Sets — Paper 3 · IGCSE Mathematics 0580

9 (a)  = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14} F = {x: x is a factor of 14} P = {x: x is a prime number less than 14} (i) Write down the elements in set F. F = { … } [2] (ii) Write down the elements in set P. P = { … } [2] (iii) F P (a) Complete the Venn diagram. [2] (b) Write down n ( F + P ) . … [1] (c) A number is chosen at random from the universal set . Write down the probability that the number is in the set F , P . … [2] (b) Write 195 as a product of its prime factors. … [2]

11 marks

Mark scheme: 9(a)(i) 1, 2, 7, 14 2 B1 for 3 correct and one omission or for 4 correct and one extra 9(a)(ii) 2, 3, 5, 7, 11, 13 2 B1 for 5 correct and one omission or for 6 correct and one extra 9(a)(iii)(a) 1, 14 2, 7 3, 5, 11, 13 2 FT their (a)(i) and their (a)(ii) 4, 6, 8, 9, 10, 12 B1FT for two or three sections correct 9(a)(iii)(b) 2 1 FT from their diagram 9(a)(iii)(c) 4 2 FT from their diagram for the numerator oe 7 k B1 for , k ⩽ 14 14 9(b) 3 × 5 × 13 2 B1 for 3, 5, 13 or 65 × 3 or 39 × 5 or 15 × 13

This question in 0580/32 Feb/March 2020

9 (a) Use set notation to describe the shaded region in each Venn diagram. A B … A B … [2] (b)  = {x : x is a natural number G15} F = {x : x is a factor of 12} O = {x : x is an odd number} (i) Complete the Venn diagram to show the elements of these sets. F O 10 2 7 [2] (ii) Write down one number that is in set O, but not in set F. … [1] (iii) Find n ( F , O ) . … [1] (iv) A number is chosen at random from . Work out the probability that this number is in set O. … [1] Question 10 is printed on the next page.

7 marks

Mark scheme: 9(a) A ∪ B A ∩ B 2 B1 for each 9(b)(i) 2 B1 for 2 or 3 correctly completed regions 9(b)(ii) One of 5, 7, 9, 11, 13, 15 1 FT their Venn diagram 9(b)(iii) 12 1 FT their Venn diagram 9(b)(iv) 8 1 FT their Venn diagram oe 15

This question in 0580/31 May/June 2020

8 (a) COMMONWEALTH Lindon picks a letter at random from this word. 1 Explain why the probability that he picks a letter M is not . 10 … [1] (b) Tickets for athletics or swimming or hockey or diving are placed in a box. A ticket is picked at random from the box. Sport Athletics Swimming Hockey Diving Probability 0.12 0.09 0.4 Complete the table. [2] (c) In a group of 40 students, • 24 students like football • 19 students like cricket • 10 students like football but not cricket. Football Cricket Complete the Venn diagram. [3] (d)  = {x : x is a positive integer less than 20} A = {x : x is an even number} B = {x : x is a multiple of 3} A B 2 4 3 6 8 10 9 12 14 15 18 16 1 5 7 11 13 17 19 (i) Write down n ( A ) . … [1] (ii) List the elements of set B. B = { … } [2] (iii) One of these 19 numbers is picked at random. Work out the probability that this number is (a) not in set A and not in set B, … [1] (b) in A , B . … [1] (iv) Complete the statement. A + B = {x : x is … } [1]

12 marks

Mark scheme: 8(a) There are 2 M’s or 12 letters 1 8(b) 0.39 oe 2 M1 for 1– (0.12 + 0.09 + 0.4) oe 8(c) Football Cricket 3 B1 for 10 B1FT for 14 and 5 10 14 5 or their 10 + their 14 = 24 and their 14 + their 5 = 19 11 B1FT for 11 or 40 – (their 10 + their 14 + their 5) 8(d)(i) 9 cao 1 8(d)(ii) 3 6 9 12 15 18 2 B1 for 4 or 5 correct and no extras 8(d)(iii)(a) 7 1 oe 19 8(d)(iii)(b) 12 1 oe 19 8(d)(iv) Even and a multiple of 3 1 or a multiple of 6 oe

