MATHEMATICS (EXTENDED) 0580 - Math Medicine
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43 SEKOLAH BUKIT SION – IGCSE MATH REVISION MATHEMATICS (EXTENDED) 0580 REVISION 1B SET NOTATION
Transcript of MATHEMATICS (EXTENDED) 0580 - Math Medicine
43 SEKOLAH BUKIT SION – IGCSE MATH REVISION
MATHEMATICS (EXTENDED) 0580
REVISION 1B
SET NOTATION
44 SEKOLAH BUKIT SION – IGCSE MATH REVISION
NOTES: SET NOTATIONS:
45 SEKOLAH BUKIT SION – IGCSE MATH REVISION
1. (a) You may use this Venn diagram to help you answer part (a). 𝜉 ={x : 1 ≤ x ≤ 12, x is an integer} M ={odd numbers} N = {multiples of 3}
(i) Find n(N).
Answer: ………………………………………… [1]
(ii) Write down the set M ∩ N.
Answer: ………………………………………… [1]
(iii) Write down a set P where P ⊂ M.
Answer: ………………………………………… [1] (b) Shade (𝐴 ∪ 𝐶) ∩ 𝐵′
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2. (a) In this part, you may use this Venn diagram to help you answer the questions.
In a class of 30 students, 25 students study French (F), 18 study Spanish (S). One student does not study French or Spanish.
(i) Find the number of students who study French and Spanish.
Answer: ………………………………………… [2]
(ii) One of the 30 students is chosen at random.
Find the probability that this student studies French but not Spanish.
Answer: ………………………………………… [1]
(iii) A student who does not study Spanish chosen at random. Find the probability that this student studies French.
Answer: ………………………………………… [1]
(b)
On this Venn diagram, shade the region 𝑅 ∩ (𝑃 ∪ 𝑄)′ . [1]
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3. 30 students were asked if they had a bicycle (B), a mobile phone (M) and a computer (C).
The results are shown in the Venn diagram.
(a) Work out the value of x.
Answer: ………………………………………… [1]
(b) Use set notation to describe the shaded region in the Venn diagram.
Answer: ………………………………………… [1]
(c) Find n(C ⋂ (M ∪ B)’).
Answer: ………………………………………… [1]
(d) Two students are chosen at random from the students who have computers. Find the probability that each of these students has a mobile phone or no bicycle?
Answer: ………………………………………… [3]
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4.
(a) Use the information in the Venn diagram to complete the following. (i) P ∩ Q = { ………………………………..} [1]
(ii) P’∪ Q = { ………………………………..} [1]
(iii) n(P ∪ Q)’ = ………………… [1]
(c) On the Venn diagram shade the region P’ ∩ Q. [1]
(d) Use a set notation symbol to complete the statement. {f, g, h} ……… P [1]
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5. E = {x : 1 < x < 10, where x is an integer} A = {square numbers} B = {1, 2, 3, 4, 5, 6}
(a) Write all the elements of E in their correct place in the Venn diagram.
[2]
(b) List the elements of (A ∪ B)’.
Answer: ………………………………………… [1]
(c) Find n(A ∩ B’).
Answer: ………………………………………… [1] (d)
Shade the region 𝐵 ∩ (𝑇 ∪ 𝑃)!. [1]
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6.
In the Venn diagram, E = {children in a nursery} B = {children who received a book for their birthday} T = {children who received a toy for their birthday} P = {children who received a puzzle for their birthday} x children received a book and a toy and a puzzle. 6 children received a toy and a puzzle.
(a) 4 children received a book and a toy. 5 children received a book and a puzzle. 7 children received a puzzle but not a book and not a toy. Complete the Venn diagram above. [3]
(b) There are 40 children in the nursery. Using the Venn diagram, write down and solve an equation in x.
Answer: ………………………………………… [3]
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7. 11 students are asked if they like rugby (R) and if they liked 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: ………………………………………… [1]
(b) On the Venn diagram shade the region R’ ∩ F ’. [1]
8. Shade the required region on each Venn diagram. [2]
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9. The Venn diagram shows the number of elements in sets A, B and C.
(a) n(A ∪ B ∪ C) = 74 Find x.
Answer: ………………………………………… [2] (b) n(E) = 100
Find y.
Answer: ………………………………………… [1]
(c) Find the value of n((A ∪ B)’ ∩ C).
Answer: ………………………………………… [1]
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10. E = {1, 2, 3, 4, 5, 6, 7, 8, 9} E = {x : x is an even number} F = {2, 5, 7} G = {x : x2 – 13x + 36 = 0}
(a) List the elements of set E.
Answer: ………………………………………… [1]
(b) Write down n(F).
Answer: ………………………………………… [1]
(c) (i) Factorise x2 – 13x + 36.
Answer: ………………………………………… [2]
(ii) Using your answer to part (c) (i), solve x2 – 13x + 36 = 0 to find the two elements of G.
Answer: ………………………………………… [1]
(d) Write all the elements of E in their correct place in the Venn diagram. [2]
(e) Use set notation to complete the following statements. (i) F ∩ G = …………. [1]
(ii) 7 …… E [1]
(iii) n(E …… F) = 6 [1]
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11.
E = {240 passengers who arrive on a flight in Cyprus}
H = {passengers who are on holiday}
C = {passengers who hire a car}
(a) Write down the number of passengers who
(i) are on holiday,
Answer: ………………………………………… [1]
(ii) hire a car but not on holiday
Answer: ………………………………………… [1]
(b) Find the value of n(H ∪ C ’).
Answer: ………………………………………… [1]
(c) One of the 240 passengers is chosen at random. Write down the probability that this passenger (i) hires a car,
Answer: ………………………………………… [1]
(ii) is on holiday and hires a car.
Answer: ………………………………………… [1]
