GCSE · Venn diagrams & set notation

Venn diagramsExam-style questions

Building a Venn diagram from worded information — why you fill the overlap first and work outwards, what the number in a region actually counts, the universal set and the "neither" region outside the circles, and how the grand total pins down whichever region is missing.

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13 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 1Level 2Level 3Level 4Level 5
  1. 1
    3030 students were asked whether they play football (F) or tennis (T).ξFT1258Work out how many students play neither sport.
    Level 1 · 2 marksTry it
  2. 2
    Here is a Venn diagram.ξ4AB736How many elements are in set AA?
    Level 1 · 1 markTry it
  3. 3
    In a class of 2525 students, 1515 have a cat, 99 have a dog and 44 have both. Draw a Venn diagram (or reason it out) and find how many have a cat but not a dog.
    Level 1 · 1 markTry it
  4. 4
    There are 3030 students in a class. Each student was asked whether they have a sister and whether they have a brother.

    The Venn diagram shows the results. SS is the group who have a sister and BB is the group who have a brother.ξ5SB1168(a) Write down the number of students who have a sister.

    (b) Write down the number of students who have a brother but not a sister.

    (c) Work out the number of students who have at least one sibling.
    Level 2 · 4 marksTry it
  5. 5
    8585 students were asked whether they study Spanish and whether they study German.
    • 4747 study Spanish,
    • 3333 study German,
    • 1515 study both Spanish and German.
    (a) Draw a Venn diagram to show this information.

    (b) Work out how many of the 8585 students study exactly one of the two languages.
    Level 3 · 5 marksTry it

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