Cambridge IGCSE Mathematics 0580 — 2019 May/June Paper 3 · Variant 3

1 (a) Write this number in figures. One million three hundred and two thousand five hundred and ninety-six. ................................................. [1] (b) (i) Two numbers are added together to give the number in the box immediately above. 2 5 – 3 – 4 Complete the diagram. [2] (ii) Two numbers are multiplied together to give the number in the box immediately above. 5 – 3 – 4 Complete the diagram. [3] (c) Write these in order of size, starting with the smallest. 5 -1 18.4% .183 # 10 5-1 27 ....................... 1 ....................... 1 ........................ 1 ....................... [2] smallest (d) Work out 142 as a percentage of 304. ............................................. % [1] (e) (i) Find the highest common factor (HCF) of 28 and 98. ................................................. [2] (ii) Find the lowest common multiple (LCM) of 28 and 98. ................................................. [2] (f) The average distance from Earth to Mars is .225 # 108 km. A space ship travels from Earth to Mars at an average speed of .58 # 104 km/h. Find how long, in hours, the journey takes. ....................................... hours [2]

Mark scheme: Question Answer Marks Partial Marks 1(a) 1 302 596 1 1(b)(i) −5 2 B1 for −7 −7 B1FT for 2 + their −7 1(b)(ii) −180 3 B1 for −15 −15 12 B1 for 12 and B1FT for their −15 × their 12 1(c) 5 2 M1 for 3 in correct order or for 1.83 × 10−1 18.4% 5−1 27 5 three of [ =]0.185.... , [18.4% =] 0.184, 27 [1.83 × 10−1 =] 0.183, [5−1=] 0.2 1(d) 46.7 or 46.71... 1 1(e)(i) 14 2 B1 for answer of 2 or 7 or 2 × 7 or 2 × 2 × 7 and 2 × 7 × 7 or list (28 =) 2, 2, 7 and (98 =)2, 7, 7 1(e)(ii) 196 2 B1 for 28, 56, 84, 112,… and 98, 196 or [1 ×]2 × 2 × 7 × 7 or 196k 1(f) 3880 or 3879[⋅…] 2 M1 for 2.25 × 108 ÷ 5.8 × 104 oe or 3.88(0...) × 103 or 3.879… × 103 or figs (388 or 3879…) as the answer

More questions on The four operations

2 Three quadrilaterals are shown on a 1 cm2 grid. y 8 7 6 5 4 3 2 1 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 8 x – 1 – 2 – 3 A – 4 B – 5 – 6 – 7 – 8 (a) Write down the mathematical name of the shaded quadrilateral. ................................................. [1] (b) For the shaded quadrilateral (i) measure the perimeter, ............................................ cm [1] (ii) work out the area. .......................................... cm2 [1] (c) Describe fully the single transformation that maps the shaded quadrilateral onto (i) quadrilateral A, .................................................................................................................................................... .................................................................................................................................................... [2] (ii) quadrilateral B. .................................................................................................................................................... .................................................................................................................................................... [3] (d) On the grid, (i) reflect the shaded quadrilateral in the line x = 1, [2] 1 (ii) enlarge the shaded quadrilateral by scale factor , centre (- 1, 0) . [2] 2

Mark scheme: 2(a) Trapezium 1 2(b)(i) 16 or 15.8 to 16.2 1 2(b)(ii) 14 1 2(c)(i) Translation 2 B1 for each  −9     −8  2(c)(ii) Rotation 3 B1 for each 90˚ clockwise oe [about] (0, 0) oe 2(d)(i) Correct shape 2 B1 for reflection in x = k or y = 1 Vertices (−1, 4), (−1, 6), (−5, 6), (−5, 1) 2(d)(ii) Correct shape 2 B1 for any enlargement, SF 12 with different Vertices centre (3, 0.5), (3, 3), (1, 3), (1, 2)

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3 The music teacher at a school forms an orchestra. The instruments in the orchestra are 36 string, 15 woodwind and 12 brass. (a) Write the ratio string : woodwind : brass in its simplest form. ................ : ................ : ................ [2] (b) The 36 string instruments are violins, cellos and double basses in the ratio violins : cellos : double basses = 9 : 2 : 1. (i) Show that the number of violins is 27. [1] (ii) Work out the number of cellos and the number of double basses. Cellos ................................................ Double basses ................................................ [2] (c) The 15 woodwind instruments are oboes, flutes and clarinets. 20% of these instruments are oboes. There are twice as many flutes as clarinets. Find the number of flutes. ................................................. [2] 1 (d) Of the 12 brass instruments, are trumpets, 3 are trombones and the remainder are horns. 3 Find the number of horns. ................................................. [2] (e) The music teacher needs to buy all the instruments for the orchestra. Number of Price of each Cost ($) instruments instrument ($) String 36 131 4716 Woodwind 15 217 Brass 12 221 (i) Complete the table. [1] (ii) Find the total cost of all the instruments. $ ................................................ [1] (f) The school is given 65% of the total cost of all the instruments. Find how much more money is needed. $ ................................................ [2]

