Cambridge IGCSE Mathematics 0580 — 2023 Oct/Nov Paper 3 · Variant 1

1 (a) Write the number six and a half million in figures. ................................................. [1] (b) Write 37 508 correct to the nearest thousand. ................................................. [1] (c) 6 9 100 28 31 1000 32 36 From this list of numbers, write down (i) a factor of 18 ................................................. [1] (ii) a multiple of 12 ................................................. [1] (iii) a square number ................................................. [1] (iv) a prime number ................................................. [1] (v) an irrational number. ................................................. [1] (d) Put one pair of brackets in each statement to make it correct. (i) 24 - 4 # 3 + 2 = 62 [1] (ii) 24 - 4 # 3 + 2 = 4 [1] 3 (e) Write as a decimal. 4 ................................................. [1] 3(f) Work out of 126. 7 ................................................. [1] (g) Write down the value of the reciprocal of 0.5 . ................................................. [1] 2 1(h) Without using a calculator, work out 5 - 2 . 3 5 You must show all your working and give your answer as a mixed number in its simplest form. ................................................. [3]

Mark scheme: Question Answer Marks Partial Marks 1(a) 6 500 000 1 1(b) 38 000 1 1(c)(i) 6 or 9 1 1(c)(ii) 36 1 1(c)(iii) 9 or 36 1 1(c)(iv) 31 1 1(c)(v) 1000 1 1(d)(i) (24 − 4)  3 + 2 = 62 1 1(d)(ii) 24 − 4  (3 + 2) = 4 1 1(e) 0.75 1 1(f) 54 1 1(g) 2 1 1(h) 17 11 B1 Correct step for dealing with mixed or 17 k 11k 3 5 numbers, allow e.g. or 3k 5 k 85 33 M1 FT Correct method to find a common and denominator 15 15 3 157 cao A1 Alternative methods 2 1 10 3 7 3 − B1, and M1, 3 15 cao 3 5 15 15 A1 510 and 3 M1, 3 157 cao B1 A1 15 215 10 3 7 and M1, 3 15 cao B1A1 15 15

More questions on Types of number

2 (a) The diagram shows a circle. NOT TO SCALE (i) The diameter of this circle is 168 mm. Write down the radius of this circle. .......................................... mm [1] (ii) On the diagram, draw a chord of this circle. [1] (b) The scale drawing shows the position of ship A and the position of ship B. The scale is 1 cm represents 6 km. North B North A Scale : 1 cm to 6 km Another ship, C, is 45 km from ship B on a bearing of 124°. (i) On the scale drawing, mark the position of ship C. [2] (ii) Find the actual distance of ship C from ship A. ........................................... km [2] (c) (i) Show that the interior angle of a regular octagon is 135°. [1] (ii) NOT TO SCALE Show that two regular octagons and a square meet at a point without any gaps. [1] (d) E F NOT TO 49° SCALE D The diagram shows points D, E and F on the circumference of a circle. DF is a diameter of the circle. Find angle EDF. Angle EDF = ................................................. [2]

Mark scheme: 2(a)(i) 84 1 2(a)(ii) Any chord 1 2(b)(i) Accurate position marked 2 B1 for accurate distance or accurate angle 2(b)(ii) 57 2 FT their diagram for 1 and 2 marks B1 for 9.2 to 9.6 seen or M1 for their length  6 2(c)(i) 360 ( 8 − 2 )  180 M1 180 – or 8 8 2(c)(ii) 135 + 135 + 90 = 360 M1 2(d) 41 2 M1 for 180 – 90 – 49 oe or angle DEF identified as 90°

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3 (a) The bar chart shows the country in which each of 80 students live. 24 20 16 Frequency 12 8 4 0 Australia Brazil China India USA Country (i) How many of these students live in Brazil? ................................................. [1] (ii) In which country do the largest number of these students live? ................................................. [1] (iii) How many more of these students live in China than live in Australia? ................................................. [1] (iv) Find the percentage of these students who live in the USA. ..............................................% [2] (b) In Hobart, the temperature at 8 am was -3 °C and the temperature at 3 pm was 7 °C. (i) Find the difference in the temperatures between 8 am and 3 pm. ............................................ °C [1] (ii) The temperature at 10 pm was 12 °C lower than at 3 pm. Find the temperature at 10 pm. ............................................ °C [1] (c) The table shows the favourite language that each of 80 students studies. Language Frequency French 12 Spanish 26 English 42 Total 80 Complete the pie chart to show this information. [4]

