Sets And Venn Diagrams Igcse Questions 57262a

Calculate the percentage increase from 2004 to 2006.

SETS AND VENN DIAGRAMS IGCSE QUESTIONS May 2006 Paper 2

% [2]

Answer(b)

17 n(A) = 18, n(B) = 11 and n(A ∪ B)′ = 0. (a) Label the Venn diagram to show the sets A and B where n(A ∪ B) = 18. Write down the number of elements in each region. 2

1

For Examiner’s Use

The table shows the maximum daily temperatures during one week in Punta Arenas. Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

Sunday

2°C

3°C

1°C

2.5°C

–1.5°C

1°C

2°C

[2] (a) By how many degrees did the maximum temperature change between Thursday and Friday?

2

(b) Draw another Venn diagram to show the sets AAnswer and B where n(A ∪ B) = 29. (a) ...................................................... Write down the number of elements in each region. (b) What is the difference between the greatest and the least of these temperatures?

[1]

Answer (b) ......................................................

[1]

Nyali paid $62 for a bicycle. She sold it later for $46. What was her percentage loss?

[2]

November 2002 Paper 2 © UCLES 2006

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Answer ........................................................%

[2]

0580/02, 0581/02 Jun 06

Three sets A, B and K are such that A ⊂ K, B ⊂ K and A ∩ B = Ø. Draw a Venn diagram to show this information.

[2] 4

Alejandro goes to Europe for a holiday. He changes 500 pesos into euros at an exchange rate of 1 euro = 0.975 pesos. How much does he receive in euros? Give your answer correct to 2 decimal places.

Answer ...................................................euros 5

Write the four values in order, smallest first.

[2]

(b) Calculate the perimeter of the triangle.

Answer(b)

November 2006 Paper 2

cm [1]

11 (a) Shade the region A ∩ B.

A

B

[1] (b) Shade the region (A ∪ B)′. A

B

[1] 5

(c) Shade the complement of set B. 11 M is proportional to the cube of r. When r = 3, M = 21.6. When r = 5, find the value of M.

A

B

For Examiner's Use

[1]

November 2007 Paper 2

© UCLES 2006

Answer M =

0580/02/N/06

[3]

[Turn Over

12 A and B are sets. Write the following sets in their simplest form. (a) A ∩ A'.

Answer(a)

[1]

Answer(b)

[1]

(b) A ∪ A'.

(c) (A ∩ B) ∪ (A ∩ B' ).

6

5d + 4w 11 Make d the subject of the formula c = . Answer(b) 2w

[1]

For Examiner's Use

(c) (A ∩ B) ∪ (A ∩ B' ).

3 Answer(c) 3a

[1]

4

+ . Answer d = 8 5 June 2010 Paper 2.1 13 A rectangle has sides of length 6.1 cm and 8.1 cm correct to 1 decimal place. Complete the statement about the perimeter of the rectangle. 4

Write as a single fraction

12 Q = {2, 4, 6, 8, 10} and R = {5, 10, 15, 20}. 15 ∈ P, n(P) = 1 and P ∩ Q = Ø.

For Examiner's Use

[3]

[2]

Answer

Label each set and complete the Venn diagram to show this information.

5

Write 28 × 82 × 4-2 in the form 2n. Answer

cm

perimeter <

cm [3]

[2]

Answer © UCLES 2007

6

[Turn over

0580/02/O/N/07

Change 64 square metres into square millimetres. Give your answer in standard form. [3]

mm2 [2]

Answer

13 Solve the simultaneous equations. June 2010 Paper 2.2

2x + y =7 2

7 A

2x − y = 17

B

2

C

The shaded area in the diagram shows the set (A ∩ C ) ∩ B'. Write down the set shown by the shaded area in each diagramAnswer below. x = [3]

y=

A

B

© UCLES 2010

A

B

0580/21/M/J/10

C

C

[2]

Answer .................................................. [3] May 2003 Paper 2

11

Write each of these four numbers in the correct place in the Venn Diagram below. 5 112 4 2.6,!! ,!!√12,!! 7 10 Rooms in a hotel are numbered from 1 to17 19. Rooms are allocated at random as guests arrive.

√

For Examiner's Use

(a) What is the probability that the first guest to arrive is given a room which is a prime number? (1 is not a prime number.) Rational numbers

Integers

[2]

Answer (a)

(b) The first guest to arrive is given a room which is a prime number. What is the probability that the second guest to arrive is given a room which is a prime number? [4] Answer (b) 0580/2, 0581/2 Jun 2003

[1]

May 2005 Paper 2

11 n( ) = 21, n(A ∪ B) = 19, n(A ∩ B' ) = 8 and n(A) = 12. Complete the Venn diagram to show this information. Answer A

.......

B

.......

.......

.......

[3]

x 2x

.

M=

12

2x x

Find (a) 2M, Answer (a)

[1]

Answer (b)

[2]

(b) M2.