This question in 0580/32 Oct/Nov 2020

8 (a) A baker puts some cakes in the oven at 5.50 pm. The cakes take 20 minutes to bake. 12 11 1 10 2 9 3 8 4 7 5 6 Complete the clock diagram to show the time when the cakes are baked. [1] (b) A recipe uses 550 g of flour to make 8 cakes. Work out the amount of flour needed to make 360 cakes. Give your answer in kilograms. … kg [3] (c) NOT TO Bag A Bag B Bag C SCALE 850 g 950 g 1250 g 55 cents 60 cents 80 cents Work out which bag of flour is the best value. Show all your working. Bag … [3] (d) One cake costs 24 cents to make. The baker sells each cake for 65 cents. Calculate the percentage profit the baker makes on each cake. … % [2] (e) The baker asks some customers if they like lemon cake (L) and if they like chocolate cake (C). The Venn diagram shows the results. L C Kab Bel Yesa Jai Haji Var Rea Nera Esh Ada Chir Taj (i) Complete the statement. n() = … [1] (ii) Work out the fraction of the customers who like lemon cake or chocolate cake but not both. … [1] (iii) Use set notation to complete the statement. {Jai, Nera} = … [1] (iv) What does the Venn diagram show about Taj? … [1]

13 marks

Mark scheme: 8(a) 10 past 6 shown on clock face 1 diagram 8(b) 24.75 3 550 × 360 M2 for oe 8 × 1000 550 × 360 or M1 for oe 8 or B1 for figs 2475 or figs 248 8(c) B 3 M2 for 3 correct divisions shown but either With correct comparisons made of not evaluated to enough accuracy or wrong the 3 bags with suitable accuracy bag selected shown or M1 for 2 correct divisions shown for 2 bags 8(d) 171 or 170.8… 2 65 − 24 M1 for [×100] 24 65 or × 100 [−100] 24 65 or −[×100]1 24 8(e)(i) 12 1 8(e)(ii) 3 1 or equivalent fraction 4 8(e)(iii) L ∩ C 1 8(e)(iv) Correct statement 1

This question in 0580/32 Feb/March 2021

9 (a)  = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} E = {x: x is an even number} M = {x: x is a multiple of 3} E M (i) Complete the Venn diagram. [2] (ii) Write down n ( E , M ) . … [1] (iii) A number is chosen at random from the universal set . Write down the probability that the number is in the set E + M . … [2] (b) Meg says that an even number cannot be a prime number. Is she correct? Give a reason for your answer. … because … [1]

6 marks

Mark scheme: 9(a)(i) 2 B1 for 2 or 3 regions correct 1 5 E M 7 2 11 4 6 3 8 12 9 10 9(a)(ii) 8 1 FT their (a)(i) 9(a)(iii) 1 2 FT their (a)(i) oe 6 B1FT for 2 or their n ( E ∩ M ) 9(b) No 2 is even and a prime oe 1

This question in 0580/31 May/June 2021

2 (a) A B Use set notation to describe the shaded region. … [1] (b)  = {x : x is a natural number G 16 } (i) Write down all the square numbers in the universal set, . … [2] (ii) Write down the six prime numbers in the universal set, . … , … , … , … , … , … [2] (iii) M = {x : x is a multiple of 3} F = {x : x is a factor of 15} (a) Complete the Venn diagram to show the elements of these sets. M F 2 9 1 16 11 13 7 8 [2] (b) Write down all the odd numbers that are not in set M and not in set F. … [1] (c) Find n ( M + F) . … [1] (d) A number is chosen at random from the universal set, . Find the probability that this number is in set F. … [1]

10 marks

Mark scheme: 2(a) A  B 1 2(b)(i) 1 4 9 16 2 B1 for 3 correct and none incorrect or for all correct and one extra incorrect 2(b)(ii) 2, 3, 5, 7, 11, 13 2 B1 for 5 correct and none or one incorrect 2(b)(iii)(a) 2 B1 for 2 or 3 regions correct 4 10 6 3 12 15 5 14 2(b)(iii)(b) 7 11 13 1 FT their Venn diagram 2(b)(iii)(c) 2 1 FT their Venn diagram 2(b)(iii)(d) 4 1 n( F ) oe FT their Venn diagram for 16 16

