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Practise 28 exam-style questions on Venn diagrams and sets for Edexcel GCSE Maths (Non-calculator). Write your answer as you would in the exam and get it marked in seconds against the mark scheme, point by point, with an AI tutor on hand if you get stuck.
Here are 4 of the questions in this topic, each with a model answer, an explanation of why it earns the marks and the mark scheme an examiner would use.
T = {people who like tea}
C = {people who like coffee}
Use set notation to describe the set of people who like tea but do not like coffee.
\(T \cap C'\)
'Like tea' is T and 'do not like coffee' is \(C'\) (the complement of C). 'But' means both must be true, so use the intersection symbol \(\cap\).
B1 for \(T \cap C'\)
accept \(C' \cap T\)
\(\xi = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}\)
The Venn diagram shows the sets A, B and C.
List the members of \((A \cup B) \cap C'\).
\(A \cup B\) = {2, 3, 4, 6, 8, 9, 10, 12}
\(C'\) = {5, 7, 8, 9, 10, 11}
\((A \cup B) \cap C'\) = {8, 9, 10}
Work out the bracket first, then find the elements that are also outside C. In the diagram these are the regions inside A or B but outside circle C.
M1 for \(A \cup B\) = {2, 3, 4, 6, 8, 9, 10, 12} or \(C'\) = {5, 7, 8, 9, 10, 11}
correct answer with no working scores full marks
A1 for 8, 9, 10
cao, any order
A and B are two events.
P(A) = 0.6 and P(B) = 0.45
The probability that neither A nor B happens is 0.1
Work out the probability that exactly one of A and B happens.
\(P(A \cup B) = 1 - 0.1 = 0.9\)
\(P(A \cap B) = 0.6 + 0.45 - 0.9 = 0.15\)
A only: 0.6 − 0.15 = 0.45. B only: 0.45 − 0.15 = 0.3
P(exactly one) = 0.45 + 0.3 = 0.75
Fill in a Venn diagram: the inside of the circles has probability 0.9. Adding P(A) and P(B) counts the overlap twice, so the extra 0.15 is the overlap. 'Exactly one' means A only or B only.
M1 for \(P(A \cup B) = 1 - 0.1 = 0.9\)
correct answer with no working scores full marks
M1 for \(P(A \cap B) = 0.6 + 0.45 - 0.9 = 0.15\)
A1 for 0.75
oe
The Venn diagram shows the number of people in each region of sets A and B.
There are 50 people in \(\xi\).
One of the 50 people is chosen at random.
Work out the probability that this person is in A.
\(2x + (x + 3) + (3x - 1) + 6 = 50\)
\(6x + 8 = 50\)
\(6x = 42\), so \(x = 7\)
A only: \(2x = 14\). A and B: \(x + 3 = 10\)
n(A) = 14 + 10 = 24
P(A) = \(\dfrac{24}{50} = \dfrac{12}{25}\)
All four regions add up to the 50 people in the universal set, which gives an equation in \(x\). Set A includes both the 'A only' region and the overlap.
M1 for \(2x + (x + 3) + (3x - 1) + 6 = 50\)
correct answer with no working scores full marks
M1 for \(6x + 8 = 50\) or \(x = 7\)
M1 for n(A) = 14 + 10 = 24
ft their \(x\)
A1 for \(\dfrac{12}{25}\)
oe, e.g. \(\dfrac{24}{50}\), 0.48
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