A black marble is weighed and its mass, m grams, is 35 g correct to the nearest 5 g. Complete the statement about the value of m. … G m 1 … [2] (d) Each marble is a sphere of diameter 3 cm. On the grid, draw an accurate net of the smallest closed box a marble can fit in. NOT TO SCALE [2]

12 marks

Mark scheme: 6 6 (a) (i) oe 1 11 1 (ii) 4 2 M1 for 10 black marbles or is 5 marbles 3 (b) (i) 155 1 (ii) 3 w + 10b = 290 oe 1 (iii) [w] 20 3 M1FT for correct method to eliminate one [b] 23 variable A1 for w = 20 A1 for b = 23 If zero scored, SC1 for either: 2 correct answers given or 2 values satisfying one of their original equations (c) 32.5 , 37.5 1,1 SC1 for both answers correct but reversed (d) correct net 2 M1 for 5 correctly placed 3 cm by 3 cm squares and one incorrect or missing

This question in 0580/32 Feb/March 2017

5 Simone makes a fruit cake. (a) (i) The recipe needs 175 g sugar, 200 g butter and 225 g flour. Write the ratio sugar : butter : flour in its simplest form. … : … : … [2] (ii) The recipe needs a total of 600 g of fruit. The ratio sultanas : currants : raisins = 4 : 3 : 1. Work out the mass of each type of fruit. Sultanas = … g Currants = … g Raisins = … g [3] (b) The cake can be made in either a cylindrical tin or a square-based tin. (i) The cylindrical tin has radius 10 cm. NOT TO In this tin the cake is 5 cm high. SCALE Show that the volume of the cake is 1600 cm3, correct to 2 significant figures. [2] (ii) In the square-based tin, the cake is 4 cm high. NOT TO The volume of the cake is 1600 cm3. SCALE Work out the length of a side of the base of this tin. … cm [2] (c) The mass, m grams, of the cake is 1340 g, correct to the nearest 20 g. Complete the statement about the value of m. … G m < … [2] (d) The number of kilocalories (kcal) in one quarter of the cake is 1290 kcal. The whole cake is cut into 12 equal pieces. (i) Calculate the number of kilocalories in one piece of cake. … kcal [2] (ii) The daily recommended number of kilocalories for Simone is 2000 kcal. Work out the number of kilocalories in one piece of cake as a percentage of 2000 kcal. … % [1]

14 marks

Mark scheme: 5(a)(i) 7 : 8 : 9 2 M1 for 35 : 40 : 45 oe If zero scored, SC1 for 7,8,9 in wrong order 5(a)(ii) 300 3 600 M1 for or better 225 ( 4 + 3 + 1) 75 and A1 for one correct answer in the correct place or for two correct answers not in the correct place 5(b)(i) π ×102 × 5 M1 1570 to 1571 A1 5(b)(ii) 20 2 M1 for 1600 = 4 ×l 2 or better 5(c) 1330 1 1350 1 SC1 for correct but answers reversed 5(d)(i) 430 2 M1 for 1290 × 4 or for recognising that 1290 is 3 pieces 5(d)(ii) 21.5 1FT their ( d )( i ) 1FT is × 100 2000

This question in 0580/33 May/June 2017

7 Nora makes a birthday cake. (a) Nora has a packet containing 250 g of cherries. 7 She uses of the cherries in the cake. 10 Find the mass of cherries she has left. … g [2] (b) The cake is made by putting a small cylinder of cake on top of a large cylinder of cake. The radius of the large cylinder is 15 cm. 8 cm The radius of the small cylinder is 8 cm. The height of each cylinder is 10 cm. NOT TO 10 cm SCALE 10 cm 15 cm (i) Calculate the total volume of the cake. … cm3 [3] (ii) Nora wraps a ribbon around the large cylinder. The ribbon is 4 cm longer than needed to go all the way around this cylinder. Calculate the length of this ribbon. … cm [3] (c) The mass, m grams, of the cake is 1250 g, correct to the nearest 10 g. Complete this statement about the value of m. … G m 1 … [2]

10 marks

Mark scheme: 7(a) 75 2 7  M1 for − 1  × 250 oe  10  or B1 for answer 175 7(b)(i) 9080 or 9079 to 9081 3 M2 for π × 82 × 10 + π × 152 × 10 soi or M1 for π × 8 2 [× 10 or × 20 ] soi or π × 15 2 [× 10 or × 20 ] soi 7(b)(ii) 98.2 or 98.3 3 M1 for 2 × π × 15 soi or 98.24 to 98.26 M1 for their circumference + 4 7(c) 1245, 1255 2 B1 for one correct or both values correct but reversed

This question in 0580/31 Oct/Nov 2018

5 (a) Draw all the lines of symmetry on the rectangle below. [2] (b) Work out the size of one interior angle of a regular hexagon. … [3] (c) The diagram shows a plan of a garden. 40 m NOT TO 10 m SCALE 24 m 24 m 12 m 12 m Work out the area of the garden. … m2 [3] (d) A NOT TO x° SCALE 132° B C D The diagram shows an isosceles triangle, ABC. BCD is a straight line. Find the value of x. x = … [2] (e) The diagram shows a hollow metal pipe in the shape of a cylinder. NOT TO SCALE 18 cm (i) This diagram shows the cross-section of the pipe. NOT TO 7.5 cm SCALE 6 cm Work out the shaded area. … cm2 [3] (ii) The cylinder is 18 cm long. Work out the volume of the metal. … cm3 [1] (iii) Work out the curved surface area of the outside of the pipe. … cm2 [3]

