Cambridge IGCSE Mathematics 0580 — 2018 May/June Paper 3 · Variant 2

1 (a) Find the value of (i) the square root of 19 044, ............................................. [1] (ii) 27. ............................................. [1] (b) n is an integer and 120 < n < 140. Find the value of n when it is (i) a multiple of 45, n = ....................................... [1] (ii) a square number, n = ....................................... [1] (iii) a factor of 402, n = ....................................... [1] (iv) a cube number. n = ....................................... [1] 21 - 15 # 3 (c) Work out the value of . 18 ' 6 - 4 ............................................. [2] 19.2 # 8.64 (d) Estimate the value of by rounding each number in the calculation to 1 significant 31.6 ' 6.32 figure. Show all your working by filling in the calculation below. ..................... # ..................... = ..................... [2] ..................... ' .....................

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 138 1 1(a)(ii) 128 1 1(b)(i) 135 1 1(b)(ii) 121 1 1(b)(iii) 134 1 1(b)(iv) 125 1 1(c) 24 2 B1 for numerator of −24 or denominator of −1 or answer of –24 1(d) 20 × 9 M1 M1 for all correct roundings 30 ÷ 6 12 A1 If 0 scored SC1 for 3 correct roundings or 20.[0] and 9.0[0] and 30.[0] and 6.0[0]

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2 y 8 7 6 5 4 3 2 1 x 0 –8 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8 –1 A –2 –3 –4 –5 –6 (a) Write down the mathematical name of the shaded quadrilateral shown on the grid. ............................................. [1] (b) Describe fully the single transformation that maps the shaded quadrilateral onto quadrilateral A. ............................................................................................................................................................. ............................................................................................................................................................. [3] (c) Complete this statement with a fraction in its simplest form. The area of quadrilateral A is .......................... of the area of the shaded quadrilateral. [3] (d) On the grid, draw the image of - 4 (i) shape A after a translation by the vector , [2] c 7 m (ii) shape A after a rotation of 180° about the origin, [2] (iii) shape A after a reflection in the line x = 2. [2]

Mark scheme: 2(a) Trapezium 1 2(b) Enlargement 3 B1 for each 1 [Scale factor] oe 3 [Centre] (−5, −5) 2(c) 1 3  1  2 B2 for   9  3  or B1 for [shaded area] 13.5 or [area of A] 1.5 seen 1.5 M1 for oe their13.5 2(d)(i) Image at (−6, 6),(−5, 6),(−5, 5), 2  − 4  k (−7, 5) B1 for image of A at   or   k  7 2(d)(ii) Image at (1, 1), (1, 2), (3, 2), (2, 1) 2 B1 for 180° rotation with incorrect centre 2(d)(iii) Image at (5, −2), (5, −1), (6, −1), 2 B1 for reflection in y = 2 or in x = k (7, −2)

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3 A car company has three sales people, Anna, Mustapha and Joshua. (a) During March, Anna sold 21 cars, Mustapha sold 12 cars and Joshua sold 15 cars. Write down and simplify the ratio of the number of cars they sold during March. Anna : Mustapha : Joshua = .......... : .......... : ........... [2] (b) Each month, they receive a bonus which is proportional to the number of cars they sell. The total bonus in March is $1248. (i) Show that Anna receives a bonus of $546. [1] (ii) Calculate the bonuses received by Mustapha and Joshua. Mustapha $ .................................... Joshua $ .................................... [2] 3 (c) The total bonus of $1248 is of the total profit in March. 7 Calculate the total profit in March. $ ................................................ [2] (d) Ella wants to buy a car with a price of $13 500. The company reduces this price by 16%. Ella then pays a deposit of $500. Show that the amount left for her to pay is $10 840. [2] (e) Ella borrows $10 840 from a bank. She pays this back over 3 years at a rate of $340 per month. (i) Show that the total amount she pays back during the 3 years is $12 240. [1] (ii) Calculate the percentage increase from $10 840 to $12 240. ..........................................% [3]

Mark scheme: 3(a) 7 : 4 : 5 2 B1 for any correct ratio other than 21 : 12 : 15, not in simplest form 3(b)(i) 7 B1 oe × 1248 16 3(b)(ii) [Mustapha] 312 2 B1 for each [Joshua] 390 or 1248 M1 for × k where k = 12 or 15 21 + 12 + 15 1248 or × k oe where their 7 + their 4 + their 5 k = their 4 or their 5 3(c) 2912 2 M1 for 1248 ÷ 3 [× 7] 3(d) 13 500 – 0.16 × 13 500 − 500 M2 M1 for 0.16 × 13 500 or 0.84 × 13 500 seen or 0.84 × 13 500 − 500 3(e)(i) 3 × 12 × 340 B1 3(e)(ii) 12.9 or 12.91 to 12.92 3 12240 − 10840 M2 for [× 100 ] 10840 12240 or × 100 [ − 100 ] or 10840  12240   − 1  [× 100 ]  10840  12240 or M1 for 12240 – 10840 or oe 10840

