Cambridge IGCSE Mathematics 0580 — 2024 Feb/March Paper 3 · Variant 2

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

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

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2 (a) Fuel Fuel Garage A Garage B $1.41 per litre $1.50 per litre (i) Tiya buys 55 litres of fuel from garage A. Work out the change she receives from $100. $ ................................................. [2] (ii) Work out how much cheaper it is to buy 20 litres of fuel from garage A than from garage B. $ ................................................. [2] (iii) These are the amounts that 6 people spend on fuel at garage A. $63 $84.50 $72.23 $46 $54.10 $80 Calculate the mean number of litres that they buy. ......................................... litres [3] (iv) The cost of fuel at garage B increases from $1.50 to $1.53 . Calculate the percentage increase. ..............................................% [2] 2(b) The fuel tank of a car is full. 5 It takes 39 more litres of fuel to fill the tank. Work out the number of litres of fuel in a full tank. ......................................... litres [3] (c) (i) Use 1 litre = .022 gallons to complete this conversion graph. 30 25 20 Gallons 15 10 5 0 0 10 20 30 40 50 60 70 80 90 100 Litres [2] (ii) Use 1 litre = .022 gallons to complete this statement. 1 gallon = .............................. litres. [1] (d) A cylindrical tank for storing fuel has radius 1.5 metres and height 8 metres. Calculate the volume of the tank in litres. ......................................... litres [3]

Mark scheme: 2(a)(i) 22.45 2 M1 for 100 − 55 1.41 oe or B1 for 77.55 2(a)(ii) 1.8[0] 2 M1 for (1.50 − 1.41)  20 oe or B1 for 30 and 28.2[0] seen 2(a)(iii) 47.3 or 47.26… 3 M2 for 63 + 84.5 + 72.23 + 46 + 54.10 + 80 oe 6  1.41 or M1 for 63 + 84.5 + 72.23 + 46 + 54.10 + 80 oe 1.41 63 + 84.5 + 72.23 + 46 + 54.10 + 80 or oe 6 2(a)(iv) 2 2 1.53 − 1.50 M1 for  100  oe 1.50 1.53 or  100  −100 oe 1.50  1.53  or  − 1   100  oe  1.50  2(b) 65 3 5 M2 for 39  oe 3 3 or M1 for 39 is equivalent to or for 5 39 3 5 if 0 scored then SC1 for 39  oe 2 2(c)(i) A straight line through (0,0) and (100,22) 2 B1 for a straight line drawn through the origin or for 2 correct points plotted 2(c)(ii) 4.55 or 4.545… 1 2(d) 56500, 56600 or 56540 to 56560…. 3 M2 for  1.5 2 ×8×1000 oe or  150 2 ×800÷1000 oe or M1 for  1.5 2 ×8 oe or  150 2 ×800 oe or B1 for final answer figs 565 to 566 If 0 scored, SC1: for their volume in m3 1000 or for their volume in cm3 1000 or for stating clearly 1m3=1000l or 1000 cm3=1l

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3 (a) In triangle DEF, DE = 6 cm and DF = 4. 8 cm . Using a ruler and compasses only, construct triangle DEF. Leave in your construction arcs. The line EF has been drawn for you. E F [2] (b) B A C T D F G E (i) Write down the letter of the triangle that is congruent to triangle T. ................................................. [1] (ii) Write down the letter of the triangle that is similar but not congruent to triangle T. ................................................. [1] (c) NOT TO SCALE h 62° 62° 7 cm The diagram shows an isosceles triangle. (i) Show that the perpendicular height, h, is 6.58 cm, correct to 3 significant figures. [3] (ii) Calculate the area of the triangle. Give the units of your answer. ........................................... ...................... [3] (iii) Kalpit tries to arrange some of these triangles to make a regular polygon with centre O. O NOT TO SCALE 7 cm 7 cm 62° 62° 7 cm Show that Kalpit cannot make a regular polygon. [3]

Mark scheme: 3(a) Correct triangle drawn with construction 2 B1 for correct triangle drawn with arcs. incorrect or no arcs or for 2 correct arcs drawn If 0 scored, SC1 for reversed triangle with arcs. 3(b)(i) G 1 3(b)(ii) F 1 3(c)(i) 7 M2 h [h=] tan 62 oe M1 for tan62 = oe 2 7 2 6.582 to 6.583 A1 3(c)(ii) 23[.0] or 23.03 to 23.04… 2 1 M1 for 7 6.58 oe 2 cm2 1 3(c)(iii) 360 M2 M1 for 180 −2 62 oe 180 −2 62 6.4… which is not integer oe A1