Mark scheme: 3(a) 12 : 5 : 4 2 B1 for 36 : 15 : 12 oe 3(b)(i) 9 1 × 36 (9 + 2 + 1) 3(b)(ii) [Cellos] 6 2 B1 for each [Double basses] 3 3(c) 8 2 B1 for 3 [oboes] seen 3(d) 5 2 B1 for 4 [trumpets] seen 3(e)(i) [Woodwind] 3255 1 [Brass] 2652 3(e)(ii) 10 623 1 FT their (e)(i) 3(f) 3718.05 2 M1 for (1 – 0.65) × their (e)(ii) oe

More questions on Ratio and proportion

4 (a) Complete the table of values for y = 5 + 2 x - x 2 . x -2 -1 0 1 2 3 4 y 2 5 6 -3 [2] (b) On the grid, draw the graph of y = 5 + 2x - x 2 for - 2 G x G 4 . y 7 6 5 4 3 2 1 0 –2 –1 1 2 3 4 x –1 –2 –3 [4] (c) (i) On the grid, draw the line of symmetry. [1] (ii) Write down the equation of the line of symmetry. ................................................. [1] (d) Use your graph to find the solutions of the equation 5 + 2x - x 2 = 4 . x = ....................... or x = ..................... [2] (e) (i) On the grid, draw a line from (- 1, 2) to (1, 6) . [1] (ii) Find the equation of this line in the form y = mx + c . y = ................................................ [3]

Mark scheme: 4(a) −3 5 2 2 B1 for 2 correct 4(b) Correct curve 4 B3FT for 6 or 7 points correct B2FT for 4 or 5 points correct B1FT for 2 or 3 points correct 4(c)(i) Ruled line x = 1 drawn 1 4(c)(ii) x = 1 1 4(d) −0.5 to −0.3 and 2.3 to 2.5 2 B1 for each If 0 scored, B1 for y = 4 drawn 4(e)(i) Correct ruled continuous line 1 4(e)(ii) [y =] 2x + 4 3 B2 for [y =] 2x + k rise or M1 for run B1 for kx + 4 , k ≠ 0, or c = 4

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5 The scale drawing shows a play area, ABCDE. The scale is 1 centimetre represents 3 metres. D h E C A B Scale: 1 cm to 3 m (a) Find the actual distance h in metres. h = ............................................. m [2] (b) Find the actual area of triangle CDE. ............................................ m2 [3] (c) A straight path crosses the play area from C to AB. It is equidistant from CB and CD. Using a straight edge and compasses only, construct the path. Show all your construction arcs. [2] (d) There is a circular pool in the play area. The pool has a diameter of 8 m. Calculate (i) the circumference of the pool, .............................................. m [2] (ii) the area of the pool. ............................................ m2 [2]

Mark scheme: 5(a) 10.8 to 12 2 B1 for 3.6 cm to 4.0 cm measured 5(b) 191 to 220 3 B1 for 11.8 to 12.2 measured or 35.4 to 36.6 M1 for 0.5 × their (a) × their actual EC oe 5(c) Correct ruled bisector of angle BCD 2 B1 for correct angle bisector with with correct arcs no/incorrect arcs, or two pairs of supporting arcs or correct line short of AB with or without arcs 5(d)(i) 25.1 or 25.13 to 25.14 2 M1 for 8 × π oe 5(d)(ii) 50.3 or 50.26 to 50.272 2 M1 for π (0.5 × 8)2 oe

More questions on Circles, arcs and sectors

6 (a) D p° s° E NOT TO SCALE q° 34° r° t° A B C In the diagram, ABC is a straight line. AD is parallel to BE, angle BAD = 34° and AB = BD . (i) Complete the statements. (a) p = ................ because ....................................................................................................... [2] (b) q = ................ because ....................................................................................................... [2] (ii) Work out the value of r and the value of s. r = ................................................ s = ................................................ [2] (iii) Find the value of t and give a reason for your answer. t = ................ because ......................................................................................................... [2] (b) A B NOT TO SCALE O C D In the diagram, B and D are points on the circumference of a circle, centre O. AC is a straight line touching the circle at B only and BD is a straight line through O. Complete the statement. Angle ABD = ................ because ..................................................................................................... ............................................................................................................................................................ [2]

Mark scheme: 6(a)(i)(a) 34 2 B1 for each Isosceles [triangle] 6(a)(i)(b) Their p 2 B1 for each Alternate [angles] 6(a)(ii) [r =] 112 2 B1 for 180 − 34 − their (a)(i)(a) [s =] 56 B1 for 90 − their (a)(i)(b) 6(a)(iii) 34 2 B1 for each Corresponding [angles] or angles [on a straight] line [add up to] 180 6(b) 90 2 B1 for each Angle [between] tangent [and] radius (or diameter)