17 marks

Mark scheme: 5(a) Two correct lines 2 B1 for 1 correct line and no diagonals or 2 correct lines and one diagonal 5(b) 120 3 M2 for 180 − (360 ÷ 6) oe or (6 – 2) × 180 ÷ 6 oe or M1 for 360 ÷ 6 oe or (6 – 2) × 180 oe 5(c) 736 3 M2 for 40 × 24 − (24 − 10) × (40 − 2 × 12) oe or M1 for one of these two areas or B1 for one of 14 or 16 seen OR M2 for 2 × (24 × 12) + 10 × (40 − 2 × 12) or M1 for one of these three areas or B1 for one of 14 or 16 seen OR M2 for 40 × 10 + 2 × (24 – 10) × 12 or M1 for one of these three areas or B1 for one of 14 or 16 seen 5(d) 84 2 M1 for 180 − 2 × (180 − 132) or better or B1 for 48 seen 5(e)(i) 63.6 or 63.61 to 63.63 3 M2 for 7.52 × π − 62 × π or better or M1 for 7.52 × π or 62 × π or better 5(e)(ii) 1140 or 1150 or 1144 to 1146 1 FT their (e)(i) × 18 evaluated 5(e)(iii) 848 or 848.2 to 848.4 3 M2 for 2 × π × 7.5 × 18 or better or M1 for 2 × π × 7.5 or better If 0 scored SC1 for 679 or 678.5 to 678.7

This question in 0580/32 Oct/Nov 2018

8 (a) A cylinder has a radius of 6 cm and a height of 17 cm. Show that the volume of this cylinder is 1923 cm3, correct to 4 significant figures. [2] (b) Q NOT TO SCALE P R O Points P, Q and R are on the circumference of a semicircle, centre O and radius 8 cm. Angle POQ = 90°. Calculate the shaded area. … cm2 [5]

7 marks

Mark scheme: 8(a) π × 62 × 17 M1 1922.6 to 1922.91 A1 8(b) 36.5 or 36.53 to 36.54… 5 B2 for 100.53 to 100.54… or 32π or M1 for [0.5 ×] π × 82 oe and B2 for 64 or M1 for [0.5 ×] 16 × 8 oe

This question in 0580/31 May/June 2019

2 (a) B A O C In the diagram, A, B and C are points on the circle, centre O. (i) On the diagram, draw a chord. [1] (ii) Explain why angle ABC is 90°. … [1] (b) The length of the edge of a cube is 8 cm. Calculate the surface area of this cube. … cm2 [2] (c) A cuboid measures 5 cm by 4 cm by 2 cm. (i) Calculate the volume of this cuboid. Give the units of your answer. … … [3] (ii) On the 1 cm2 grid, draw an accurate net of this cuboid. One face has been drawn for you. [3]

10 marks

Mark scheme: 2(a)(i) Chord correctly drawn 1 2(a)(ii) Angle [in a] semicircle [is 90º] 1 2(b) 384 2 M1 for 8 × 8[× 6] 2(c)(i) 40 2 M1 for 5 × 4 × 2 cm3 1 2(c)(ii) Correct net 3 B2 for 4 more correct faces in correct position B1 for 2 or 3 more correct faces in correct position

This question in 0580/31 Oct/Nov 2019

6 (a) NOT TO 3 cm SCALE 2 cm 6 cm The diagram shows a cuboid. On the 1 cm2 grid, complete the net of the cuboid. One face has been drawn for you. [3] (b) A cube has a surface area of 384 cm2. Find the length of one of its sides. … cm [3] (c) 4 cm NOT TO SCALE 12 cm 7 cm The diagram shows a right-angled triangular prism. Work out the volume of the prism. … cm3 [3]

9 marks

Mark scheme: 6(a) Correct ruled net of cuboid 3 B2 for 3 or 4 further correct faces drawn in the correct places or B1 for 1 or 2 further correct faces drawn in the correct places 6(b) 8 3 M1 for 384 ÷ 6 M1dep for their 64 6(c) 168 3 M2 for (7 × 4 ÷ 2) × 12 oe or M1 for (7 × 4 ÷ 2) or their area × 12

This question in 0580/32 May/June 2020

3 (a) NOT TO SCALE 6 m 8 m The diagram shows a rectangular patio with sides 6 m and 8 m. (i) Work out the perimeter of the patio. … m [1] (ii) Henri covers the patio floor with square tiles. The tiles are 0.5 m by 0.5 m. Work out the number of tiles he needs. … [2] (b) The diagram shows the net of a solid on a 1 cm2 grid. (i) Write down the mathematical name for the solid. … [1] (ii) Work out the volume of the solid. … cm3 [2] (c) A square has perimeter 12x. Find an expression, in terms of x, for the area of the square. Give your answer in its simplest form. … [3] (d) B NOT TO SCALE A C 10 cm The diagram shows a semicircle with diameter AC. B is a point on the circumference and AB = BC. Work out the area of triangle ABC. … cm2 [3]

12 marks

Mark scheme: 3(a)(i) 28 1 3(a)(ii) 192 2 8 6 M1 for × oe 0.5 0.5 or B1 for 16 and 12 or 4 tiles = 1 m2 soi 3(b)(i) Cuboid 1 3(b)(ii) 10 2 M1 for 5 × 2 [× 1] 3(c) 9x 2 3  12 x  2 M2 for   oe  4  12 x or M1 for oe 4 If 0 scored, SC1 for final answer kx 2 3(d) 25 3 B1 for height is 5 [cm] 1 M1 for × 10 × 5 oe 2

This question in 0580/33 May/June 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

