Cambridge IGCSE Mathematics 0580 — 2013 May/June Paper 2 · Variant 1
0580/21/M/J/13 · 26 questions · 70 marks · ≈79 min
The question paper and its mark scheme, free to read here and free to download. This is Cambridge’s own paper, exactly as it was sat.
Question paper12 pages
Mark scheme4 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · One January day in Munich, the temperature at noon was 3°C
1 One January day in Munich, the temperature at noon was 3°C. For Examiner′s At midnight the temperature was –8°C. Use Write down the difference between these two temperatures. Answer .......................................... °C [1] _____________________________________________________________________________________
Mark scheme: Qu. Answers Mark Part Marks 1 11 or –11 1
Q2 · Calculate 5.7 – 1.032
2 (a) Calculate 5.7 – 1.032 . Write down all the numbers displayed on your calculator. Answer(a) ............................................... [1] (b) Write your answer to part (a) correct to 3 decimal places. Answer(b) ............................................... [1] _____________________________________________________________________________________
Mark scheme: 2 (a) 1.32656... 1 (b) 1.327 1ft
Q3 · Pedro and Eva do their homework
3 Pedro and Eva do their homework. Pedro takes 84 minutes to do his homework. The ratio Pedro’s time : Eva’s time = 7 : 6. Work out the number of minutes Eva takes to do her homework. Answer ........................................ min [2] _____________________________________________________________________________________
Mark scheme: 3 72 2 M1 for 84 ÷ 7
Q4 · 50° NOT TO 55° SCALE a° Use the information in the diagram to fi nd the value of a
4 50° NOT TO 55° SCALE a° Use the information in the diagram to fi nd the value of a. Answer a = ............................................... [2] _____________________________________________________________________________________
Mark scheme: 4 105 2 M1 for 180 – 55 – 50 or B1 for 55 or 75 seen in the correct angle inside the triangle 3 k
Q5 · For 1 3 5 Show that 1 ÷ = 8
For 1 3 5 Show that 1 ÷ = 8. Examiner′s 2 16 Use Do not use a calculator and show all the steps of your working. Answer [2] _____________________________________________________________________________________
Mark scheme: 3 k 5 correct working; 2 M1 for 2 k 3k 16n e.g. × = 8 3 k 16n 2 k 3n and A1 for × = 8 2 k 3n 2
Question 6
6 Factorise completely. 12xy – 3x2 Answer ............................................... [2] _____________________________________________________________________________________
Mark scheme: 6 3x(4y – x) final answer 2 B1 for 3(4xy – x2) or x(12y – 3x)
Q7 · D N C A M B The diagram shows a square ABCD
7 D N C A M B The diagram shows a square ABCD. M is the midpoint of AB and N is the midpoint of CD. (a) Complete the statement. The line MN is the locus of points inside the square which are ........................................................................................................................................... [1] (b) Shade the region inside the square containing points which are nearer to AB than to BC and nearer to A than to B. [1] _____________________________________________________________________________________
Mark scheme: 7 (a) Equidistant from A and B 1 (or C and D or AD and BC) (b) 1
Question 8
8 Solve the inequality. For Examiner′s 3x – 1 Ğ 11x + 2 Use Answer ............................................... [2] _____________________________________________________________________________________
Mark scheme: 8 x ≥−3 oe 2 M1 for –3 ≤ 8x oe 8 If 0 then SC1 for −3 with incorrect inequality. 8
Q9 · An equilateral triangle has sides of length 16.1 cm, correct to the nearest millimetre
9 An equilateral triangle has sides of length 16.1 cm, correct to the nearest millimetre. Find the lower and upper bounds of the perimeter of the triangle. Answer Lower bound = ......................................... cm Upper bound = ......................................... cm [2] _____________________________________________________________________________________
Mark scheme: 9 48.15, 48.45 cao 2 B1 B1 If 0 then M1 for 16.0 and 16.15 soi
Question 10
10 Factorise completely. ap + bp – 2a – 2b Answer ............................................... [2] _____________________________________________________________________________________
Mark scheme: 10 (a + b)(p – 2) 2 B1 p(a + b) – 2(a + b) or a(p – 2) + b(p – 2) 4 4 k
