This document has 20 pages. Any blank pages are indicated.[Turn overCambridge IGCSE™MATHEMATICS0580/42Paper 4 (Extended)May/June20242 hours 30 minutesYou must answer on the question paper.You will need: Geometrical instrumentsINSTRUCTIONS●Answer all questions.●Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.●Write your name, centre number and candidate number in the boxes at the top of the page.●Write your answer to each question in the space provided.●Do not use an erasable pen or correction fluid.●Do not write on any bar codes.●You should use a calculator where appropriate.●You may use tracing paper.●You must show all necessary working clearly.●Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.●For r, use either your calculator value or 3.142.INFORMATION●The total mark for this paper is 130.●The number of marks for each question or part question is shown in brackets [ ].*6406182559*DC (PQ/CT) 329213/3© UCLES 2024
20580/42/M/J/24© UCLES 20241 (a)A fruit drink is made using 1.5 litres of apple juice and 450 millilitres of mango juice.Write the ratio apple juice : mango juice in its simplest form. ....................... : ....................... [2](b)One litre of fruit drink is shared between three cups.The amount in the cups is in the ratio 9 : 6 : 10.Calculate the number of millilitres in each cup........................ ml , ....................... ml , ....................... ml [3](c)A shop buys bottles of the fruit drink for $3.20 each.It sells them at a profit of 15%.Calculate the selling price of each bottle of fruit drink.$ ................................................ [2](d)The number of bottles of fruit drink sold has grown exponentially at a constant rate of 2.5% per year.5 years ago, the shop sold 16 620 bottles.Calculate the number of bottles sold this year. ................................................. [2]
30580/42/M/J/24© UCLES 2024[Turn over(e)NOT TOSCALE23cm18.5cmdcmThe bottles of juice are 18.5 cm tall, correct to the nearest millimetre.They are stored on shelves.The distance between the shelves is 23 cm, correct to the nearest centimetre. Calculate the lower bound for the distance, d cm, between the top of a bottle and the shelf above it. ............................................ cm [3]
40580/42/M/J/24© UCLES 20242 (a)NOT TOSCALE38°a°b°The diagram shows a straight line intersecting two parallel lines.Find the value of a and the value of b.a= ................................................b= ................................................ [2](b)Calculate the interior angle of a regular 12-sided polygon. ................................................. [2]
50580/42/M/J/24© UCLES 2024[Turn over(c)f°g°56°OMNPABNOT TOSCALEThe diagram shows a circle, centre O.The points M, N and P lie on the circumference of the circle.AMB is a tangent to the circle at M.Find the value of f and the value of g.f= ................................................g= ................................................ [3](d)k°24°27°NOT TOSCALEThe diagram shows a cyclic quadrilateral.Find the value of k.k= ................................................ [2]
60580/42/M/J/24© UCLES 20243 (a)The table shows the time that each of 40 students takes to travel to school.Time (m minutes)m0101Gm10251Gm20541Gm40061GFrequency318154(i) Calculate an estimate of the mean. .......................................... min [4](ii)On the grid, draw a histogram to show the information in the table.21010203040Time (minutes)5060m0Frequencydensity[3](iii)Two students are selected at random from the 40 students.Calculate the probability that one student takes more than 25 minutes and the other student takes 10 minutes or less to travel to school. ................................................. [3]