3 (a) Write down the mathematical name for this (i) quadrilateral, … [1] (ii) solid. … [1] (b) The area of a square is 64 cm2. Work out the length of one side of the square. … cm [1] (c) The length, l, of a rectangle is 3 cm longer than the width, w. The perimeter of the rectangle is 26 cm. Calculate the length, l, and the width, w. l = … cm w = … cm [3] (d) A cuboid measures 6 cm by 3 cm by 1 cm. (i) On the 1 cm2 grid, draw an accurate net of this cuboid. One face has been drawn for you. [3] (ii) Calculate the surface area of the cuboid. … cm2 [2]

11 marks

Mark scheme: 3(a)(i) Trapezium 1 3(a)(ii) Cylinder 1 3(b) 8 1 3(c) 8 3 M2 for 4w = 20 oe 5 or M1 for w + w + 3 + w + w + 3 = 26 oe If 0 scored, SC2 for correct answers reversed or SC1 for 2 answers where l + w = 13 3(d)(i) Correct net 3 B2 for 4 more correct faces in correct position or B1 for 2 or 3 more correct faces in correct position 3(d)(ii) 54 2 M1 for [2 ×] (6 × 3 + 6 × 1 + 3 × 1) oe

This question in 0580/32 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

7 (a) The diagram shows the net of a cuboid on a 1 cm 2 grid. A N B M C L D K E J F I G H (i) The net is folded to form the cuboid. (a) Write down which two corners join to corner A. … [1] (b) Write down the edge which joins with KL. … [1] (ii) Find the total surface area of the cuboid. … cm2 [2] (iii) Find the volume of the cuboid. … cm3 [2] (b) The diagram shows a cylinder with length L cm. The radius of the cylinder is 3.2 cm and the volume is 775 cm 3. NOT TO SCALE L cm (i) Calculate the value of L. L = … [3] (ii) Calculate the volume of a solid sphere with radius 3 cm. 4 3 [The volume, V, of a sphere with radius r is V = rr .] 3 … cm3 [2] (iii) Four of these spheres are placed inside the cylinder. Calculate the percentage of the cylinder that is empty. … % [3]

14 marks

Mark scheme: 7(a)(i)(a) C and G 1 7(a)(i)(b) HI 1 7(a)(ii) 76 2 M1 for one relevant area calculation 7(a)(iii) 40 2 M1 for 5 × 2 × 4 oe 7(b)(i) 24.1 or 24.08 to 24.09… 3 775 M2 for oe π × 3.2 2 or M1 for [775 =] π × 3.22 × L or better 7(b)(ii) 113 or 113.09 to 113.11… 2 4 × π × 33 M1 for oe 3 7(b)(iii) 41.6 to 41.7 3 775 −×4 their (b)(ii) M2 for [× 100] oe 775 4 × their (b)(ii) or [100 –] × 100 oe 775 or M1 for 775 – 4 × their (b)(ii) oe 4 × their (b)(ii) or oe 775 If 0 scored, SC1 for answer 85.4 to 85.42

This question in 0580/31 Oct/Nov 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

5 (a) A closed box, in the shape of a cuboid, has length 5 cm, width 4 cm and height 2 cm. (i) Draw a net of the box on the 1cm2 grid. [3] (ii) A container is a cube with volume 1m3. Work out the maximum number of these boxes that can be packed into this container. … [3] (b) A shop sells three different sized boxes of rice. The boxes all have the same cost per kilogram. NOT TO SCALE Box A Box B Box C 80 rupees $3.50 750 g 1.35 kg (i) Work out the cost in rupees of box B. … rupees [2] (ii) $1 = 64 rupees. Calculate the mass of box C. Give your answer in kilograms. … kg [3] (c) Change 75cm3into litres. Give your answer in standard form. … litres [2]

13 marks

Mark scheme: 5(a)(i) Correct ruled net 3 B2 for 4 or 5 correct rectangles drawn in correct positions relative to each other or B1 for one correct face drawn 5(a)(ii) 25 000 3 100 × 100 × 100 M2 for oe 2 × 4 × 5 or M1 for 100 × 100 × 100 or 0.02×0.04×0.05 or 2×4×5 or 50, 25, 20 If 0 scored, SC1 for final answer figs 25 5(b)(i) 144 2 figs135 1.35 80 750 M1 for or or or 750 figs750 750 80 oe or B1 for 1350 or 0.75[0] 5(b)(ii) 2.1 3 3.5 × 64 × figs75 M2 for oe 80 80 or M1 for 3.5× 64 or 64 5(c) 7.5 × 10−2 cao 2 75 M1 for oe 1000 If 0 scored, SC1 for correctly converting their number to standard form, provided their number is <1

This question in 0580/32 Feb/March 2022

4 (a) NOT TO SCALE 4 cm 7 cm 3 cm The diagram shows a right-angled triangular prism. (i) On the 1 cm 2 grid, complete a net of this prism. One face has been drawn for you. [4] (ii) Work out the volume of this prism. … cm3 [2] (b) NOT TO SCALE The diagram shows a rectangle with 6 congruent circles inside. Each circle touches the adjacent circles and the sides of the rectangle. The radius of each circle is 8 cm. (i) Show that the length of the rectangle is 48 cm. [1] (ii) Find the area of the rectangle. Give the units of your answer. … … [3] (iii) Calculate the percentage of the rectangle that is shaded. … % [3]

