Sets — Paper 4 · IGCSE Mathematics - International 0607

8 The 150 members of a sports club were asked if they played cricket (C), hockey (H) or tennis (T). Some members play none of the three sports. The Venn diagram shows the numbers of members who play the three sports. U H C 12 35 24 8 13 15 27 T (a) Calculate the number of members who play none of the three sports. … [1] (b) Two of the 150 members are picked at random. Calculate the probability that (i) they both play hockey and tennis but not cricket, … [2] (ii) they are both members of the set (C , H ) + T l. … [3] (c) Three of the members who play tennis are chosen at random. Calculate the probability that none of them play cricket. … [3]

9 marks

Mark scheme: 8(a) 16 1 8(b)(i) 7 2 15 14 oe M1 for × oe with no extra 745 150 149 products 8(b)(ii) 497 3 71 70 oe M2 for × oe with no extra 2235 150 149 products or M1 for 35 + 12 + 24 soi by 71 8(c) 1640 3 42 41 40 oe M2 for × × oe with no extra 5673 63 62 61 products 15 + 27 42 or M1 for soi by 15 + 27 + 8 + 13 63

This question in 0607/42 Oct/Nov 2018

5 The Venn diagram shows the sets A, B and C. U A B C U = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13} A = {prime numbers} B = {factors of 12} C = {multiples of 3} (a) List the elements of set A. … [1] (b) Write all the elements of U in the correct parts of the Venn diagram above. [3] (c) List the elements of (A , B )' . … [1] (d) Find n (( B , C ) + A') . … [1]

6 marks

Mark scheme: 5(a) 2, 3, 5, 7, 11, 13 1 5(b) Correct Venn diagram 3 B2 for 1 or 2 errors/omissions or B1 for 3 or 4 errors/omissions 5(c) 8, 9, 10 1 FT their Venn diagram 5(d) 4 1 FT their Venn diagram

This question in 0607/43 May/June 2019

4 The Venn diagram shows the number of students who like sweets (S) and the number of students who like nuts (N). U S N 27 7 13 3 (a) (i) Find the number of students who like nuts. … [1] (ii) Find the number of students who like sweets or nuts but not both. … [1] (b) (i) Find n(U). … [1] (ii) Find n( S , N) . … [1] (iii) Find n( S l , N) . … [1] (c) One of these students is chosen at random. Find the probability that this student likes nuts but not sweets. … [1] (d) Two of these students are chosen at random. Find the probability that they both like sweets and nuts. … [2] (e) Two students who like sweets are chosen at random. Find the probability that they both also like nuts. … [3]

11 marks

Mark scheme: 4(a)(i) 20 1 4(a)(ii) 40 1 4(b)(i) 50 1 4(b)(ii) 47 1 4(b)(iii) 23 1 4(c) 13 1 FT their (b)(i) 50 4(d) 3 2 7 6 oe M1 for × 175 their 50 their 50 − 1 4(e) 7 3 7 6 oe M2 for × 187 34 33 7 6 or M1 for × p p − 1

This question in 0607/43 Oct/Nov 2020

8 The Venn diagram shows the sets A, B and C. U A B C U = {integers from 10 to 20, including 10 and 20} A = {prime numbers} B = {multiples of 3} C = {multiples of 4} (a) List the elements of set A. … [1] (b) Write all the elements of U in the correct parts of the Venn diagram. [2] (c) List the elements of ( A , B ) l. … [1] (d) Find n(( A , B ) + C l ) . … [1]

5 marks

Mark scheme: 8(a) [A =] 11, 13, 17, 19 1 8(b) 2 B1 for at least 8 elements correct A 11 13 10 17 19 14 20 B 15 12 16 C 18 8(c) 10, 14, 16, 20 1 FT their Venn diagram 8(d) 6 1 FT their Venn diagram

This question in 0607/42 May/June 2022

7 (a) Shade the region indicated below each of these Venn diagrams. U U A B P Q ( A , B ) l ( P + Q l ) , ( P l + Q ) [2] (b) Bag A Bag B Bag A contains 4 white balls and 3 black balls. Bag B contains 4 white balls and 5 black balls. A ball is taken at random from bag A. If the ball is white, it is replaced in Bag A. If the ball is black, it is put in bag B. A ball is then taken at random from bag B. Find the probability that (i) the ball taken from bag A is white, … [1] (ii) both balls are black, … [2] (iii) the balls are different colours. … [3]

