Cambridge IGCSE Mathematics Paper 2 (Extended) February/March 2024 PDF

Cambridge IGCSE™ * 2 7 6 5 3 0 3 7 6 9 * MATHEMATICS 0580/22 Paper 2 (Extended)...

Cambridge IGCSE™ * 2 7 6 5 3 0 3 7 6 9 * MATHEMATICS 0580/22 Paper 2 (Extended) February/March 2024 1 hour 30 minutes You must answer on the question paper. You will need: Geometrical instruments INSTRUCTIONS 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 70. The number of marks for each question or part question is shown in brackets [ ]. This document has 12 pages. DC (PQ/CGW) 327786/3 © UCLES 2024 [Turn over  2 1 A night bus runs from 21 50 to 05 18 the next day. Work out the number of hours and minutes that the night bus runs.................... h.................... min 2 Calculate 5.76 + 2.8 3.................................................. 3 Simplify 4m + 7k - m + 3k.................................................. 4 b cm NOT TO SCALE c cm d cm a cm Base The diagram shows the net of a cuboid with its base shaded. The length of the cuboid is 10 cm, its width is 4 cm and its height is 5 cm. Write down the values of each of a, b, c and d. a =........................., b =........................., c =........................., d =......................... © UCLES 2024 0580/22/F/M/24  3 5 There are 20 cars in a car park and 3 of the cars are blue. (a) James wants to draw a pie chart to show this information. Find the angle of the sector for the blue cars in this pie chart.................................................. (b) One of the 20 cars is picked at random. Find the probability that this car is not blue.................................................. 6 y 5 B 4 3 2 A 1 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 x Write AB as a column vector. AB = f p 7 As the temperature increases, the number of people who go swimming increases. Write down the type of correlation that this statement describes.................................................. © UCLES 2024 0580/22/F/M/24 [Turn over  4 8 (a) The nth term of a sequence is n 2 - 3. Find the first three terms of this sequence................ ,............... ,............... (b) These are the first five terms of a different sequence. 1 3 9 27 81 Find the nth term of this sequence.................................................. 9 The line y = 2x - 5 intersects the line y = 3 at the point P. Find the coordinates of the point P. (....................... ,.......................) © UCLES 2024 0580/22/F/M/24  5 10 S 5.3 cm R 4.4 cm NOT TO 3.8 cm SCALE P 8.7 cm Q The diagram shows a trapezium PQRS. Calculate the area of the trapezium.......................................... cm 2 1 5 11 Without using a calculator, work out 1 -. 4 6 You must show all your working and give your answer as a fraction in its simplest form.................................................. © UCLES 2024 0580/22/F/M/24 [Turn over  6 12 Farid spins a three-sided spinner with sides labelled A, B and C. The probability that the spinner lands on C is 0.35. Farid spins the spinner 40 times. Calculate the number of times he expects the spinner to land on C.................................................. 13 The bearing of B from A is 107°. Calculate the bearing of A from B.................................................. 14 A train, 1750 metres long, is travelling at 55 km/h. Calculate how long it will take for the whole train to completely cross a bridge that is 480 metres long. Give your answer in seconds, correct to the nearest second................................................ s © UCLES 2024 0580/22/F/M/24  7 15 y 4 3 2 1 B A – 10 – 9 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 x –1 –2 C –3 –4 –5 –6 (a) Describe fully the single transformation that maps (i) triangle A onto triangle B.......................................................................................................................................................................................................................................................................................... (ii) triangle A onto triangle C........................................................................................................................................................................................................................................................................................... (b) Draw the image of triangle A after a rotation, 90° clockwise, about (1, 3). © UCLES 2024 0580/22/F/M/24 [Turn over  8 16 x is an integer. % = {x : 1 G x G 10 } P = {x : x is an even number} Q = {x : x is a multiple of 5}  P Q Complete the Venn diagram. 17 The height of each of 200 people is measured. The table shows the results. Height (h cm) 100 1 h G 120 120 1 h G 130 130 1 h G 150 150 1 h G 190 Frequency 32 55 64 49 Calculate an estimate of the mean height............................................. cm 18 Find the highest common factor (HCF) of 28x 5 and 98x 3.................................................. © UCLES 2024 0580/22/F/M/24  9 19 15 Speed (m/s) NOT TO SCALE 0 20 140 190 Time (seconds) The speed–time graph shows information about a bus journey. Calculate the total distance travelled by the bus.............................................. m 20 C NOT TO 5.6 cm SCALE 23° A 4.9 cm B Calculate the area of triangle ABC.......................................... cm 2 © UCLES 2024 0580/22/F/M/24 [Turn over  10 21 (a) 5 3 = 3h Write down the value of h. h =................................................ (b) Simplify `4x 3j. 3................................................. 22 y is inversely proportional to the square of (x + 3). When x = 5, y = 0.375. Find y in terms of x. y =................................................ © UCLES 2024 0580/22/F/M/24  11 23 (a) On the axes, sketch the graph of y = cos x , for 0° G x G 360°. y 1 0 180° 360° x –1 (b) Solve the equation cos x = 0.294 for 0° G x G 360°. x =.................. or x =.................. 24 x 2 - 16x + a can be written in the form (x + b) 2. Find the value of a and the value of b. a =................................................ b =................................................ Questions 25 and 26 are printed on the next page. © UCLES 2024 0580/22/F/M/24 [Turn over  12 25 A bag contains 2 green buttons, 5 red buttons and 6 blue buttons. Two buttons are taken at random from the bag without replacement. Calculate the probability that the two buttons are different colours.................................................. 26 A is the point (6, 1) and B is the point (2, 7). Find the equation of the perpendicular bisector of AB. Give your answer in the form y = mx + c. y =................................................. Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. Cambridge Assessment International Education is part of Cambridge Assessment. Cambridge Assessment is the brand name of the University of Cambridge Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge. © UCLES 2024 0580/22/F/M/24