13 marks

Mark scheme: 4(a)(i) Fully correct net 4 B1 for 5  7 rectangle and B2 for 3 correct faces in the correct places or B1 for 1 or 2 correct faces in the correct places 4(a)(ii) 42 2 1 M1 for 2  4  3  7 oe 4(b)(i) 2  8  3 or 16 + 16 + 16 1 or 16  3 or 8  6 or 8 + 8 + 8 + 8 + 8 + 8 4(b)(ii) 1536 2 M1 for 32  48 oe cm2 1 4(b)(iii) 21.5 or 21.45 to 21.47 3 M1 for π  82 [ 6] oe (b)(ii)  their 1206 M1 for  100  oe (b)(ii) their 1206 or 100    100 oe (b)(ii)  their 1206  or  1   100  oe  (b)(ii) 

This question in 0580/31 May/June 2022

4 (a) The diagram shows the net of a cuboid. NOT TO SCALE 5 cm 7.8 cm A (i) Work out the area of the shaded rectangle, A. … cm2 [2] (ii) The volume of the cuboid is 468 cm 3. Complete the statement. The dimensions of the cuboid are … cm by … cm by … cm [2] (b) A cylinder has a radius of 8 cm and a height of 12 cm. Calculate, in terms of r, the volume of the cylinder. … cm3 [2] (c) NOT TO 7 cm SCALE 12 cm The diagram shows a circle with a diameter of 7 cm and a parallelogram with a base of 12 cm. The circle touches two of the sides of the parallelogram. Calculate the shaded area. … cm2 [3]

9 marks

Mark scheme: 4(a)(i) 39 2 M1 for 7.8  5 or B1 for 7.8 and 5 marked on two correct sides of rectangle A 4(a)(ii) 5 7.8 12 2 468 468 M1FT for oe or for 7.8  5 their(i) 4(b) 768π final answer 2 M1 for π  82  12 oe 4(c) 45.5 or 45.51 to 45.52 3 M2 for 12  7  π  3.52 oe or M1 for 12  7 oe or M1 for π  3.52 oe

This question in 0580/32 May/June 2022

3 Miguel works in an office. (a) It takes Miguel 40 minutes to drive to work. (i) He leaves home at 07 45. What time does he arrive at work? … [1] (ii) Miguel drives to work at an average speed of 57 km/h. Show that he drives 38 km. [2] (b) White paper costs w cents per sheet and pink paper costs p cents per sheet. Miguel uses 56 sheets of white paper and 21 sheets of pink paper. Write down an expression, in terms of w and p, for the total cost, in cents, of the paper he uses. … cents [2] (c) Miguel has a closed box of pens. The box is in the shape of a cuboid measuring 20 cm by 12 cm by 7 cm. Calculate the surface area of the box. … cm2 [3] (d) Miguel records the length of time of each telephone call he receives, correct to the nearest minute. 7 15 6 28 8 21 17 19 20 12 11 19 12 3 20 23 14 9 4 18 (i) Complete the frequency table. You may use the tally column to help you. Time (minutes) Tally Frequency 0 - 5 6 - 10 11 - 15 16 - 20 21 - 25 26 - 30 [2] (ii) Draw a bar chart to show this information. Complete the scale on the frequency axis. Frequency 0 0 – 5 6 – 10 11 – 15 16 – 20 21 – 25 26 – 30 Time (minutes) [3] (iii) Use the bar chart to write down the modal group. … — … [1]

14 marks

Mark scheme: 3(a)(i) 08 25 1 3(a)(ii) 40 2 40 57  [= 38] M1 for or 57  40 60 60 3(b) 56w + 21p final answer 2 B1 for 56w or 21p in final answer or for 56w + 21p seen then spoilt 3(c) 928 3 M2 for [2 ](20  12 + 20  7 + 12  7) oe or M1 for (20  12) or (20  7) or (12  7) 3(d)(i) 2 4 5 6 2 1 2 B1 for 4 or 5 correct frequencies If 0 scored SC1 for correct tallies if frequency column blank or all frequencies correct but not in the frequency column 3(d)(ii) Suitable scales on y-axis 1 Bars at correct height 1 FT their frequency Bars equal width 1 3(d)(iii) 16 – 20 1 FT their bar chart

This question in 0580/31 Oct/Nov 2022

6 (a) Write down the mathematical name of this solid. … [1] (b) B C A D 104° NOT TO SCALE x° E The diagram shows triangle BCE and a straight line ABCD. BE = CE and angle ABE = 104°. Find the value of x. x = … [2] (c) Work out the size of one interior angle of a regular polygon with 15 sides. … [2] (d) B y° O NOT TO A 38° SCALE C A, B and C are points on a circle, centre O. (i) Write down the mathematical name of the line BC. … [1] (ii) Draw a tangent to the circle at point B. [1] (iii) The area of the circle is 245.5 cm 2. Calculate AB. AB = … cm [3] (iv) Find the value of y. y = … [2]

12 marks

Mark scheme: 6(a) Cylinder 1 6(b) 28 2 M1 for 180 – 104 oe 6(c) 156 2 360 (15 − 2 )180 M1 for 180 – oe or oe 15 15 6(d)(i) Chord 1 6(d)(ii) Tangent drawn at point B 1 6(d)(iii) 17.7 or 17.67 to 17.68 3 M2 for [2] 245.5  π oe or M1 for 245.5 ÷ π oe 6(d)(iv) 52 2 M1 for 180 – 90 – 38 oe or B1 for [angle ACB =] 90 correctly identified

