EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Venn Diagrams and Set Notation
Venn diagrams and set notation · Probability · Lesson 6 of 6 · 15 marks · 30 minutes
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Instructions
• Answer all the questions.
• Write your answers in the spaces provided.
• The marks for each question are shown in brackets - use this as a guide to how much to write.
• The answers are on separate pages at the back. Attempt every question before you look at them.
• Answer all questions. Show your working.
Question 1 NON-CALCULATOR (2 marks)
xi= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {even numbers} and B = {multiples of 3}. List the members of A ∩ B.
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(Total for Question 1 = 2 marks)
Question 2 NON-CALCULATOR (2 marks)
Using the same sets, list the members of A'.
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(Total for Question 2 = 2 marks)
Question 3 NON-CALCULATOR (4 marks)
40 students were asked whether they take music (M) and art (R). 22 take music, 15 take art and 8 take both. Complete the Venn diagram.
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(Total for Question 3 = 4 marks)
Question 4 NON-CALCULATOR (2 marks)
One of the 40 students is chosen at random. Use your Venn diagram to work out the probability that the student takes neither music nor art.
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(Total for Question 4 = 2 marks)
Question 5 NON-CALCULATOR (2 marks)
Write down the number of students in M ∪ R.
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(Total for Question 5 = 2 marks)
Question 6 NON-CALCULATOR (3 marks)
One of the 40 students is chosen at random. Given that the student takes art, work out the probability that they also take music.
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(Total for Question 6 = 3 marks)
TOTAL FOR PAPER = 15 MARKS
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Answers and mark scheme
Check your answer only once you have written one.
Question 1 (2 marks)
A ∩ B = {6}.
• A = {2, 4, 6, 8, 10} and B = {3, 6, 9} M1
• {6} A1
Question 2 (2 marks)
A' = {1, 3, 5, 7, 9}.
• Odd numbers seen M1
• {1, 3, 5, 7, 9} A1
Question 3 (4 marks)
M only 14, overlap 8, R only 7, outside the circles 11.
• Overlap 8 B1
• M only 14 B1
• R only 7 B1
• Outside 11 B1
Question 4 (2 marks)
11/40.
• 11 M1
• 11/40 A1
Question 5 (2 marks)
14 + 8 + 7 = 29.
• Adding the three regions M1
• 29 A1
Question 6 (3 marks)
15 students take art, and 8 of these also take music. The probability is 8/15.
• 15 as the total M1
• 8/15 A1
• A correct conclusion C1