Mark scheme: 3(a)(i) 9 1 3(a)(ii) India 1 3(a)(iii) 7 1 3(a)(iv) 23.75 2 19 M1 for [ 100] 80 3(b)(i) 10 1 3(b)(ii) −5 1 3(c) Correct pie chart 4 B3 for 2 correct sectors or B2 for 1 correct sector or for 54°, 117° and 189° 360 k or M1 for or 4.5 or  360 80 80 (k = 12, 26 or 42)

More questions on Statistical charts and diagrams

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]

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

More questions on Surface area and volume

5 A railway line has three stations, Town, Port and Cove. Train A leaves Town for Cove and train B leaves Cove for Town. Both trains stop at Port. 25 Cove B 20 Distance from Town (km) 15 Port 10 5 A Town 0 14 00 14 10 14 20 14 30 14 40 14 50 Time (a) Write down the time that train B leaves Cove. ................................................. [1] (b) Write down how long train A stops at Port. .......................................... min [1] (c) How many more minutes does train A take to complete the whole journey than train B? .......................................... min [2] (d) Write down the time that the two trains pass each other. ................................................. [1] (e) Work out the average speed of train A between Town and Cove in kilometres per hour. ......................................... km/h [3]

Mark scheme: 5(a) 14 10 1 5(b) 4 1 5(c) 2 2 B1 for 40 or 38 5(d) 14 25 1 5(e) 34.5 3 23 M2 for  60 oe 40 23 or M1 for their time

More questions on Time

6 y 10 9 8 7 6 5 4 A 3 2 1 B x - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 6 7 8 - 1 C - 2 - 3 - 4 - 5 - 6 (a) Describe fully the single transformation that maps triangle A onto triangle B. ..................................................................................................................................................... ..................................................................................................................................................... [2] (b) Describe fully the single transformation that maps triangle A onto triangle C. ..................................................................................................................................................... ..................................................................................................................................................... [3] (c) On the grid, draw the image of triangle A after a reflection in the line y = 6 . [2]

Mark scheme: 6(a) Translation 2 B1 for each  2     −3  6(b) Enlargement 3 B1 for each (sf = ) 3 (centre = ) (4, 6) 6(c) Correct reflection 2 B1 for correct reflection in line y = k points (1, 7), (1, 9), (5, 9)

More questions on Transformations

7 (a) Simplify. 5a + 3b + 2a - 4b ................................................. [2] (b) P = 8x + 3y Find the value of x when P = 21 and y =-5 . x = ................................................ [2] (c) Make v the subject of the formula S = kv2 . v = ................................................ [2] (d) Multiply out and simplify. ( x - 3)( x + 5) ................................................. [2] (e) Nasser has x marbles. Selina has 15 more marbles than Nasser. Hanif has 3 times as many marbles as Selina. In total they have 150 marbles. Find the value of x. x = .................................................. [5]

Mark scheme: 7(a) 7a – b final answer 2 B1 for 7a or –b in final answer or 7a – b seen then spoilt 7(b) 4.5 2 M1 for 21 = 8x + 3  −5 oe or better 7(c) S 2 2 S final answer M1 for v = or S = k  v k k 7(d) x2 + 2x – 15 final answer 2 B1 for three correct terms from x2 – 3x + 5x – 15 7(e) 18 5 B1 for x + 15 or 3  their (x + 15) oe M1 for x + their (x + 15) + their (3( x + 15)) = 150 or better M1 for 5x + 60 = 150 or better or their linear equation simplified to ax + b = 150 M1 for their [ax + b = c] 150 − b solved to x = a