This question in 0580/31 Oct/Nov 2022

5 (a) NOT TO SCALE This rectangle has an area of 12 cm2 and a perimeter of 16 cm. NOT TO SCALE This shape is made from six of these rectangles. Find the area and perimeter of this shape. Area = … cm2 Perimeter = … cm [4] (b) NOT TO SCALE 11.7 cm 8.4 cm 16 cm Find the area of this triangle. … cm2 [2] (c) A circle has a circumference of 28 cm. Work out the radius of the circle. … cm [2] (d) A cube has a volume of 125 m3. Work out the surface area of the cube. … m2 [3]

11 marks

Mark scheme: 5(a) [a =] 72 4 B1 for [a =] 72 [p =] 52 AND B3 for [p =] 52 or B1 for lengths of 6 and 2 M1 for use of 6l + 8w 5(b) 67.2 2 16  8.4 M1 for oe 2 If M0 scored, SC1 for 101 to 101.4 …. 5(c) 4.46 2 M1 for 28 ÷ 2π oe 5(d) 150 3 M2 for 6 × ( 3 125 )2 oe or M1 for 3 125 oe

This question in 0580/32 May/June 2023

3 (a) The diagram shows a shape on a 1 cm 2 grid. Work out the area of the shape. … cm2 [1] (b) 7 cm NOT TO SCALE 12 cm Work out the perimeter of the rectangle. … cm [1] (c) A square has an area of 841 cm 2. Work out the length of one side of the square. … cm [1] (d) The diagram shows a cuboid made from 1 cm 3 cubes. NOT TO SCALE (i) Work out the volume of the cuboid. … cm3 [1] (ii) Write down the dimensions of a different cuboid that can be made using all of the cubes. … cm by … cm by … cm [1] (e) NOT TO SCALE The diagram shows three small circles and one large circle. The large circle has radius 20 cm. The small circles each have radius 4 cm. Work out the shaded area. Give your answer in terms of r. … cm2 [3] (f) The exterior angle of a 9-sided regular polygon is 40°. (i) Work out the size of the interior angle of this polygon. … [1] (ii) NOT TO SCALE x° x° The diagram shows a regular pentagon inside part of a regular 9-sided polygon. Work out the value of x. x = … [4]

13 marks

Mark scheme: 3(a) 9.5 1 3(b) 38 1 3(c) 29 1 3(d)(i) 48 1 3(d)(ii) Correct dimensions 1 3(e) 352π cao nfww 3 M2 for π20 2 3 π4 2 oe or M1 for π20 2 or π4 2 oe 3(f)(i) 140 1 3(f)(ii) 16 4 B2 for 108 360 or M1 for 180  oe or 5  5  2   180 oe 5 AND 140  108 M1 for or 2 their (f)(i)  their108 2

This question in 0580/33 May/June 2023

4 (a) The diagram shows a cuboid. NOT TO 2 cm SCALE 3 cm 5 cm (i) On the 1cm2 grid, complete the net of the cuboid. One face has been drawn for you. [3] (ii) Calculate the surface area of the cuboid. … cm2 [2] (b) The diagram shows two solids: a cube and a right-angled triangular prism. NOT TO SCALE 4 cm 6 cm 9 cm x cm Both solids have the same volume. Calculate the value of x. x = … [4]

9 marks

Mark scheme: 4(a)(i) Fully correct net 3 B2 for 3 or 4 extra correct faces in the correct places or B1 for 1 or 2 extra correct faces in the correct places 4(a)(ii) 62 2 M1 for [2 ] (5  2 + 3  2 + 5  3) oe 4(b) 12 4 M3 for 18x = 216 oe or 216 ÷ 18 oe OR M1 for 63 or 6  6  6 or 216 1 M1 for  4  x  9 oe or 18x 2 M1 for their 18x = 216 oe or better

This question in 0580/31 Oct/Nov 2023

5 (a) Zena records the number of letters she posts on each of 12 days. 3 7 3 8 7 1 0 6 5 1 7 2 (i) Write down the mode. … [1] (ii) Find the median. … [2] (b) Zena posts 6 parcels. • The lightest parcel has a mass of 4.6 kg. • The heaviest parcel has a mass of 6.2 kg. • The other 4 parcels have a mean mass of 5.01 kg. Calculate the mean mass of the 6 parcels. … kg [3] (c) Zena pays 105 euros to post a parcel. The exchange rate is $1 = 0.84 euros. Work out the cost in dollars to post the parcel. $ … [1] (d) The cost to post a box increases from $22.68 to $44. Work out the percentage increase in the cost. … % [2] (e) The diagram shows a parcel in the shape of a cuboid. NOT TO SCALE 3 cm 2 cm 6 cm (i) Complete the net of the parcel on the 1 cm 2 grid. Two faces have been drawn for you. [2] (ii) Find the volume of the parcel. … cm3 [1]

12 marks

Mark scheme: 5(a)(i) 7 1 5(a)(ii) 4 2 M1 for an ordered list of at least the first 7 or last 7 values or B1 for 3 and 5 both identified 5(b) 5.14 3 M2 for (4 × 5.01 + 4.6 + 6.2) ÷ 6 oe or M1 for 4 × 5.01 + 4.6 + 6.2 or B1 for 20.04 5(c) 125 1 5(d) 94 or 94.00… 2 44 − 22.68 M1 for [×100] 22.68  44  or  − 1  [×100]  22.68  44 or ×100 [– 100] 22.68 5(e)(i) Fully correct net 2 B1 for 2 or 3 correct extra faces in correct places 5(e)(ii) 36 nfww 1

