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Exam-Style Questions.Problems adapted from questions set for previous Mathematics exams. |
1. | GCSE Higher |
If the universal set is the set of positive even numbers less than 30 and:
$$A = \{4, 8, 12, 16, 20, 24, 28\}$$ $$B = \{6, 12, 18, 24, 28\}$$(a) Complete the Venn diagram with this information.
A number is chosen at random from the universal set.
(b) What is the probability that the number is in the set \(A \cap B\)?
2. | GCSE Higher |
(a) Complete the Venn diagram with the following information.
$$\mathscr{E}= \{1,2,3,4,5,6,7,8,9,10,11,12\}$$ $$A = \{ \text{odd numbers}\}$$ $$B = \{ \text{factors of 24} \}$$(a) Complete the Venn diagram with this information.
A number is chosen at random from the universal set.
(b) What is the probability that the number is in the set \(A \cap B\)?
3. | GCSE Higher |
(a) Complete the Venn diagram to represent this information:
$$\mathscr{E} = \{-4, -3, -2, -1, 0, 1, 2, 3, 4\}$$ $$A = \{1,2,3,4\}$$ $$B = \{-4,-2,2,4\}$$
A number is chosen at random from the universal set \( \mathscr{E} \).
(b) What is the probability that the number is in the set \(A \cap B\)?
4. | GCSE Higher |
(a) Use set notation to describe the shaded regions.
(b) Draw a 3-set Venn diagram showing the intersecting sets A, B and C.
\(U\) = {Integers \( x\;| \quad 5 \le x \le 20 \)}
A = {Multiples of \(5\)}
B = {Integers \( x\;| \quad 7 \le x \le 13\)}
C = {Factors of \(48\)}
Write all the elements of \(U\) in the correct parts of the Venn diagram.
(c) List the members of the set \(A \cap B \cap C'\).
(d) List the members of the set \((A \cup C)' \cap B\).
(e) Find \(n((B \cup C) \cap A')\).
5. | GCSE Higher |
The Venn diagram represents a collection of 40 books on sale in an online store.
P represents the books available in paperback format.
D represents the books available in digital format.
(a) One book from the collection is picked at random. Work out the probability that the book is available in digital format.
(b) One of the books that is available in paperback format is picked at random. Work out the probability that this book is also available in digital format.
6. | GCSE Higher |
(a) Use set notation to describe the shaded region in the Venn diagram on the left.
(b) Shade the region in the Venn diagram in the centre that represents \( C \cap D' \)
(c) Shade the region in the Venn diagram on the right that represents \( (E \cap F) \cup G' \)
7. | GCSE Higher |
80 students are asked if they like History (\(H\)) and if they like Geography (\(G\)).
7 say they do not like History and do not like Geography.
45 say they like History.
54 say they like Geography.
(a) Draw a Venn diagram to represent this situation.
A student is chosen at random.
(b) Find the probability that this student likes History and likes Geography.
Two students are chosen at random.
(c) Find the probability that they both like Geography.
Two students who like History are chosen at random.
(d) Find the probability that they both also like Geography.
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