Cambridge IGCSE Mathematics Paper 2 Non-calculator (Extended) Specimen Paper B PDF

Cambridge IGCSE™ *0123456789* MATHEMATICS0580/02 Paper 2 Non-calculator (Extended) For examination from 2025 SPECIMEN PAPER B 2 h...

Cambridge IGCSE™ *0123456789* MATHEMATICS0580/02 Paper 2 Non-calculator (Extended) For examination from 2025 SPECIMEN PAPER B 2 hours 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. Calculators must not be used in this paper. You may use tracing paper. You must show all necessary working clearly. INFORMATION The total mark for this paper is 100. The number of marks for each question or part question is shown in brackets [ ]. This document has 16 pages. © Cambridge University Press & Assessment 2023 [Turn over v1  2 List of formulas 1 Area, A, of triangle, base b, height h. A = 2 bh Area, A, of circle of radius r. A = rr 2 Circumference, C, of circle of radius r. C = 2rr Curved surface area, A, of cylinder of radius r, height h. A = 2rrh Curved surface area, A, of cone of radius r, sloping edge l. A = rrl Surface area, A, of sphere of radius r. A = 4rr 2 Volume, V, of prism, cross-sectional area A, length l. V = Al 1 Volume, V, of pyramid, base area A, height h. V = 3 Ah Volume, V, of cylinder of radius r, height h. V = rr 2 h 1 Volume, V, of cone of radius r, height h. V = 3 rr 2 h 4 Volume, V, of sphere of radius r. V = 3 rr 3 -b ! b 2 - 4ac For the equation ax2 + bx + c = 0, where a ≠ 0, x= 2a For the triangle shown, A a b c = = sin A sin B sin C a 2 = b 2 + c 2 - 2bc cos A c b 1 Area = 2 ab sin C B a C © Cambridge University Press & Assessment 2023 0580/02B/SP/25  3 Calculators must not be used in this paper. 1 Write the ratio 12 : 30 in its simplest form. ........................ :.................... 2 Write down the number of lines of symmetry of a kite................................................. 3 The stem-and-leaf diagram shows the number of minutes taken by each of 18 students to complete a task. 1 2 3 6 9 2 1 2 2 3 4 8 8 9 3 1 4 5 5 9 9 Key: 1 | 2 represents 12 minutes (a) Find the range.................................... minutes (b) Find the median.................................... minutes (c) A student draws a pie chart to show the information in the stem-and-leaf diagram. Complete the table for the angles on the pie chart. Number of minutes (t) Angle on pie chart (°) 10 < t ⩽ 20 20 < t ⩽ 30 30 < t ⩽ 40  © Cambridge University Press & Assessment 2023 0580/02B/SP/25 [Turn over  4 3 14 4 Work out 7 #. 15 Give your answer as a fraction in its simplest form................................................. 5 Find the size of an interior angle of a regular decagon................................................. 6 Convert 5.7 litres into cm3........................................... cm3 7 Write these numbers in order, starting with the smallest. 3 1 0.143 16% 20 6 .................... ,.................... ,..................... ,.................... smallest © Cambridge University Press & Assessment 2023 0580/02B/SP/25  5 8 Jude has a fair 8-sided spinner numbered 1 to 8. 2 1 3 8 4 7 5 6 (a) Jude spins the spinner once. Find the probability that the spinner lands on (i) a number greater than 6................................................ (ii) an even number or a multiple of 7................................................. (b) Jude spins the spinner 240 times. Work out the expected number of times the spinner lands on a number greater than 6................................................. © Cambridge University Press & Assessment 2023 0580/02B/SP/25 [Turn over  6 9 Using a ruler and pair of compasses only, construct a rhombus with side length 6 cm and a diagonal of length 9.5 cm. One side has been drawn for you.  10 The time that Rafiq works is divided into meetings, planning and working on a computer. One day, Rafiq is 3 in meetings for of the time 4 1 planning for 5 of the time working on a computer for the remaining 25 minutes of the time. Work out the total time that Rafiq works this day. Give your answer in hours and minutes. .................... hours.................... minutes © Cambridge University Press & Assessment 2023 0580/02B/SP/25  7 11 (a) Expand. 2x(3x2 – 8x)................................................ (b) (i) Factorise. x2 – 192................................................ (ii) Work out. 812 – 192................................................ 