Q11 · 11 Write 27x12 3 in its simplest form
1 11 Write 27x12 3 in its simplest form. ^ h Answer ............................................... [2] _____________________________________________________________________________________
Mark scheme: 11 3x4 2 B1 for kx4 or 3xk IGCSE – May/June 2013 0580 21
Q12 · For Examiner′s 2 Use 1 3 5 R F 11 students are asked if they like rugby (R) and if they…
12 For Examiner′s 2 Use 1 3 5 R F 11 students are asked if they like rugby (R) and if they like football (F). The Venn diagram shows the results. (a) A student is chosen at random. What is the probability that the student likes rugby and football? Answer(a) ............................................... [1] (b) On the Venn diagram shade the region R' ∩ F' . [1] _____________________________________________________________________________________
Mark scheme: 12 (a) 3 1 11 (b) 1
Q13 · Martina changed 200 Swiss francs (CHF) into euros (€)
13 Martina changed 200 Swiss francs (CHF) into euros (€). The exchange rate was €1 = 1.14 CHF. Calculate how much Martina received. Give your answer correct to the nearest euro. Answer € ...................................... [3] _____________________________________________________________________________________
Mark scheme: 13 175 cao final answer 3 B2 for 175.4 ... or M1 for 200 ÷ 1.14
Q14 · Bruce invested $420 at a rate of 4% per year compound interest
14 Bruce invested $420 at a rate of 4% per year compound interest. Calculate the total amount Bruce has after 2 years. Give your answer correct to 2 decimal places. Answer $ ...................................... [3] _____________________________________________________________________________________
Mark scheme: 14 454.27 cao final answer 3 M1 for 420 × (1+ 1004 )2 oe and A1 for 454 or 454.2 to 454.3 or SC2 for answer 34.27 or SC1 for answer 34.2 to 34.3
Q15 · A sphere has a volume of 80 cm3
15 A sphere has a volume of 80 cm3. For Examiner′s Use Calculate the radius of the sphere. 4 [The volume, V, of a sphere with radius r is V = 3 πr 3 .] Answer ......................................... cm [3] _____________________________________________________________________________________
Mark scheme: 15 2.67 or 2.672 to 2.67301 3 M2 for 3 (80 ÷ 43 π ) oe or M1 for 80 ÷ ( 43π ) oe
Q16 · A water pipe has a circular cross section of radius 0.75 cm
16 A water pipe has a circular cross section of radius 0.75 cm. Water fl ows through the pipe at a rate of 16 cm/s. Calculate the time taken for 1 litre of water to fl ow through the pipe. Answer ............................................ s [3] _____________________________________________________________________________________
Mark scheme: 16 35.4 or 35.36 to 35.37 3 M2 for 1000 ÷ (π × 0.752 ×16) oe or M1 for π × 0.752 ×16 oe or 1000 ÷ ( π × .0 75 2 )
Q17 · Find the equation of the line passing through the points (0, –1) and (3, 5)
17 Find the equation of the line passing through the points (0, –1) and (3, 5). For Examiner′s Use Answer ............................................... [3] _____________________________________________________________________________________
Mark scheme: 17 y = 2x − 1 3 B2 for y = mx – 1 or y = 2x + c or 2x – 1 or B1 for gradient = 2, B1 for c = –1 6 5 − −1 or SC1 for or 3 [3−0]
Q18 · Factorise x2 + x – 30
18 (a) Factorise x2 + x – 30. Answer(a) ............................................... [2] (x - 5)(x + 4) . (b) Simplify x2 + x - 30 Answer(b) ............................................... [1] _____________________________________________________________________________________
Mark scheme: 18 (a) (x + 6)(x–5) 2 SC1 for (x + a)(x + b) where ab = –30 or a + b (b) x + 4 1 final answer x + 6 6 k
Q19 · T varies inversely as the square root of u
19 t varies inversely as the square root of u. For Examiner′s t = 3 when u = 4. Use Find t when u = 49. Answer t = ............................................... [3] _____________________________________________________________________________________
Mark scheme: 6 k 19 or 0.857[1…] 3 M1 for t = oe 7 u A1 for k = 6
Q20 · R Q S NOT TO r M SCALE O p P OPQR is a parallelogram, with O the origin
