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Set language and notation Question Paper 1 Level Subject Exam Board Topic Sub Topic Booklet
IGCSE Maths Edexcel Number and Algebra Set language and notation Question Paper 1
59 minutes
Time Allowed: Score:
/49
Percentage:
/100
Grade Boundaries: 9
8
7
6
5
4
3
2
1
>90%
80%
70%
60%
50%
40%
30%
20%
10%
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1 E = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} A = {odd numbers} P = {prime numbers} List the of the set (i)
A ∩ P,
...................................................................... . . . . . . . . . . . . . . . . . . . . . . . .
(ii)
A∪ P.
...................................................................... . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 1 is 2 marks)
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2 (a) E = {Students in Year 12} G = {Students who study German} F = {Students who study French} M = {Students who study Maths} (i) G ˆ M = Ø Use this information to write a statement about the students who study German in Year 12
. . . . . .................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................................................................................................................................... . . . . .. . . . . . . . . . . . . . . . . . .
(ii) Preety is a student in Year 12 Preety ∉ F. Use this information to write a statement about Preety.
. . . . . .................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................................................................................................................................... . . . . .. . . . . . . . . . . . . . . . . . .
(2) (b) A = {2, 4, 6, 8, 10} A ˆ B = {2, 4} A ‰ B = {1, 2, 3, 4, 6, 8, 10} List all the of set B.
.................................................................... . . . . . . . . . . . . . . . . . . . . . . . . .
(2) (Total for Question 2 is 4 marks)
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3 A and B are two sets. n(E ) = 37 n(A) = 22 n( A ∩ B ) = 12 n( A ∪ B ) = 30 (a) Complete the Venn Diagram to show the numbers of elements. E B
A ..............
..............
..............
..............
(2) (b) Find
(i) n( A ∩ B′ )
...........................................
(ii) n( A′ ∪ B′ )
...........................................
(2) (Total for Question 3 is 4 marks)
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4 A, B and C are three sets. A ∩ B = Ø and C ‡ A
E
A
(a) Complete the Venn diagram to show the sets B and C
(2)
(b) On the Venn diagram, shade the region that represents A ∩ C /
(1)
(Total for Question 4 is 3 marks) 5 There are 31 students in a class. The only languages available for the class to study are French and Spanish. 17 students study French. 15 students study Spanish. 6 students study neither French nor Spanish. Using a Venn diagram, or otherwise, work out how many students study only one language.
........................................ . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 5 is 4 marks)
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6 The Venn diagram shows a universal set E and three sets A, B and C.
E
A
B 3 7
6
2
C 10
Κ '*Κ $!numbers of elements. Find (i))
( A ∪ B) .......................................... . . . . . . . . . . . . . . . . . . . .
(ii) i
( A′ )
.......................................... . . . . . . . . . . . . . . . . . . . .
(iii) n ( B ∩ C′ )
.......................................... . . . . . . . . . . . . . . . . . . . .
(iv) v
( A′ ∪ B′ )
.......................................... . . . . . . . . . . . . . . . . . . . .
(Total for Question 6 is 4 marks)
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7 E = {even numbers} A = {2, 4, 6, 8, 10} (a) B is a set such that A ∩ B = {4, 8} The set B has 3 . List the of one possible set B.
........................................... . . . . . . . . . . . . . . . . . . . . . . . .
(2) (b) C is a set such that A ∩ C = Ø The set C has 3 . List the of one possible set C.
........................................... . . . . . . . . . . . . . . . . . . . . . . . .
(1) (Total for Question 7 is 3 marks)
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8
5 of the students in a group are male. 9 5 of the female students in the group are right-handed. 6 (a) Work out the fraction of students in the group who are right-handed females.
.......... . . . . . . . . . . . . . . . . . . . . . . . . . .
(3) (b) Find the smallest possible number of students in the group.
.......... . . . . . . . . . . . . . . . . . . . . . . . . . .
(2) (Total for Question 8 is 5 marks) 9
S = {s, q, u, a, r, e} V = {a, e, i, o, u} List the of the set (i) S ˆ V
......................................... . . . . . . . . . . . . . . . . . . . . . . . . . .
(ii) S ‰ V
......................................... . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 9 is 2 marks)
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10 (a) A = {s, u, p, e, r} B = {c, o, m, p, u, t, e, r} List the of the set (i) A ˆ B ................................................................................................