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4 (a) A shop sells 58 televisions in one week. The bar chart shows the number of televisions that the shop sells on five of the days. 16 14 12 10 Number of 8 televisions 6 4 2 0 Monday Tuesday Wednesday Thursday Friday Saturday Sunday (i) Write down the number of televisions that the shop sells on Monday. ................................................. [1] (ii) Find the fraction of the televisions that the shop sells on Sunday. ................................................. [1] (iii) The number of televisions that the shop sells on the other two days is in the ratio Wednesday : Friday = 2 : 3. Complete the bar chart. [4] (iv) Write down the mode. ................................................. [1] (b) A television has a price of $550. This price is reduced by 4%. Calculate the new price of this television. $ ................................................. [2] (c) The scatter diagram shows the prices of different sized televisions. Price Television size Write down the type of correlation shown in the scatter diagram. ................................................. [1] (d) Hemang buys two televisions. The probability that a television is faulty is 0.02 . 1st television 2nd television faulty .............. faulty 0.02 not faulty .............. faulty .............. .............. not faulty not faulty .............. (i) Complete the tree diagram. [2] (ii) Find the probability that Hemang buys two faulty televisions. ................................................. [2] (iii) The shop sells 4150 televisions in one year. Calculate the expected number of faulty televisions. ................................................. [1]

Mark scheme: 4(a)(i) 3 1 4(a)(ii) 11 1 cao 58 4(a)(iii) Completely correct bar chart 4 B3 for a bar height 8 drawn for Wednesday or a bar height 12 drawn for Friday. or 58 −−3 4 − 4 − 16 − 11 M2 for  k , 2 + 3 k = 1,2 or 3 or M1 for 58 −−−−3 4 4 16 − 11 oe If 0 scored SC1 for 2 bars drawn correctly from their identified values in working 4(a)(iv) Saturday 1 4(b) 528 2  4  M1 for 550   1 −  oe  100  or B1 for 22 4(c) Positive 1 4(d)(i) 0.02 2 B1 for 0.98 correctly placed once on tree 0.98 or for 0.02 correctly placed twice on tree. 0.98 0.02 0.98 oe 4(d)(ii) 0.0004 oe 2 M1 for 0.02 × 0.02 4(d)(iii) 83 1

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5 (a) (i) Complete the table of values for y =- x 2 + 5x + 7 . x -1 0 1 2 3 4 5 6 y 11 11 1 [3] (ii) On the grid, draw the graph of y =- x 2 + 5x + 7 for - 1 G x G 6 . y 14 13 12 11 10 9 8 7 6 5 4 3 2 1 – 1 0 1 2 3 4 5 6 x [4] (iii) (a) Write down the equation of the line of symmetry of the graph. ................................................. [1] (b) The points ( -8, -97) and ( t, -97) also lie on the graph of y =- x 2 + 5 x + 7 . Use symmetry to find the value of t. t = ................................................. [1] (b) Write down the gradient of the line y = 9x - 4 . ................................................. [1] (c) Write down the equation of a line parallel to y =-5x + 19 . y = ................................................. [1] (d) y 7 6 L 5 4 3 2 1 – 4 – 3 – 2 – 1 0 1 2 3 4 x – 1 – 2 – 3 Find the equation of line L in the form y = mx + c . y = ................................................. [2] (e) Make x the subject of the formula y = mx + c . x = ................................................. [2]

Mark scheme: 5(a)(i) 1, 7, 13, 13, 7 3 B2 for 3 or 4 correct or B1 for 1 or 2 correct 5(a)(ii) Completely correct curve 4 B3FT for 7 or 8 correctly plotted points or B2FT for 5 or 6 correctly plotted points or B1FT for 3 or 4 correctly plotted points 5(a)(iii)(a) x = 2.5 oe 1 5(a)(iii)(b) 13 1 5(b) 9 1 5(c) y = −5 x + k where k  19 1 5(d)  y =  − x + 2 final answer 2 B1 for  y =  − x + c or  y =  mx + 2 where m is their gradient 5(e) − c 2 M1 for a correct first step  x = y oe final answer m y c y −=c mx or = x + m m