20 R Q S NOT TO r M SCALE O p P OPQR is a parallelogram, with O the origin. M is the midpoint of PQ. OM and RQ are extended to meet at S. = p and = r. (a) Find, in terms of p and r, in its simplest form, (i) , Answer(a)(i) = ............................................... [1] (ii) the position vector of S. Answer(a)(ii) ............................................... [1] 1 (b) When = – 2 p + r , what can you write down about the position of T ? Answer(b) ................................................................................................................................. [1] _____________________________________________________________________________________
Mark scheme: 20 (a) (i) p + 12 r 1 (ii) 2p + r 1ft 2 × their (i) (b) Midpoint of RQ 1 IGCSE – May/June 2013 0580 21
Q21 · For Examiner′s Use NOT TO SCALE 12 cm 135° 12 cm The diagram shows a sector of a circle…
21 For Examiner′s Use NOT TO SCALE 12 cm 135° 12 cm The diagram shows a sector of a circle of radius 12 cm with an angle of 135°. Calculate the perimeter of the sector. Answer ......................................... cm [3] _____________________________________________________________________________________
Mark scheme: 21 52.3 or 52.27 to 52.28 3 SC2 for 28.3 or 28.7 to 28.8 135 If 0, M2 for × π × 24 + 2 × 12 360 135 or M1 for ×π × 24 360
Q22 · Write as a single fraction in its simplest form
22 Write as a single fraction in its simplest form. 2 3 + x + 3 x + 2 Answer ............................................... [3] _____________________________________________________________________________________
Mark scheme: 22 5 x + 13 3 B1 for common denominator (x + 3)(x + 2) seen oe final answer ( x + 3)( x + 2) M1 for 2(x + 2) + 3(x + 3) soi
Q23 · For Examiner′s F C Use 6 cm NOT TO SCALE D A 5 cm E 12 cm B The diagram shows a…
23 For Examiner′s F C Use 6 cm NOT TO SCALE D A 5 cm E 12 cm B The diagram shows a triangular prism of length 12 cm. Triangle ABC is a cross section of the prism. Angle BAC = 90°, AC = 6 cm and AB = 5 cm. Calculate the angle between the line CE and the base ABED. Answer ............................................... [4] _____________________________________________________________________________________
Mark scheme: 23 4 M1 for recognition of angle CEA 24.8 or 24.77 to 24.78 M1 for 122 + 52 6 M1 for tan = oe their AE
Q24 · 2 4 3 24 A = B = e 3 4 o e1 2 o Find (a) AB, Answer(a) AB = [2] (b) B –1, the inverse of B
1 2 4 3 24 A = B = e 3 4 o e1 2 o Find (a) AB, Answer(a) AB = [2] (b) B –1, the inverse of B. Answer(b) B –1 = [2] _____________________________________________________________________________________
Mark scheme: 24 (a) 6 7 2 B1 for 1 correct row or 1 correct column 16 17 1 a b 2 −3 1 2 −3 2 (b) or B1 for k 5 −1 4 −1 4 5 c d
Q25 · For Examiner′s Use 28 NOT TO SCALE Speed (m/s) 0 20 30 Time (seconds) The diagram shows…
25 For Examiner′s Use 28 NOT TO SCALE Speed (m/s) 0 20 30 Time (seconds) The diagram shows the speed-time graph of a car. It travels at 28 m/s for 20 seconds and then decelerates until it stops after a further 10 seconds. (a) Calculate the deceleration of the car. Answer(a) ...................................... m/s2 [1] (b) Calculate the distance travelled during the 30 seconds. Answer(b) ........................................... m [3] _____________________________________________________________________________________ Question 26 is printed on the next page.
Mark scheme: 25 (a) 1 2.8 oe (b) 3 M2 for ½(20 + 30) × 28 oe 700 or M1 for a correct area statement 2 2
Q26 · For Examiner′s Use NOT TO C SCALE D 6 cm 4 cm 15 cm A 9 cm B The diagram shows a solid…
26 For Examiner′s Use NOT TO C SCALE D 6 cm 4 cm 15 cm A 9 cm B The diagram shows a solid prism of length 15 cm. The cross section of the prism is the trapezium ABCD. Angle DAB = angle CDA = 90°. AB = 9 cm, DC = 6 cm and AD = 4 cm. Calculate the total surface area of the prism. Answer ........................................ cm2 [5]
Mark scheme: 26 420 5 M1 for [CB =] 4 2 + (9 − 6) 2 M1 for their CB from Pythagoras × 15 M1 for [2 ×] 12 ( 6 + 9) × 4 M1 for 4 × 15, 9 × 15, 6 × 15 with intention to add
What was in this paper
The subtopics covered by these 26 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
4Ratio and proportion3Surface area and volume2Vectors in two dimensions2Angles1Area and perimeter1Circles, arcs and sectors1Equations of linear graphs1Fractions, decimals and percentages1Inequalities1Introduction to probability1Limits of accuracy1Money1Powers and roots1Pythagoras’ theorem and trigonometry1Rates1Symmetry1The four operations1Using a calculator1What you needed in this session
Cambridge’s own grade thresholds for 2013 May/June, Paper 2 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.