(ii) A ‰ B ................................................................................................
(2)
(b) X = {prime numbers} Y = {factors of 12} Is it true that X ˆ Y = ‡? Tick (9) the appropriate box.
Yes
No
Explain your answer. . . . . . . ............................................................................................ . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .
(1)
(Total for Question 10 is 3 marks)
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12 A garage tests cars for faults. There are three types of fault – braking, steering and lighting. A car fails the test if it has one or more of these three types of fault. Last week, 11 cars had braking faults 9 cars had steering faults 7 cars had lighting faults no car had both steering faults and lighting faults 2 cars had both braking faults and steering faults 3 cars had both braking faults and lighting faults. By drawing a Venn Diagram, or otherwise, find the number of cars which failed the test last week.
.... . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 12 is 3 marks)
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13 E = {even numbers} A = {factors of 8} B = {factors of 20} List the of A ˆ B
......................................................
(Total for Question 13 is 2 marks)
14 E = {positive whole numbers less than 13} A = {even numbers} B = {multiples of 3} C = {prime numbers} (a) List the of the set (i) A ˆB .................................................................................................
(ii) B ‰C .................................................................................................
(2) (b) Is it true that 14 A? Tick (9) the appropriate box.
Yes
No
Explain your answer. . . . . ............................................................................................ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1) (Total for Question 14 is 3 marks)
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15 (a) A = {p, r, a, g, u, e} B = {p, a, r, i, s} C = {b, u, d, a, p, e, s, t} List the of the set (i) A
B
..................................................................... . . . . . . . . . . . . . . . . . . . . . . . .
(ii) B
C
..................................................................... . . . . . . . . . . . . . . . . . . . . . . . .
(2) (b) D = {r, o, m, e} E = {l, i, s, b, o, n} F = {b, e, r, l, i, n} Put one of the letters D, E or F in the box below to make the statement correct.
A
=Ø
Explain your answer. . . . . . . . .................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................................................................................ . . .. . . . . . . . . . . . . . . . . . .
(1)
(Total for Question 15 is 3 marks)
Set language and notation Question Paper 1 Level Subject Exam Board Topic Sub Topic Booklet
IGCSE Maths Edexcel Number and Algebra Set language and notation Question Paper 1
59 minutes
Time Allowed: Score:
/49
Percentage:
/100
Grade Boundaries: 9
8
7
6
5
4
3
2
1
>90%
80%
70%
60%
50%
40%
30%
20%
10%
Save My Exams! – The Home of Revision
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1 E = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} A = {odd numbers} P = {prime numbers} List the of the set (i)
A ∩ P,
...................................................................... . . . . . . . . . . . . . . . . . . . . . . . .
(ii)
A∪ P.
...................................................................... . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 1 is 2 marks)
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2 (a) E = {Students in Year 12} G = {Students who study German} F = {Students who study French} M = {Students who study Maths} (i) G ˆ M = Ø Use this information to write a statement about the students who study German in Year 12
. . . . . .................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................................................................................................................................... . . . . .. . . . . . . . . . . . . . . . . . .
(ii) Preety is a student in Year 12 Preety ∉ F. Use this information to write a statement about Preety.
. . . . . .................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................................................................................................................................... . . . . .. . . . . . . . . . . . . . . . . . .
(2) (b) A = {2, 4, 6, 8, 10} A ˆ B = {2, 4} A ‰ B = {1, 2, 3, 4, 6, 8, 10} List all the of set B.
.................................................................... . . . . . . . . . . . . . . . . . . . . . . . . .
(2) (Total for Question 2 is 4 marks)
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3 A and B are two sets. n(E ) = 37 n(A) = 22 n( A ∩ B ) = 12 n( A ∪ B ) = 30 (a) Complete the Venn Diagram to show the numbers of elements. E B
A ..............
..............
..............
..............
(2) (b) Find
(i) n( A ∩ B′ )
...........................................
(ii) n( A′ ∪ B′ )
...........................................