This question in 0580/33 Oct/Nov 2023

7 (a) The scale drawing shows the position of a castle, C. The scale is 1 centimetre represents 2 kilometres. North C Scale: 1 cm to 2 km Micah walks at 4.8 km/h for 3 hours on a bearing of 236° from C, to his house, H. Mark the position of H on the scale drawing. [3] (b) A restaurant, R, is on a bearing of 083° from C. (i) Work out the bearing of C from R. … [2] (ii) The distance, d km, from R to C is 5 km, correct to the nearest kilometre. Complete this statement about the value of d. … G d 1 … [2] (c) A model of the castle is made. On the model, the length of one of the castle walls is 5 centimetres. The actual length of the wall is 90 metres. Find the scale of the model in the form 1| n . 1| … [2] (d) The castle has two kitchens with rectangular floors. F G B C NOT TO SCALE 5.6 m 9.2 m A 8.4 m D E x m H Rectangle ABCD is mathematically similar to rectangle EFGH. Calculate the value of x. x = … [2] (e) The castle has a cylindrical tower. The tower has a radius of 2.4 m and a height of 25 m. Calculate the curved surface area of the tower. Give the units of your answer. … … [3] Question 8 is printed on the next page.

14 marks

Mark scheme: 7(a) H correctly marked 3 B2 for H 7.2 cm from C 7.2 cm from C on bearing 236° or M1 for 4.8×3 B1 for H on bearing 236 from C 7(b)(i) 263 2 M1 for 83  180 oe or indicates correct angle on diagram 7(b)(ii) 4.5 5.5 2 B1 for each If 0 scored SC1 for both correct but reversed 7(c) [1 : ] 1800 2 M1 for 5 : 9000 or 0.05:90 9000 90 or or 5 0.05 or B1 for answer figs 18 7(d) 13.8 2 9.2 5.6 M1 for  oe or better x 8.4 7(e) 377 or 376.9 to 377.04 2 M1 for 2 2.4  25 m2 1

This question in 0580/31 May/June 2024

8 B 3.6 m A NOT TO SCALE 4.7 m E F 1.7 m C D 5.5 m The diagram shows a plan, ABCDE, of the floor of a room in Jo’s house. F is a point inside the room. (a) (i) Show that EF = 1.9 m . [1] (ii) Work out AF. AF = … m [1] (b) Calculate the area of the floor. … m2 [3] (c) A cupboard in the room is in the shape of a cuboid. The area of the base of the cupboard is 1.2 m2 and the height of the cupboard is 2.3 m. Calculate the volume of the cupboard. Give the units of your answer. … … [2] (d) Jo buys 275 floor tiles which cost $1.64 each. Calculate the total cost of the floor tiles. $ … [1] (e) Jo builds a patio in the shape of a semicircle with radius 2.3 m. Calculate the area of the patio. … m2 [2] Question 9 is printed on the next page.

10 marks

Mark scheme: 8(a)(i) 5.5 – 3.6 [= 1.9] 1 8(a)(ii) 3 1 8(b) 23 3 M2 for 4.7 × 3.6 + 1.9 × 1.7 + 0.5 × 1.9 × their (a)(ii) or 3.6 ×their(a)(ii) + 5.5 × 1.7 + 0.5 × 1.9 × their(a)(ii) or 5.5 × 4.7 − 0.5 × 1.9 × their (a)(ii) or 0.5  (3.6 + 5.5)  their (a)(ii) + 1.7  5.5 or 0.5  (1.7 + 4.7)  1.9 + 3.6  4.7 or M1 for 4.7 × 3.6 + 1.9 × 1.7 or 3.6 × their (a)(ii) + 5.5 × 1.7 or 0.5 × 1.9 × their (a)(ii) or 5.5 × 4.7 or 0.5  (3.6 + 5.5)  their (a)(ii) or 0.5  (1.7 + 4.7)  1.9 8(c) 2.76 1 m3 1 8(d) 451 1 8(e) 8.31 or 8.309 to 8.311 2 M1 for [0.5]π × 2.32 oe

This question in 0580/32 May/June 2024

3 Jack does a survey about cycling. (a) The bar chart shows the percentage of people in each age group who use a bicycle. 100% 80% 60% Percentage of people 40% 20% 0% 0–9 10–19 20–29 30–39 40–49 50–59 60–69 70+ Age in years (i) Write down the percentage of people aged 60 to 69 who use a bicycle. … % [1] (ii) 980 people in the survey are in the 30–39 age group. Work out how many of these people use a bicycle. … [2] (b) Jack makes 18 cycling trips in one year. Each cycling trip lasts 23 minutes. Find the total time Jack spends cycling in this year. Give your answer in hours and minutes. … h … min [2] (c) The table shows where 240 people cycle the most. Pie chart Number of people sector angle Roads 84 126° Cycle paths 72 Parks 48 Other 36 (i) Complete the table. [2] (ii) Complete the pie chart to show this information. Roads 126° [2] (d) A bicycle costs $720. Carlo pays one-fifth of the cost as a deposit. He pays the rest of the money in equal monthly payments of $16. Work out how many monthly payments Carlo makes. … [3]

12 marks

Mark scheme: 3(a)(i) 30 1 3(a)(ii) 392 2 40 M1 for  980 oe 100 3(b) 6 hours 54 mins 2 M1 for 18 × 23 oe 3(c)(i) 108 2 B1 for 1 correct angle in correct place 72 or M1 for 126[k ] where k = 1, 72, 48 54 84 or 36 or for 360[m ] where m = 1, 72, 48 or 36 240 3(c)(ii) Correct pie chart 2 FT their table if angles add up to 360 B1FT for one sector drawn correctly 3(d) 36 nfww 3  4  M2 for   720   16 oe  5  4 720 or M1 for  720 or oe 5 5 or k ÷ 16 , k ≠ 720