8 marks

Mark scheme: 7(a) Correct shading 2 B1 for each 7(b)(i) 4 1 oe 7 7(b)(ii) 9 2 3 6 oe M1 for  oe 35 7 10 7(b)(iii) 22 3 3 4 4 5 oe M2 for  +  oe 45 7 10 7 9 or M1 for one of above products

This question in 0607/43 May/June 2022

8 (a) Use set notation to describe the shaded regions. U U P Q P Q … … [2] (b) U = {Integers x 3 G x G 15 } A = {Multiples of 3} B = {Integers x 6 G x G 12 } C = {Factors of 24} (i) Write all the elements of U in the correct parts of the Venn diagram. U A B C [3] (ii) List the members of the set A + B + C l. … [1] (iii) List the members of the set ( A , C ) l + B . … [1] (iv) Find n (( B , C ) + Al) . … [1]

8 marks

Mark scheme: 8(a) ( P  Q ) oe 2 B1 for each P Q oe 8(b)(i) 3 A B 15 9 7 10 6 B2 for 10, 11, or 12 of the elements 11 3 12 8 placed correctly 5 or B1 for 7, 8 or 9 of the elements 13 placed correctly 14 4 C 8(b)(ii) 9 1 FT their diagram 8(b)(iii) 7, 10, 11 1 FT their diagram 8(b)(iv) 5 1 FT their diagram

This question in 0607/42 Oct/Nov 2022

6 (a) U = {integers from 1 to 15} P = {factors of 12} Q = {multiples of 3} (i) Complete the Venn diagram. U P Q [2] (ii) Write down the elements of P + Q . … [1] (iii) Find n ( P l + Q ) , ( P + Q l ) _ i. … [1] (b) Bag A Bag B Bag A contains 4 black balls and 3 white balls. Bag B contains 2 black balls and 4 white balls. (i) Amy picks a ball at random from bag A. She notes the colour of the ball and replaces it in bag A. Find the probability that Amy’s ball is black. … [1] (ii) Basma picks two balls at random from bag B. She notes the colour of each ball and replaces them in bag B. Find the probability that both balls are white. … [2] (iii) Basma chooses one bag at random. She picks one ball at random from this bag. Find the probability that the ball is white. … [3]

10 marks

Mark scheme: 6(a)(i) 2 B1 for 1 or 2 elements misplaced or omitted. 1 2 3 9 6 4 12 15 5 7 8 10 11 13 14 6(a)(ii) 3, 6, 12 1 FT their Venn diagram 6(a)(iii) 5 1 FT their Venn diagram 6(b)(i) 4 7 6(b)(ii) 2 2 4 3 oe M1 for  oe 5 6 5 6(b)(iii) 23 3 1 3 1 4 oe M2 for  +  42 2 7 2 6 or M1 for one of above products

This question in 0607/42 Feb/March 2024

11 32 students in a class are asked which of three activities they like. W = {students who like walking} S = {students who like swimming} C = {students who like cycling} The Venn diagram shows the number of students in each subset. U W S 8 2 3 9 4 0 5 1 C (a) One of these students is chosen at random. Complete the sentence. This student is most likely to belong in {students who like … }. [1] (b) Write down the number of students who like all three activities. … [1] (c) Find n (( S l , C) + W l ). … [1] (d) A student is chosen at random from the class. Find the probability that this student likes both walking and swimming. … [1] (e) Two of the students who like swimming are chosen at random. Find the probability that one of these students likes walking but not cycling and the other student only likes swimming. … [3] (f) Three of the 32 students are chosen at random. Find the probability that one student likes exactly one of the activities and the other two students like exactly two of the activities. … [3]

10 marks

Mark scheme: 11(a) walking 1 11(b) 9 1 11(c) 6 1 11(d) 11 1 oe 32 11(e) 6 3 2 3 3 2 oe M2 for  or  oe 91 14 13 14 13 k j or M1 for  14 13 2 3 or B1 for or seen 14 14 11(f) 3 3 16 6 5 oe M2 for [k ×] × × oe where k = 1, 2, 3 62 32 31 30 m n n − 1 or M1 for   oe 32 31 30

This question in 0607/43 Oct/Nov 2024

4 Use set notation to describe each of the shaded regions. U U Q P A B R … … [2]

2 marks

Mark scheme: 4 A  B oe 2 B1 for each ( P  Q )  R oe

This question in 0607/41 May/June 2025

16 (a) Use set notation to describe the shaded region. U A B C … [1] (b) Shade P + Q l. U P Q [1]

2 marks

Mark scheme: 16(a) 1 ( A  B )  C oe 16(b) 1

This question in 0607/43 May/June 2025