(2) (Total for Question 3 is 4 marks)
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4 A, B and C are three sets. A ∩ B = Ø and C ‡ A
E
A
(a) Complete the Venn diagram to show the sets B and C
(2)
(b) On the Venn diagram, shade the region that represents A ∩ C /
(1)
(Total for Question 4 is 3 marks) 5 There are 31 students in a class. The only languages available for the class to study are French and Spanish. 17 students study French. 15 students study Spanish. 6 students study neither French nor Spanish. Using a Venn diagram, or otherwise, work out how many students study only one language.
........................................ . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 5 is 4 marks)
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6 The Venn diagram shows a universal set E and three sets A, B and C.
E
A
B 3 7
6
2
C 10
Κ '*Κ $!numbers of elements. Find (i))
( A ∪ B) .......................................... . . . . . . . . . . . . . . . . . . . .
(ii) i
( A′ )
.......................................... . . . . . . . . . . . . . . . . . . . .
(iii) n ( B ∩ C′ )
.......................................... . . . . . . . . . . . . . . . . . . . .
(iv) v
( A′ ∪ B′ )
.......................................... . . . . . . . . . . . . . . . . . . . .
(Total for Question 6 is 4 marks)
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7 E = {even numbers} A = {2, 4, 6, 8, 10} (a) B is a set such that A ∩ B = {4, 8} The set B has 3 . List the of one possible set B.
........................................... . . . . . . . . . . . . . . . . . . . . . . . .
(2) (b) C is a set such that A ∩ C = Ø The set C has 3 . List the of one possible set C.
........................................... . . . . . . . . . . . . . . . . . . . . . . . .
(1) (Total for Question 7 is 3 marks)
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8
5 of the students in a group are male. 9 5 of the female students in the group are right-handed. 6 (a) Work out the fraction of students in the group who are right-handed females.
.......... . . . . . . . . . . . . . . . . . . . . . . . . . .
(3) (b) Find the smallest possible number of students in the group.
.......... . . . . . . . . . . . . . . . . . . . . . . . . . .
(2) (Total for Question 8 is 5 marks) 9
S = {s, q, u, a, r, e} V = {a, e, i, o, u} List the of the set (i) S ˆ V
......................................... . . . . . . . . . . . . . . . . . . . . . . . . . .
(ii) S ‰ V
......................................... . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 9 is 2 marks)
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10 (a) A = {s, u, p, e, r} B = {c, o, m, p, u, t, e, r} List the of the set (i) A ˆ B ................................................................................................
(ii) A ‰ B ................................................................................................
(2)
(b) X = {prime numbers} Y = {factors of 12} Is it true that X ˆ Y = ‡? Tick (9) the appropriate box.
Yes
No
Explain your answer. . . . . . . ............................................................................................ . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .
(1)
(Total for Question 10 is 3 marks)
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12 A garage tests cars for faults. There are three types of fault – braking, steering and lighting. A car fails the test if it has one or more of these three types of fault. Last week, 11 cars had braking faults 9 cars had steering faults 7 cars had lighting faults no car had both steering faults and lighting faults 2 cars had both braking faults and steering faults 3 cars had both braking faults and lighting faults. By drawing a Venn Diagram, or otherwise, find the number of cars which failed the test last week.
.... . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 12 is 3 marks)
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13 E = {even numbers} A = {factors of 8} B = {factors of 20} List the of A ˆ B
......................................................
(Total for Question 13 is 2 marks)
14 E = {positive whole numbers less than 13} A = {even numbers} B = {multiples of 3} C = {prime numbers} (a) List the of the set (i) A ˆB .................................................................................................
(ii) B ‰C .................................................................................................
(2) (b) Is it true that 14 A? Tick (9) the appropriate box.
Yes
No
Explain your answer. . . . . ............................................................................................ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1) (Total for Question 14 is 3 marks)
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15 (a) A = {p, r, a, g, u, e} B = {p, a, r, i, s} C = {b, u, d, a, p, e, s, t} List the of the set (i) A
B
..................................................................... . . . . . . . . . . . . . . . . . . . . . . . .
(ii) B
C
..................................................................... . . . . . . . . . . . . . . . . . . . . . . . .
(2) (b) D = {r, o, m, e} E = {l, i, s, b, o, n} F = {b, e, r, l, i, n} Put one of the letters D, E or F in the box below to make the statement correct.
A
=Ø
Explain your answer. . . . . . . . .................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................................................................................ . . .. . . . . . . . . . . . . . . . . . .
(1)
(Total for Question 15 is 3 marks)
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