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6 (a) Town S is 44 km from town R on a bearing of 117°. (i) Using a scale of 1 cm represents 8 km, mark the position of town S. North R Scale: 1 cm to 8 km [2] (ii) Anvi cycles the 44 km from R to S. She leaves R at 13 15 and cycles at a speed of 12 km/h. Work out the time she arrives at S. ................................................. [3] (b) A tower has a height of 16 metres. When Jai makes a scale drawing of the tower it has a height of 20 cm. Work out the scale Jai uses, giving your answer in the form 1 : n. 1 : ................................................. [2] (c) X, Y and Z are three towns. Z North NOT TO 9.7 km SCALE X 6 km Y X is on a bearing of 288° from Y. Z is on a bearing of 018° from Y. (i) Show that angle XYZ is 90°. [2] (ii) XY = 6 km and YZ = 9.7 km . Calculate XZ. XZ = ............................................ km [2]

Mark scheme: 6(a)(i) The position of S correctly marked on the 2 B1 for S on bearing 117° from R diagram B1 for S 5.5 cm from R 6(a)(ii) 16 55 3 B2 for 3 [h] 40 [min] 44 or M1 for 12 6(b) [1:]80 2 M1 for 20:1600 or 0.2:16 or better 1600 16 or or 20 0.2 or B1 for answer figs 8 6(c)(i) 360 − 288 + 18 oe M2 M1 for 360 − 288 or 288 − 18 If 0 scored SC1 for 72 and 18 correctly marked on the diagram 6(c)(ii) 11.4 or 11.40 to 11.41 2 M1 for 6 2 + 9.7 2 or better

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7 (a) P = 3a + 5 Find the value of P when a = 2 . P = ................................................. [1] (b) Solve these equations. (i) 7x =-42 x = ................................................. [1] (ii) 9 ( 8x - 7) = 72 x = ................................................. [3] (c) 5 8 # 5 k = 5 -24 Find the value of k. k = ................................................. [1] (d) Solve the simultaneous equations. -6x - y = 13 8x + y =- 51 x = ................................................. y = ................................................. [2] (e) n is an integer where n 2- 3 and n G 1. Write down all the possible values of n. ................................................. [2] (f) A boy walks for 35 minutes at x metres per minute. He then runs for t minutes at 160 metres per minute. Write down an expression, in terms of x and t, for the total distance, in metres, the boy travels. .............................................. m [2] (g) NOT TO SCALE x – 2 x + 5 Find an expression for the area of this rectangle. Give your answer in the form x 2 + ax + b . ................................................. [3] Question 8 is printed on the next page.

Mark scheme: 7(a) 11 1 7(b)(i) −6 1 7(b)(ii) 1.875 oe 3 M1 for a correct first step e.g. 8 x − 7 = 8 or 72 x− 63 = 72 M1FT for a correct second step e.g. 8 x = 15 or 72 x = 135 7(c) −32 1 7(d)  x =  − 19  y = 101 2 B1 for  x =  − 19 B1 for  y = 101 7(e) −2, −1, 0, 1 2 B1 for 3 correct and no extras or 4 correct and one extra 7(f) 35x + 160t final answer 2 B1 for 35x or 160t seen in final answer or 35 x + 160t seen and spoilt 7(g) x 2 + 3 x − 10 final answer 3 B2 for x 2 + 5 x − 2 x − 10 with at least 3 terms correct or B1 for ( x + 5 )( x − 2 ) oe

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8 (a) 120 people teach in a university mathematics department. Some information is shown in the table. Lecturers Professors Total Part-time 11 Full-time Total 120 One fifth of the people are professors. 30% of the people are part-time. Work out the number of full-time lecturers. ................................................. [4] (b) % = {children in a school} F = {children who like fruit} V = {children who like vegetables} 24 children like vegetables but do not like fruit. 8 children do not like fruit and do not like vegetables. n ( F + V ) = 9 n ( F ) = 3 # n ( V ) F V ........ ........ ........ ........ (i) Complete the Venn diagram. [3] (ii) Work out n ( F , V ) . ................................................. [1]

Mark scheme: 8(a) 71 nfww 4 B3 for 13 and 84 or for 25 and 96 OR B1 for 24 or 96 B1 for 36 or 84 8(b)(i) 3 If answer incorrect can score a maximum of 2 from: F V B1 for 24 and 8 correctly placed 90 9 24 B1 for 9 correctly placed B1FT for their n(F)= 3×their n(V) 8 8(b)(ii) 123 1 B1FT for their n(F V)

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