12 A force of 196 newtons is applied to a square surface of side 4.9 cm. By writing each number correct to 1 significant figure, work out an estimate of the pressure applied to the square surface. [Pressure = force ÷ area] [Pressure is measured in newtons / cm2].......................... newtons / cm2 © Cambridge University Press & Assessment 2023 0580/02B/SP/25 [Turn over  8 13 y 6 5 4 3 2 1 A –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 x –1 –2 B –3 –4 –5 (a) On the grid, draw the image of (i) triangle A after a reflection in the line y = x + 2  3 (ii) triangle A after an enlargement by scale factor with centre (1, 0).  2 (b) Describe fully the single transformation that maps triangle A onto triangle B............................................................................................................................................................................................................................................................................................................... © Cambridge University Press & Assessment 2023 0580/02B/SP/25  9 14 Write 0.38o as a fraction. Give your answer in its simplest form................................................. 15 Freya records how many minutes she takes to complete a crossword each day. On Tuesday, she takes 10% less time than on Monday. On Wednesday, she takes 50% less time than on Tuesday. On Wednesday, she takes 9 minutes to complete the crossword. Find the number of minutes Freya takes to complete the crossword on Monday.................................... minutes PQ = f p and QR = f p. 3 1 16 −1 9 Work out the length of PR................................................. © Cambridge University Press & Assessment 2023 0580/02B/SP/25 [Turn over  10 17 NOT TO SCALE 6 cm The diagram shows a sector of a circle with radius 6 cm. The area of the sector is 15π cm2. (a) Work out the perimeter of the sector. Give your answer in the form a + bπ, where a and b are integers............................................ cm (b) The sector is the cross-section of a prism of length 10 cm. Work out, giving your answer in terms of π, (i) the volume of the prism.......................................... cm3 (ii) the total surface area of the prism........................................... cm2 © Cambridge University Press & Assessment 2023 0580/02B/SP/25  11 18 (a) (i) Write x2 − 8x + 10 in the form (x − a)2 – b................................................. (ii) Sketch the graph of y = x2 − 8x + 10. On the sketch, label the coordinates of the turning point and the y-intercept. y O x  (b) A point P lies on the graph of y = x2 − 8x + 10. The gradient of the graph at P is 6. Find the coordinates of P.  (.................... ,.................... ) © Cambridge University Press & Assessment 2023 0580/02B/SP/25 [Turn over  12 19 (a) Simplify. 75 − 3................................................ (b) Rationalise the denominator and simplify. 8 1− 5................................................ 20 Expand and simplify. (2x – 3)(x + 1)(2 – 3x)................................................ © Cambridge University Press & Assessment 2023 0580/02B/SP/25  13 21 D 9 cm NOT TO SCALE C 6 cm 30° B A The diagram shows two right-angled triangles, ABC and ACD. Find the value of cos ADC. cos ADC =............................................... © Cambridge University Press & Assessment 2023 0580/02B/SP/25 [Turn over  14 22 In this question, all lengths are given in centimetres. B NOT TO SCALE D 10 2x 7.5 (x + 5) C E A Triangle ABC is mathematically similar to triangle ADE. (a) (i) Show that 2x2 + 15x – 50 = 0.  (ii) Solve by factorising 2x2 + 15x – 50 = 0.  x =.................... or x =.................... (iii) Find the length AC. AC =.......................................... cm © Cambridge University Press & Assessment 2023 0580/02B/SP/25  15 (b) The area of triangle ABC is k cm2. Find an expression for the area of the quadrilateral BCED. Give your answer in terms of k........................................... cm2 23 P Q R In the Venn diagram, shade the region P ∪ Q ′ ∪ R′.  24 Rearrange the formula to make p the subject. 2p + 3 d = 2 − py p =............................................... © Cambridge University Press & Assessment 2023 0580/02B/SP/25 [Turn over  16 25 (a) Simplify. (i) (2xy)0................................................ 2 f 2p 81m8 3 (ii) 3m................................................ (b) Find the value of x. 1 32x × 2x+3 = 4 x =............................................... 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 (Cambridge University Press & Assessment) 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. 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