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## Using Venn Diagrams Problems Worksheets

Students have long used Venn diagrams in English and Social Studies classes by the time we encourage them to use it math. Students sometimes will do a double take when they first see them being used in math class. Venn diagrams are great to evaluate the relationships. Especially when it comes to data. We can use them to visualize our data and see if there is something that separates it or connects it. These tools are primarily used in statistics, probability, and situations where we are evaluating the logic of something. Students learn how to create, read, and interpret Venn Diagrams imaging of logic statements with this collection of worksheets and lessons.

## Aligned Standard: High School Data Modeling

- Getting to Work Step-by-Step Lesson - How do all the employees get to work? There are even some that do it multiple ways.
- Guided Lesson - Examine a voters poll, the participation at an annual school dance, and what employees drink at the office.
- Guided Lesson Explanation - I feel that it is fair to disclose that number two is very difficult for most students.
- Practice Worksheet - I give you ten scenarios that I would like to know a singular part of, but they require Venn diagrams.
- Practice Worksheet 2 - I not only double up on the practice in this area, but I also give you a fitting picnic clip art.
- Matching Worksheet - Find the answers to all the complex questions I throw at you.
- Using Venn Diagrams Five Pack of Worksheets - I really tried to find situations where Venns applied. I actual did a few hours of research to see where this skill is used in the real world.
- Answer Keys - These are for all the unlocked materials above.

## Homework Sheets

Diagramming these helps out a great deal.

- Homework 1 - In an office of 40 employees, 17 travel by car, 23 travel by bike, and 10 take both cars and bikes.
- Homework 2 - How many employees in the office are not enrolled in either Car or Bike?
- Homework 3 - Now we want to find the number of students interested in participating in the different events. Let's diagram what we were told.

## Practice Worksheets

I left a template of Venn diagrams for you to work with.

- Practice 1 - There are 35 people working in a bakery. 15 people are making cakes, 20 people are making chocolate cookies, and 8 people are making both cakes and cookies. How many people in the shop are not making cakes or cookies?
- Practice 2 - 18 students are in a college class. 10 students have Samsung cell phones. 8 students have Nokia cell phones. 5 students have both a Samsung and Nokia cell phone. How many students have only a Nokia cell phone?
- Practice 3 - 10 of the students in Johnson's class like to eat oranges. 7 students like to eat cherries, and 4 students like to eat both oranges and cherries. How many students like to eat cherries, but not oranges?

## Math Skill Quizzes

We don't ask you to create Venn diagrams. Instead you are asked to apply them.

- Quiz 1 - Kenny takes a poll on favorite things to eat. 8 people like to eat candy. 10 people like to eat cookies. 7 people like to eat both candy and cookies. How many people did he poll?
- Quiz 2 - Sybil takes a poll of people's favorite dangerous animal. 7 like polar bears and 3 like sharks. 2 people like both polar bears and sharks. How many people like polar bears only?
- Quiz 3 - 10 of the students in Lea's class can swim the backstroke and 7 can swim the breaststroke. 4 students can swim both the strokes. How many students can swim the breaststroke, but not the backstroke?

## How to Use Venn Diagrams for Math Problems

This is a schematic way of representing the elements of a group or set. In Venn diagrams, you get a number of elements or a bunch of numbers, and then all you have to do is use that information to construct a Venn diagram and then figure out the rest of the information.

They can help you understand the relationships that do and do not exist between these elements. Venn diagrams help you represent a diagram in a pictorial form. It represents the intersection and overlapping of two groups in an understandable manner. This allows you to quickly and easily compare and contrast these elements.

To understand how Venn diagrams help, consider the following example: There are a total of 40 students, out of which 14 are taking English Composition, and 26 are taking Chemistry. If there are 5 students taking English and Chemistry in both classes, how many students are in neither class? And how many of them are in either class?

To solve these, lets walk through how we would approach preparing a Venn diagram for this situation. Draw two circles, one representing English (blue in our diagram) and the other representing Chemistry (red in our diagram) with a part of circles overlapping into each other. Now write the respective numbers into the parts of the circle and use the information to solve the word problem you have at hand. 14 would be placed in the blue circle, 6 in the red circle, and 5 where the overlap is. To answer these questions we need to realize that those 5 students are accounted for already in each of those classes. So that would mean that there a total of 5 less enrolled in each class. Seeing that through the Venn diagram allows us to come to that conclusion a little easier.

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## Venn Diagram Worksheets

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## 15 Venn Diagram Questions And Practice Problems (KS3 & KS4): Harder GCSE Exam Style Questions Included

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Venn diagram questions involve visual representations of the relationship between two or more different groups of things. Venn diagrams are first covered in KS1 or KS2 and their complexity and uses progress through KS3 and KS4.