More questions on Angles

7 The travel graph shows part of a train journey between station A and station C. 160 Station C 140 120 Distance (km) 100 Station B 80 60 40 20 Station A 0 12 30 13 00 13 30 14 00 14 30 15 00 15 30 Time (a) (i) Calculate, in km/h, the speed of the train between station A and station B. ......................................... km/h [2] (ii) The train leaves station B at 14 40. For how many minutes did the train stop at station B? ........................................... min [1] (iii) The train travels at a constant speed between station B and station C, arriving at 15 20. Complete the travel graph for the journey between station B and station C. [1] (iv) On which part of the journey was the train travelling faster? Between station ........... and station ........... [1] (b) Another train leaves station C at 12 45. It travels to station A at a constant speed of 62 km/h without stopping at station B. (i) Work out how long, in hours and minutes, this journey takes. .................... h ................... min [2] (ii) Write down the time this train arrives at station A. ................................................. [1] (iii) On the grid, show the journey of this train. [1] (iv) Find the distance from station A when the two trains pass each other. ............................................ km [1]

Mark scheme: 7(a)(i) 120 2 M1 for 90 ÷ their time for A to B [× 60] or B1 for 2[km/min] 7(a)(ii) 10 1 7(a)(iii) Ruled line from (14 40, 90) 1 to (15 20, 155) 7(a)(iv) A [and] B 1 7(b)(i) 2 [hours] 30 [minutes] 2 M1 for 155 ÷ 62 7(b)(ii) 15 15 1 FT their (b)(i) + 12 45 7(b)(iii) Ruled line from (12 45, 155) to 1 (their7(b)(ii), 0) 7(b)(iv) 58 to 63 1 FT their crossing point

More questions on Rates

8 (a) Kyung records the number of people in each of 24 cars on Wednesday. His results are shown below. 1 3 6 1 2 2 4 5 3 4 1 5 3 2 4 1 1 1 2 4 4 1 2 1 (i) Complete the frequency table. You may use the tally column to help you. Number in a car Tally Frequency 1 2 3 4 5 6 [2] (ii) Write down the mode. ................................................. [1] (iii) Work out the range. ................................................. [1] (iv) Work out the median. ................................................. [1] (v) Calculate the mean. ................................................. [3] (vi) One of these cars is chosen at random. Find the probability that the number of people in this car is 4. ................................................. [1] (b) Kyung also records the number of people in each of 24 cars on Saturday. The table shows the results. Number in a car 1 2 3 4 5 6 Frequency 1 2 5 13 2 1 On the grid, complete the bar chart to show these results. 14 12 10 8 Frequency 6 4 2 0 1 2 3 4 5 6 Number in a car [2] (c) Write down one comparison between the frequency tables in part (a)(i) and part (b). ............................................................................................................................................................ ............................................................................................................................................................ [1] Question 9 is printed on the next page.

Mark scheme: 8(a)(i) Correct frequencies 2 B1 for 1 frequency incorrect 8 5 3 5 2 1 or 2 incorrect but total still 24 or 8 5 3 5 2 1 in tally column If 0 scored, B1 for completely correct tallies 8(a)(ii) 1 1 8(a)(iii) 5 1 8(a)(iv) 2 1 8(a)(v) 2.625 3 M1 for ∑fx 1 × 8 + 2 × 5 + 3 × 3 + 4 × 5 + 5 × 2 + 6 × 1 M1 dep for their ∑fx ÷ 24 8(a)(vi) 5 1 FT their table oe 24 8(b) Correct bar chart 2 B1 for 2 or 3 correct bars or for all 4 heights correct 8(c) Correct generalised comparison 1

More questions on Classifying statistical data

9 Mr Razif travels by bus from Singapore to Kuala Lumpur with his wife and his four children. (a) Ticket Price Adult $32.40 Child $24.40 Family (2 adults and 3 children) $115.00 Work out how much Mr Razif saves if he buys a family ticket and one child ticket rather than six individual tickets. $ ................................................ [4] (b) The bus leaves Singapore at 12 40 and arrives in Kuala Lumpur at 17 35. Work out, in hours and minutes, the time this journey takes. .................... h ................... min [1] (c) Mr Razif changes some dollars into Malaysian ringgits. He receives 318 ringgits when the exchange rate is $1 = 4.24 ringgits. Work out how many dollars he changes. $ ................................................ [2]

Mark scheme: 9(a) 23 4 M3 for 2 × 32.4 + 4 × 24.4 – 115 – 24.4 oe OR B2 for 162.4[0] or 2 × 32.4 + 4 × 24.4 oe or M1 for 2 × 32.4 or 4 × 24.4 B1 for 139.4[0] 9(b) 4 [h] 55[min] 1 9(c) 75 2 M1 for 318 ÷ 4.24

More questions on Ratio and proportion