More questions on Equations

8 y L 6 5 4 3 2 1 x - 3 - 2 - 1 0 1 2 3 4 5 6 - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 (a) Find the equation of line L in the form y = mx + c . y = ................................................ [2] (b) (i) On the grid, draw the line y = x . [1] (ii) Write down the coordinates of the point where the line y = x intersects line L. ( ...................... , ...................... ) [1] 8(c) (i) Complete the table of values for y = . x x −5 −4 −3 −2 −1 1 2 3 4 5 y −1.6 −2.7 2.7 1.6 [3] 8 (ii) On the grid, draw the graph of y = for - 5 G x G - 1 and 1 G x G 5 . x y 8 7 6 5 4 3 2 1 x - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 [4]

Mark scheme: 8(a) [y =] 2x − 5 final answer 2 B1 for answer of 2x + c or mx – 5 (m ≠ 0) 8(b)(i) Correct ruled line 1 8(b)(ii) (5, 5) 1 FT their ruled y = x 8(c)(i) −2 −4 −8 8 4 2 3 B2 for 3, 4 or 5 correct or B1 for 1 or 2 correct 8(c)(ii) Correct curve 4 B3FT for 9 or 10 points correctly plotted or B2FT for 7 or 8 points correctly plotted or B1FT for 5 or 6 points correctly plotted

More questions on Coordinates

9 (a) Pure gold costs $42 per gram. The fraction of pure gold in an object is measured in carats. 1 One carat means of the mass of an object is pure gold. 24 Henry buys a 9-carat gold bracelet weighing 16 g. The price of the bracelet is $204. Is the price of the bracelet more or less than the cost of the pure gold in it? You must show your working. [4] (b) A clock made of metals has a mass of 1080 g. The mass of each metal in the clock is in the ratio copper : zinc : other metals = 21 : 14 : 1. Calculate the mass of copper in this clock. .............................................. g [2] (c) There are 110 people in a group. G = { people who own gold jewellery } S = { people who own silver jewellery } 18 people own both gold jewellery and silver jewellery. 46 people own gold jewellery. 11 people own no gold jewellery and no silver jewellery. G S (i) Complete the Venn diagram. [2] (ii) Write down n ( G + S ) . ................................................. [1] (iii) One of the 110 people is chosen at random. Write down the probability that this person owns gold jewellery but not silver jewellery. ................................................. [1] (d) E F Use set notation to describe the shaded region. ................................................. [1]

Mark scheme: 9(a) Less 4 1 M3 for  9  16  42 oe with working leading to 252 24 or M2 for three of these multiplied or M1 for any two of these multiplied 9(b) 630 2 1080 M1 for [ k] oe 21 + 14 + 1 where k =1,14 or 21 oe 9(c)(i) 2 B1 for two or three in the correct places 9(c)(ii) 18 1 FT their diagram 9(c)(iii) 28 1 FT their 28 from their diagram oe 110 9(d) E F cao 1

More questions on Ratio and proportion

10 (a) U P 21.4 cm 14.4 cm NOT TO 9.6 cm SCALE Q R V W 12.8 cm Triangle PQR is mathematically similar to triangle UVW. Calculate VW. VW = ........................................... cm [2] (b) ABC is a right-angled triangle. A NOT TO 9.1 cm SCALE 3.5 cm C B Calculate BC. BC = ........................................... cm [3] (c) DEF is a right-angled triangle. D 8.4 cm NOT TO SCALE 35° F E Calculate EF. EF = ............................................cm [2] (d) JKL is a right-angled triangle. 10 cm J L NOT TO 8 cm SCALE K Calculate angle JKL. Angle JKL = ................................................ [2]

Mark scheme: 10(a) 19.2 2 14.4 VW M1 for = oe or better 9.6 12.8 10(b) 8.4 3 M2 for 9.12 – 3.52 oe or better or M1 for […]2 + 3.52 = 9.12 oe or better 10(c) 6.88 to 6.881 2 [...] M1 for cos35 = oe or better 8.4  or sin 55 = oe or better 8.4 10(d) 51.3[4…] 2 10 M1 for tan[… =] oe or better 8

More questions on Right-angled triangles