This blog will look at the types of Venn diagram questions that might be encountered at KS3 and KS4, with a focus on exam style example questions and preparing for GCSEs. We will cover problem-solving questions and questions similar to those found on past papers. Each question is followed by a worked solution.

## How to solve Venn diagram questions

Venn diagram questions year 7, venn diagram questions year 8, venn diagram questions year 9, foundation gcse venn diagram questions: grades 1-5, higher gcse venn diagram questions: grades 4-9, looking for more venn diagram questions and resources, looking for more ks3 and ks4 maths questions.

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In KS3, sets and set notation are introduced when working with Venn diagrams. A set is a collection of objects. We identify a set using curly brackets. For example, if set \mathrm{A} contains the odd numbers between 1 and 10 , then we can write this as: A = \{1, 3, 5, 7, 9\}.

Venn diagrams sort objects, called elements, into two or more sets.

This diagram shows the set of elements \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} sorted into the following sets.

Set \mathrm{A} = factors of 10

Set \mathrm{B} = even numbers

The numbers in the overlap (intersection) belong to both sets. Those that are not in set \mathrm{A} or set \mathrm{B} are shown outside of the circles.

Different sections of a Venn diagram are denoted in different ways.

\xi represents the whole set, called the universal set.

\emptyset represents the empty set, a set containing no elements.

Let’s check out some other set notation examples!

In KS3 and KS4, we often use Venn diagrams to establish probabilities. We do this by reading information from the Venn diagram and applying the following formula.

For Venn diagrams we can say

## 15 Venn Diagram Questions & Practice Problems (KS3 & KS4) Worksheet

Download this free worksheet on Venn diagrams. This set of 15 Venn diagram questions and answer key will help you prepare for GCSE maths!

## KS3 Venn diagram questions

In KS3, students learn to use set notation with Venn diagrams and start to find probabilities using Venn diagrams. The questions below are examples of questions that students may encounter in Years 7, Year 8 and Year 9.

1. This Venn diagram shows information about the number of people who have brown hair and the number of people who wear glasses.

How many people have brown hair and glasses?

The intersection, where the Venn diagrams overlap, is the part of the Venn diagram which represents brown hair AND glasses. There are 4 people in the intersection.

2. Which set of objects is represented by the Venn diagram below?

We can see from the Venn diagram that there are two green triangles, one triangle that is not green, three green shapes that are not triangles and two shapes that are not green or triangles. These shapes belong to set D.

3. Max asks 40 people whether they own a cat or a dog. 17 people own a dog, 14 people own a cat and 7 people own a cat and a dog. Choose the correct representation of this information on a Venn diagram.

There are 7 people who own a cat and a dog. Therefore, there must be 7 more people who own a cat, to make a total of 14 who own a cat, and 10 more people who own a dog, to make a total of 17 who own a dog.

Once we put this information on the Venn diagram, we can see that there are 7+7+10=24 people who own a cat, a dog or both.

40-24=16 , so there are 16 people who own neither.

4. The following Venn diagrams each show two sets, set \mathrm{A} and set \mathrm{B} . On which Venn diagram has \mathrm{A}^{\prime} been shaded?

\mathrm{A}^{\prime} means not in \mathrm{A} . This is shown in diagram \mathrm{B.}

5. Place these values onto the following Venn diagram and use your diagram to find the number of elements in the set \text{S} \cup \text{O}.

\xi = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} \text{S} = square numbers \text{O} = odd numbers

\text{S} \cup \text{O} is the union of \text{S} or \text{O} , so it includes any element in \text{S} , \text{O} or both. The total number of elements in \text{S} , \text{O} or both is 6.

6. The Venn diagram below shows a set of numbers that have been sorted into prime numbers and even numbers.

A number is chosen at random. Find the probability that the number is prime and not even.

The section of the Venn diagram representing prime and not even is shown below.

There are 3 numbers in the relevant section out of a possible 10 numbers altogether. The probability, as a fraction, is \frac{3}{10}.

7. Some people visit the theatre. The Venn diagram shows the number of people who bought ice cream and drinks in the interval.

Ice cream is sold for £3 and drinks are sold for £2. A total of £262 is spent. How many people bought both a drink and an ice cream?

Money spent on drinks: 32 \times £2 = £64

Money spent on ice cream: 16 \times £3 = £48

£64+£4=£112 , so the information already on the Venn diagram represents £112 worth of sales.

£262-£112 = £150 , so another £150 has been spent.

If someone bought a drink and an ice cream, they would have spent £2+£3 = £5.

£150 \div £5=30 , so 30 people bought a drink and an ice cream.