This question in 0580/33 May/June 2022

9 (a) Pure gold costs $42 per gram. The fraction of pure gold in an object is measured in carats. 1 One carat means of the mass of an object is pure gold. 24 Henry buys a 9-carat gold bracelet weighing 16 g. The price of the bracelet is $204. Is the price of the bracelet more or less than the cost of the pure gold in it? You must show your working. [4] (b) A clock made of metals has a mass of 1080 g. The mass of each metal in the clock is in the ratio copper : zinc : other metals = 21 : 14 : 1. Calculate the mass of copper in this clock. … g [2] (c) There are 110 people in a group. G = { people who own gold jewellery } S = { people who own silver jewellery } 18 people own both gold jewellery and silver jewellery. 46 people own gold jewellery. 11 people own no gold jewellery and no silver jewellery. G S (i) Complete the Venn diagram. [2] (ii) Write down n ( G + S ) . … [1] (iii) One of the 110 people is chosen at random. Write down the probability that this person owns gold jewellery but not silver jewellery. … [1] (d) E F Use set notation to describe the shaded region. … [1]

11 marks

Mark scheme: 9(a) Less 4 1 M3 for  9  16  42 oe with working leading to 252 24 or M2 for three of these multiplied or M1 for any two of these multiplied 9(b) 630 2 1080 M1 for [ k] oe 21 + 14 + 1 where k =1,14 or 21 oe 9(c)(i) 2 B1 for two or three in the correct places 9(c)(ii) 18 1 FT their diagram 9(c)(iii) 28 1 FT their 28 from their diagram oe 110 9(d) E F cao 1

This question in 0580/31 Oct/Nov 2023

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]

8 marks

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)

This question in 0580/32 Feb/March 2024

7 (a) % = {students in a group} M = {students who pass the mathematics test} S = {students who pass the science test} 142 students are in the group. 105 students pass the mathematics test. 82 students pass the mathematics test and pass the science test. 17 students do not pass the mathematics test and do not pass the science test. M S (i) Complete the Venn diagram. [2] (ii) Find n ( M , S ). … [1] (iii) One of these students is picked at random. Find the probability that this student passes the science test but does not pass the mathematics test. … [1] (b) A B Use set notation to describe the shaded region. … [1] (c) In a town, the number of students, n, who take the science test is 10 600, correct to the nearest hundred. Complete this statement about the value of n. … G n 1 … [2] (d) The table shows the number of students in another town who took the science test in 2022 and 2023. Year 2022 2023 Number of students 15 800 17 064 Calculate the percentage increase in the number of students from 2022 to 2023. … % [2] (e) The number of students who took the mathematics test in 2022 is 18 400. The ratio number of students who passed : number of students who did not pass is 4 : 1. Work out the number of students who passed. … [2]

11 marks

Mark scheme: 7(a)(i) 2 B1 for 2 or 3 numbers in the correct places 7(a)(ii) 125 1 FT their diagram with one value in each of the 3 regions of M and S, providing total <142 7(a)(iii) 20 1 their 20 oe FT providing their 20 < 142 142 142 7(b) A ∩ B 1 7(c) 10 550 10 650 2 B1 for one correct or SC1 for both correct and reversed 7(d) 8 nfww 2 17 064 − 15 800 M1 for [× 100] 15 800  17 064  or  − 1  [× 100]  15 800  17 064 or  100 [- 100] oe 15 800 7(e) 14 720 2 18400 M1 for [× k] (where k = 1 or 4) oe 1 + 4

This question in 0580/32 Oct/Nov 2024

26 Li asks 28 students if they speak English (E) and if they speak Spanish (S). 15 students speak English. 12 students speak Spanish. 6 do not speak English and do not speak Spanish. % E S (a) Complete the Venn diagram. [2] (b) Write down how many students speak English but do not speak Spanish. … [1] (c) Find n ( E , S ) . … [1]

4 marks

Mark scheme: 26(a) 2 B1 for one value in the correct place. 26(b) 10 1 FT their diagram (dep total = 28) 26(c) 22 1 FT their diagram (dep total = 28)

This question in 0580/31 May/June 2025