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4 (a) Complete the table of values for y = 5x − x2. x −1 0 1 2 3 4 5 6 y 0 6 6 −6 [2] (b) On the grid, draw the graph of y = 5x − x2 for - 1 G x G 6. y 8 7 6 5 4 3 2 1 x –1 0 1 2 3 4 5 6 –1 –2 –3 –4 –5 –6 –7 –8 [4] (c) Write down the equation of the line of symmetry of the graph. ............................................. [1] (d) (i) Complete the table of values for y = 1.5x − 2. x 0 2 5 y [2] (ii) On the grid, draw the graph of y = 1.5x − 2 for - 1 G x G 6. [2] (iii) Use your graphs to write down the solutions to the equation 1.5x − 2 = 5x − x2. x = ................................... or x = ................................... [2]

Mark scheme: 4(a) −6 4 4 0 2 B1 for 2 or 3 correct 4(b) Correct smooth curve 4 B3FT for 7 or 8 correct plots or B2FT for 5 or 6 correct plots or B1FT for 3 or 4 correct plots 4(c) x = 2.5 cao 1 4(d)(i) −2 1 5.5 2 B1 for 2 correct 4(d)(ii) Correct continuous ruled line from 2 B1FT for 2 or 3 correct plots x = −1 to x = 6 4(d)(iii) [x =] −0.6 to −0.4 and 3.9 to 4.1 2 B1FT for each

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5 The scale drawing represents three sides, AB, BC and CD, of a wildlife park. The scale is 1 centimetre represents 50 metres. A B C D Scale: 1 cm to 50 m (a) Find the actual distance AB in metres. ......................................... m [2] (b) Point E is 550 metres from A and 600 metres from D. Use a ruler and compasses only to find the point E and draw the lines AE and DE. [3] (c) Two straight paths cross the wildlife park, ABCDE. Using a straight edge and compasses only, construct (i) the path that bisects angle ABC, [2] (ii) the path that is equidistant from point C and point D. [2] (d) The path from B crosses over a circular lake with radius 150 m. The centre of the lake is on this path and is 350 m from B. (i) On the scale drawing, construct the lake. [3] (ii) Calculate the actual circumference of the lake in metres. ......................................... m [2]

Mark scheme: 5(a) 250 2 B1 for 5 [ cm] oe 5(b) Correct point E joined to A and D 3 B2 for correct point E with arcs without with ruled lines and with arcs lines or correct ruled shape without arcs or B1 for drawing AE = 11 cm or drawing DE = 12 cm or correct point E without arcs and lines 5(c)(i) Correct ruled bisector of angle ABC B2 B1 for a correct ruled angle bisector with which reaches DE with two correct no/wrong arcs or two correct pairs of arcs pairs of arcs 5(c)(ii) Correct ruled perpendicular bisector B2 B1 for a correct ruled perpendicular of side CD which reaches AE with bisector with no/wrong arcs or two correct two correct pairs of arcs pairs of arcs 5(d)(i) Constructed circle, centre 7 cm from 3 3FT along their (c)(i) B along bisector of ABC, with radius B1 for a circle, centre 7 cm from B, any 3 cm radius M1 for a circle, radius 3 cm seen anywhere 5(d)(ii) 942 or 943 or 942.4 to 942.6 2 M1 for (2 × 150)π or 300π soi

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6 The 262 students at a college each study one of the languages shown in the table. French German Spanish Italian Japanese Total Boys 27 48 19 123 Girls 32 54 12 Total 53 30 262 (a) Complete the table. [3] (b) Find the probability that (i) a girl, chosen at random, studies Spanish, ............................................. [1] (ii) a boy, chosen at random, studies French or Italian, ............................................. [1] (iii) a student, chosen at random, does not study German. ............................................. [1] (c) 72 students each study one of the sciences shown in the table. The results are to be shown in a pie chart. Science Number of students Pie chart sector angle Biology 25 125° Chemistry 16 Physics 31 (i) Complete the table. [2] (ii) Complete the pie chart. [2]

Mark scheme: 6(a) 3 B2 for 6 or 7 correct F G S I J Tot B 21 8 or B1 for 3, 4 or 5 correct G 30 11 139 Tot 57 102 20 6(b)(i) 54 1 FT their table oe isw their139 6(b)(ii) 46 1 oe isw 123 6(b)(iii) 209 1 oe isw 262 6(c)(i) [Chemistry] 80° 2 B1 for each [Physics] 155° or if 0 scored M1 for 125 ÷ 25 or 360 ÷ 72 or 5 If 0 scored SC1 for the two angles adding to 235° 6(c)(ii) Two correct lines on the pie chart 2 2FT only if (c)(i) angles total 235° B1 for a correct sector of 125° or 80° or 155°