## KS4 Venn diagram questions

At KS4, students are expected to be able to take information from word problems and put it onto a Venn diagram involving two or three sets. The use of set notation is extended and the probabilities become more complex. In the higher tier, Venn diagrams are used to calculate conditional probability.

Venn diagrams appear on exam papers across all exam boards, including Edexcel, AQA and OCR. Questions, particularly in the higher tier, may involve other areas of maths, such as percentages, ratio or algebra.

8. 50 people are asked whether they have been to France or Spain.

18 people have been to France. 23 people have been to Spain. 6 people have been to both.

By representing this information on a Venn diagram, find the probability that a person chosen at random has not been to Spain or France.

6 people have been to both France and Spain. This means 17 more have been to Spain to make 23 altogether, and 12 more have been to France to make 18 altogether. This makes 35 who have been to France, Spain or both and therefore 15 who have been to neither.

The probability that a person chosen at random has not been to France or Spain is \frac{15}{50}.

9. Some people were asked whether they like running, cycling or swimming. The results are shown in the Venn diagram below.

One person is chosen at random. What is the probability that the person likes running and cycling?

9 people like running and cycling (we include those who also like swimming) out of 80 people altogether. The probability that a person chosen at random likes running and cycling is \frac{9}{80}.

10. ξ = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16\}

\text{A} = \{ even numbers \}

\text{B} = \{ multiples of 3 \}

By completing the following Venn diagram, find \text{P}(\text{A} \cup \text{B}^{\prime}).

\text{A} \cup \text{B}^{\prime} means \text{A} or not \text{B} . We need to include everything that is in \text{A} or is not in \text{B} . There are 13 elements in \text{A} or not in \text{B} out of a total of 16 elements.

Therefore \text{P}(\text{A} \cup \text{B}^{\prime}) = \frac{13}{16}.

11. ξ = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}

A = \{ multiples of 2 \}

By putting this information onto the following Venn diagram, list all the elements of B.

We can start by placing the elements in \text{A} \cap \text{B} , which is the intersection.

We can then add any other multiples of 2 to set \text{A}.

Next, we can add any unused elements from \text{A} \cup \text{B} to \text{B}.

Finally, any other elements can be added to the outside of the Venn diagram.

The elements of \text{B} are \{1, 2, 3, 4, 6, 12\}.

12. Some people were asked whether they like strawberry ice cream or chocolate ice cream. 82\% said they like strawberry ice cream and 70\% said they like chocolate ice cream. 4\% said they like neither.

By putting this information onto a Venn diagram, find the percentage of people who like both strawberry and chocolate ice cream.

Here, the percentages add up to 156\%. This is 56\% too much. In this total, those who like chocolate and strawberry have been counted twice and so 56\% is equal to the number who like both chocolate and strawberry. We can place 56\% in the intersection, \text{C} \cap \text{S}

We know that the total percentage who like chocolate is 70\%, so 70-56 = 14\%-14\% like just chocolate. Similarly, 82\% like strawberry, so 82-56 = 26\%-26\% like just strawberry.

13. The Venn diagram below shows some information about the height and gender of 40 students.

A student is chosen at random. Find the probability that the student is female given that they are over 1.2m.

We are told the student is over 1.2m. There are 20 students who are over 1.2m and 9 of them are female. Therefore the probability that the student is female given they are over 1.2m is \frac{9}{20}.

14. The Venn diagram below shows information about the number of students who study history and geography.

H = history

G = geography

Work out the probability that a student chosen at random studies only history.

We are told that there are 100 students in total. Therefore:

x = 12 or x = -3 (not valid) If x = 12, then the number of students who study only history is 12, and the number who study only geography is 24. The probability that a student chosen at random studies only history is \frac{12}{100}.

15. 50 people were asked whether they like camping, holiday home or hotel holidays.

18\% of people said they like all three. 7 like camping and holiday homes but not hotels. 11 like camping and hotels. \frac{13}{25} like camping.

Of the 27 who like holiday homes, all but 1 like at least one other type of holiday. 7 people do not like any of these types of holiday.

By representing this information on a Venn diagram, find the probability that a person chosen at random likes hotels given that they like holiday homes.

Put this information onto a Venn diagram.

We are told that the person likes holiday homes. There are 27 people who like holiday homes. 19 of these also like hotels. Therefore, the probability that the person likes hotels given that they like holiday homes is \frac{19}{27}.

Third Space Learning’s free GCSE maths resource library contains detailed revision lessons with step-by-step instructions on how to solve Venn diagram problems, as well as worksheets with Venn diagram practice questions and more GCSE exam questions.

Take a look at the Venn diagram lessons today – more are added every week.

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