This question in 0580/31 Oct/Nov 2024

7 (a) NOT TO 10 cm SCALE 4 cm 7 cm Find the perimeter of the triangle. … cm [1] (b) The diagram shows a shape made from rectangles. 18.6 cm 4 cm NOT TO 7 cm 7 cm SCALE 13.5 cm Calculate the area of the shape. … cm2 [3] (c) The diagram shows a right-angled triangle ABC. B NOT TO 27.2 cm SCALE A C 24 cm Calculate the area of the triangle. … cm2 [5] (d) Calculate the volume of a sphere with diameter 5.25 cm. 4 [The volume, V, of a sphere with radius r is V = rr 3.] 3 … cm3 [2]

11 marks

Mark scheme: 7(a) 21 1 7(b) 118.1 cao 3 M2 for 18.6 × 4 + (13.5 – 4) × (18.6 –7 – 7) oe or 2 × 4 × 7 + 13.5 × (18.6 –7 –7) oe or 18.6 × 13.5 – 2 ×7 × (13.5 – 4) oe or 2×4×7+ (13.5–4)×(18.6–7–7)+ (18.6– 7–7)×4 oe or B1 for 9.5 or 4.6 seen 7(c) 153.6 cao 5 B3 for 12.8 or M2 for 27.22 – 242 oe or M1 for AB2 + 242 = 27.22 oe AND M1 for 0.5 × 24 × their AB oe 7(d) 75.8 or 75.76 to 75.78 2 4  5.25 3 M1 for   oe 3  2 

This question in 0580/31 Oct/Nov 2024

8 (a) The diagram shows the net of a solid. 10 cm x cm NOT TO SCALE x cm (i) Write down the mathematical name of the solid. … [1] (ii) Find the volume of the solid when x = 4 . … cm3 [2] (iii) Write down an expression, in terms of x, for the volume of the solid. … cm3 [1] (iv) Find the value of x when the volume of the solid is 360 cm3. x = … [2] (b) (i) Complete the table of values for y = 2 x 2 + x . x 0 1 2 3 4 5 y 0 3 10 [2] (ii) On the grid, draw the graph of y = 2 x 2 + x for 0 G x G 5 . y 60 50 40 30 20 10 0 0 1 2 3 4 5 x [3] (iii) Use your graph to solve the equation 2x 2 + x = 30 for 0 G x G 5 . x = … [1]

12 marks

Mark scheme: 8(a)(i) Cuboid 1 8(a)(ii) 160 2 M1 for 4 × 4 × 10 oe 8(a)(iii) 10x2 oe final answer 1 8(a)(iv) 6 nfww 2 M1 for 10x2 = 360 oe or better or their (a)(iii) = 360 oe or better or 360 ÷10 8(b)(i) 21, 36, 55 2 B1 for 2 correct 8(b)(ii) Correct smooth curve 3 B2FT for 5 or 6 points correctly plotted or B1FT for 3 or 4 points correctly plotted 8(b)(iii) 3.5 to 3.7 1 FT their value of x when y = 30

This question in 0580/31 Oct/Nov 2024

4 (a) Calculate the volume of a cylinder with radius 7.8 cm and height 15 cm. … cm3 [2] (b) A cube has a volume of 3375 cm3. Calculate the surface area of this cube. … cm2 [3] (c) Area A = 37 000 cm2 Area B = 5.4 m2 Which of these two areas is the larger? You must show all your working. Area … [2] (d) The diagram shows a right-angled triangle ABC. A NOT TO 15 cm SCALE 7 cm B C Calculate angle ACB. Angle ACB = … [2] (e) The diagram shows a rectangle DEFG. D G NOT TO SCALE 31.2 cm 12 cm E F DE = 12 cm and DF = 31.2 cm. Calculate the area of the rectangle DEFG. … cm2 [4]

13 marks

Mark scheme: 4(a) 2870 or 2867 to 2867.4 2 M1 for π × 7.82 × 15 oe 4(b) 1350 3 3 2 M2 for 3375 oe or better or M1 for 3 3375 oe 4(c) 5.4 × 1002 = 54 000 M1 or 37 000 ÷ 1002 = 3.7 Area B A1 4(d) 27.8 or 27.81… to 27.82 2 7 M1 for sin[...] = or better 15 −1 7  or 90 − cos   oe  15  4(e) 345.6 4 B3 for 28.8 OR M2 for 31.22 – 122 oe or M1 for [...]2 + 122 = 31.22 oe M1dep for their 28.8 × 12

This question in 0580/32 Oct/Nov 2024

6 (a) The diagram shows a cuboid. NOT TO 2 cm SCALE 4 cm 4 cm On the 1 cm2 grid, complete a net of this cuboid. One face has been drawn for you. [3] (b) Three regular pentagons meet at point A. NOT TO SCALE A x° Work out the value of x. x = … [3] (c) The diagram shows two parallel lines and two straight lines. 23° 35° NOT TO SCALE y° x° (i) Find the value of x. Give a geometrical reason for your answer. x = … because … [2] (ii) Find the value of y. y = … [2]

10 marks

Mark scheme: 6(a) Fully correct net 3 B2 for 3 or 4 extra faces in the correct places B1 for 1 or 2 extra faces in the correct places 6(b) 36 3 360 180 ( 5 − 2 ) M1 for 180 − ( ) or oe 5 5 M1dep for 360 − 3 × their 108 oe 6(c)(i) 58 2 B1 for 58 Corresponding 6(c)(ii) 145 2 M1 for 180 − 35 oe or B1 for any relevant angle marked on the diagram