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7 Louise leaves home at 09 55 and cycles the 5.6 km to the supermarket at a constant speed. She takes 15 minutes to complete the journey. (a) Write down the time she arrives at the supermarket. ............................................. [1] (b) Calculate Louise’s average speed from her home to the supermarket (i) in kilometres per hour, .....................................km/h [1] (ii) in metres per second, giving your answer correct to 1 decimal place. ....................................... m/s [2] (c) Louise stays at the supermarket for 23 minutes. On the grid opposite, draw the travel graph of her journey from home and her stay at the supermarket. [2] (d) Louise’s mother leaves home at 10 07 to meet Louise at the supermarket. She cycles at a constant speed of 28 km/h. (i) Work out how long she takes for the 5.6 km journey. Give your answer in minutes. .......................................min [2] (ii) On the grid, show her mother’s journey. [1] (e) They cycle home together at a constant speed and arrive at 10 54. (i) On the grid, show their journey home. [1] (ii) Calculate, in km/h, their constant speed on the journey home. .....................................km/h [2] 7 6 Supermarket 5 4 Distance from home (km) 3 2 1 Home 0 09 50 10 00 10 10 10 20 10 30 10 40 10 50 11 00 Time

Mark scheme: 7(a) 10 10 1 7(b)(i) 22.4 1 7(b)(ii) 6.2 2 2FT their (b)(i) × 1000 ÷ (60 × 60) oe rounded to 1dp or M1 for their (b)(i) × 1000 ÷ (60 × 60) oe or 5600 ÷ (15 × 60) oe 7(c) Two correct ruled lines 2 B1FT for a line (09 55, 0) to (their 7(a), 5.6) B1FT for horizontal line (their 7(a), 5.6) to (their 7(a) + 23, 5.6) 7(d)(i) 12 2 M1 for 5.6 ÷ 28 [× 60] 7(d)(ii) Correct line 1 FT line from (10 07, 0) to (10 07 + their (d)(i), their 5.6) 7(e)(i) Correct line 1 FT line from (their 7(a) + 23, 5.6) to (10 54, 0) 7(e)(ii) 16 2 2FT 5.6 ÷ (their time in minutes) × 60 M1 for 5.6 ÷ 21 [× 60] soi or for 5.6 ÷ (their time in minutes)[× 60]

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8 (a) NOT TO SCALE 108° 136° A C B In the diagram, AB = AC. Find (i) angle BAC, Angle BAC = ............................................. [1] (ii) angle ABC. Angle ABC = ............................................. [1] (b) E NOT TO SCALE G D 72° F C B A The diagram shows a circle, centre F and diameter BG. AC is a tangent to the circle at B. BF is parallel to DE, angle GFE = 72° and angle BCD = angle CDE. (i) Write down the mathematical name of the polygon BCDEF. ............................................. [1] (ii) Explain why angle FBC is a right angle. ..................................................................................................................................................... [1] (iii) Find angle BFE, giving a reason for your answer. Angle BFE =....................... because .......................................................................................... ..................................................................................................................................................... [2] (iv) Find angle FED. Angle FED = ............................................. [1] (v) Calculate angle BCD. Angle BCD = ............................................. [4] Question 9 is printed on the next page.

Mark scheme: 8(a)(i) 116 1 8(a)(ii) 32 1 FT (180 – their (a)(i)) ÷ 2 8(b)(i) Pentagon 1 8(b)(ii) Angle [between] tangent [and] radius 1 8(b)(iii) 108 2 B1 for angle Angles [on a straight] line [add up to] B1 for reason 180 8(b)(iv) 72 1 8(b)(v) 135 4 B3FT for (540 – (90 + their (b)(iii) + their (b)(iv))) ÷ 2 oe OR B2 for 540 or M1 for (5 – 2) × 180 oe M1 for (P – (90 + their (b)(iii) + their (b)(iv))) ÷ 2 oe where P is any value >270

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9 (a) Solve the equation 3(2x − 4) = 4(x + 7). x = ....................................... [3] (b) Beindu goes to the market to buy apples and bananas. She can buy • 7 apples and 4 bananas for 85 cents or • 3 apples and 8 bananas for 93 cents. Apples cost a cents each and bananas cost b cents each. (i) This information can be used to write down two equations. One of these is 7a + 4b = 85. Write down the other equation. ................................ = ............... [2] (ii) Solve these two simultaneous equations. You must show all your working. a = ................................................... b = ................................................... [3]

Mark scheme: 9(a) 20 nfww 3 B2 for 6x – 4x = 28 + 12 or better or B1 for 6x – 12 or 4x + 28 or B1FT for correct ax = b after incorrect expansions first step 9(b)(i) 3a + 8b = 93 2 B1 for 3a + 8b 9(b)(ii) For correctly eliminating one variable M1 For correct method to equate coefficients and eliminate one variable [a =] 7 A1 [b =] 9 A1 If 0 scored SC1 for 2 values satisfying one of the original equations SC1 if no working shown, but 2 correct answers given

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