May 2007 Paper 2 4 8

On the Venn diagrams shade the regions

For Examiner's Use

(a) A′ ∩ C′, A

B

C

[1] (b) (A ∪ C ) ∩ B. A

B

C

[1] 9 Write down May 2008 Paper 2 5

(a) an irrational number, 12 = {1,2,3,4,5,6,7,9,11,16}

P = {2,3,5,7,11} S = {1,4,9,16} Answer(a) (a) Draw a Venn diagram to show this information. (b) a prime number between 60 and 70.

Answer(b)

M = {3,6,9}

[1]

[1]

10 Write as a fraction in its simplest form

x −3 + 4 . x −3 4

[2]

(b) Write down the value of n(M ′∩P). Answer(b)

Answer 13 Solve the inequality

© UCLES 2007

2 x _ 5 0580/02/J/07 K== x + 4 . 3 8

[1]

[3]

For Examiner's Use

5 3 May 2009 Paper 2 10 A mountain railway AB is of length 864 m and rises at an angle of 12o to the horizontal. 4 Shade region required eachwhen VennitDiagram. m above seainlevel is at A. A trainthe is 586 Calculate the height above sea level of the train when it reaches B. B 864 m

A B

For For Examiner's Examiner's Use Use

B

A

NOT TO SCALE

12o

A

C

A∩B∩C

[2]

A ∪ B′

Answer _2 3 ⎛ ⎞

November 2004 Paper 2 5

m [3]

⎟⎟ A = ⎜⎜ _ ⎝ 4 5⎠ = {40, 11 –1 41, 42, 43, 44, 45, 46, 47, 48, 49} Find , thenumbers} inverse of the matrix A. A =A {prime B = {odd numbers} (a) Place the 10 numbers in the correct places on the Venn diagram.

B A

Answer

6

⎛ ⎜ ⎜ ⎜ ⎝

⎞ ⎟ ⎟ ⎟ ⎠

[2]

In 2005 there were 9 million bicycles in Beijing, correct to the nearest million. The average distance travelled by each bicycle in one day was 6.5 km correct to one decimal place. Work out the upper bound for the total distance travelled by all the bicycles in one day.

[2] (b) State the value of n ( B ∩ A' ) . Answer(b)

[1] km [2]

Answer

12 Make c the subject of the formula 7

Find the co-ordinates of the mid-point of the line ing the points A(2, –5) and B(6, 9). 3c − 5 = b .

Answer (

Answer c =

© UCLES 2009 © UCLES 2004

0580/21/M/J/09 0580/02/O/N/04

,

)

[2] [3]

[Turn [Turnover over

November 2005 Paper 4 4

4

(a) All 24 students in a class are asked whether they like football and whether they like basketball. Some of the results are shown in the Venn diagram below.

F

B 7

12

2

= {students in the class}. F = {students who like football}. B = {students who like basketball}. (i) How many students like both sports?

[1]

(ii) How many students do not like either sport?

[1]

(iii) Write down the value of n(F∪B).

[1]

(iv) Write down the value of n(F ′∩B).

[1]

(v) A student from the class is selected at random. November 2008 4 10likes basketball? What isPaper the probability that this student 9

[1]

In a survey, students asked if theyislike basketball (B), football (F) and swimming (S). (vi) A100 student whoare likes football selected at random. What is the probability that this student likes basketball? The Venn diagram shows the results.

[1]

(b) Two students are selected at random from a group of 10 boys and 12 girls. Find the probability that (i) they are both girls,

F

B

(ii) one is a boy and one is a girl. 20

5

[2] [3]

25

q

17 Answer the whole of this question on one p paper. 12sheet of graph

1

f(x) = 1 −

, x ≠ 0.

x2

8

(a) x f(x)

−3 p

−2 0.75

−1 0

−0.5 −0.4 −0.3 q −3 −5.25 S

r 0.3 0.4 0.5 q −5.25 −3

1 0

2 0.75

3 p

Find the values of p and q.

[2]

42 students like swimming. (b) (i) Draw an x-axis for −3 x 3 using 2 cm to represent 1 unit and a y-axis for −11 1 cm toone represent 40 studentsusing like exactly sport. 1 unit.

(ii) the Draw the of graph = f(x) for −3 (a) Find values p, q of andy r.

x

−0.3 and for 0.3

x

3.

y

2 [1] [3] [5]

(b) students like k such that f(x) = k has no solutions. (c) How Writemany down an integer (i) all three sports, 0580/04, 0581/04 Nov 2005 (ii) basketball and swimming but not football?

[1] [1]

© UCLES 2005

[1]

40 students like exactly one sport. (a) Find the values of p, q and r.

[3]

(b) How many students like (i) all three sports,

[1]

(ii) basketball and swimming but not football?

[1]

(c) Find (i) n(B′ ),

[1]

(ii) n((B∪F )∩S ′ ).

[1]

(d) One student is chosen at random from the 100 students. Find the probability that the student (i) only likes swimming, Total marks: 45 (ii) likes basketball but not swimming.

[1] [1]

(e) Two students are chosen at random from those who like basketball. Find the probability that they each like exactly one other sport.

© UCLES 2008

0580/04/O/N/08

[3]