This question in 0580/32 Oct/Nov 2024

1 (a) (i) Li has $20. A box of cereal costs $2.29 . Work out the maximum number of boxes of cereal that Li can buy. … [2] (ii) Each box of cereal has mass 615 g. Work out the total mass of 5 boxes of cereal. Give your answer in kilograms. … kg [2] (iii) The box of cereal is a cuboid. The cuboid measures 25 cm by 20 cm by 5 cm. Work out the volume of the cuboid. … cm3 [1] (b) A cereal bar is in a box. The box is a cuboid measuring 6 cm by 3 cm by 1 cm. NOT TO 6 cm SCALE 1 cm 3 cm On the 1 cm2 grid, complete a net of the cuboid. One face has been drawn for you. [3] (c) The cereal contains fat, protein, carbohydrate and fibre. The pie chart shows the information about the masses of fat and protein. Fat 36° Protein (i) Work out the percentage of the mass of the cereal that is fat. … % [1] (ii) 60% of the mass of the cereal is carbohydrate. Complete the pie chart. [2] (iii) Work out the mass of protein in 30 g of the cereal. … g [2]

13 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 8 2 M1 for 20 ÷ 2.29 1(a)(ii) 3.075 2 M1 for 615 × 5 1(a)(iii) 2500 1 1(b) Fully correct net 3 B2 for 3 or 4 correct extra faces in correct place B1 for 1 or 2 correct extra faces in correct place 1(c)(i) 10 1 1(c)(ii) Correct pie chart 2 B1 for 216º soi 1(c)(iii) 5.67 5.666 to 5.67 2 B1 for 68 OR k M1 FT for  30 oe 360

This question in 0580/33 Oct/Nov 2024

7 (a) Write down the mathematical name for this solid. … [1] (b) x (i) Measure the size of angle x. … [1] (ii) Write down the mathematical name for this type of angle. … [1] (c) A NOT TO SCALE O C B Points A, B and C lie on the circle, centre O. AB = 11 cm and BC = 5 cm . (i) Give a geometrical reason why angle ACB is 90°. … [1] (ii) Calculate the circumference of the circle. … cm [2] (iii) Show that AC is 9.8 cm, correct to 2 significant figures. [3] (d) The surface area of a sphere is 250 cm2. Calculate the radius of the sphere. [The surface area, A, of a sphere with radius r is A = 4 r r 2 .] … cm [3]

12 marks

Mark scheme: 7(a) Cylinder 1 7(b)(i) 137 1 7(b)(ii) Obtuse 1 7(c)(i) Angle in a semicircle is 90º 1 7(c)(ii) 34. 6 or 34.55 to 34.562 2 M1 for 11 × π 7(c)(iii) 112 – 52 = AC2 M2 M1 for 52 +(…)2 = 112 96 = 9.79…or 9.80 A1 7(d) 4.46 or 4.460 … 3 250 M2 for 4 250 or M1 for 4

This question in 0580/33 Oct/Nov 2024

17 The volume of a cylinder is 863.5 cm 3. The height of the cylinder is 12.3 cm. Find the radius of the cylinder. … cm [3]

3 marks

Mark scheme: 17 4.73 or 4.726 to 4.727… 3 M2 for 863.5 ÷ 12.3π oe or M1 for πr2×12.3 = 863.5 or better

This question in 0580/31 May/June 2025

25 A bar of gold in the shape of a cuboid has dimensions 2 cm by 4 cm by 6.5 cm. The density of gold is 19. 32 g/cm 3. Calculate the mass of this bar of gold. mass :Density = D volume … g [3]

3 marks

Mark scheme: 25 1004.64 3 M1 for 2 × 4 × 6.5 oe implied by 52  mass  M1 for 19.32 = or better their 52

This question in 0580/31 May/June 2025

13 (a) The surface area of a solid cube is 121.5 cm 2 . Calculate the length of the side of the cube. … cm [3] (b) 10 cm NOT TO h SCALE 15 cm The area of the trapezium is 106.25 cm 2. (i) Calculate the height of the trapezium. … cm [2] (ii) Convert 106.25 cm 2 into m2. … m2 [1]

6 marks

Mark scheme: 13(a) 4.5 nfww 3 121.5 M2 for oe 6 121.5 or M1 for oe 6 13(b)(i) 8.5 2 1 M1 for (10 + 15)h = 106.25 oe or better 2 13(b)(ii) 0.010625 cao 1

This question in 0580/31 Oct/Nov 2025

19 The diagram shows a cylinder and a cube. NOT TO SCALE x cm 12 cm x cm 5 cm x cm The cylinder has the same volume as the cube. Find the value of x. x = … [3]

3 marks

Mark scheme: 19 9.8[0] or 9.804 to 9.805 3 M2 for x3 = π × 52 × 12 oe or M1 for π × 52 × 12 oe or for x3 = their 942.7

This question in 0580/32 Oct/Nov 2025

16 NOT TO x cm SCALE 5 cm 4 cm The diagram shows an isosceles triangle. (a) Calculate the value of x. x = … [2] (b) The triangle is one face of a square-based pyramid. Each triangular face of the pyramid is the same. On the 1 cm2 grid, draw a net of this pyramid. [3]

5 marks

Mark scheme: 16(a) 5.39 or 5.385… 2 M1 for 52 + 22 oe 16(b) Correct net of the pyramid 3 B2 for a 4 by 4 square and 4 identical isosceles triangles correctly placed on the square or 3 correct faces e.g. a 4 by 4 square and at least two correct triangles correctly placed on the square or B1 for one correct face on a net or 4 isosceles triangles with height 5 on the sides of a square

This question in 0580/33 Oct/Nov 2025