ALGEBRA 2

RESOURCE

NEW SAT MATERIAL:

SET THEORY

  • The new SAT will contain questions on set theory (union, intersection, and elements).
  • The following pages can be used as a resource for the new SAT material. Teachers may use these pages as additional SAT prep warm-ups or class enrichment.
  • Resource sheets should be completed in the order in which they are numbered.
Set Theory Sheet 1

A set is a collection of objects. Each object is called an element or member of the set. For example:

  • Annapolis is an element of the set of U.S. state capitals.
  • Six is not an element of the set of odd numbers.

Practice:

  1. Give an element of the set of integers.
  1. One-half is an element of what set of numbers?
  1. Give an element of the set of irrational numbers.

Set Theory Sheet 2

The term union is a way of discussing the combination of different sets. The union of two or more sets is the combination of the sets.

For example:

  • If set S = {2, 3, 4} and set T = {4, 5, 6}, then the union of sets S and T (which is written S T) is the set {2, 3, 4, 5, 6}.

Practice:

Given set W = {2, 4, 5, 8} and set Z = {1, 3, 6, 7} and set Q is W Z.

  1. Give an element of set Q.
  1. How many elements are in the set Q?

Given set N is the set of all odd numbers and set E is the set of all even numbers.

3. Use words to describe the elements in N E.

Set Theory Sheet 3

The term intersection is a way of discussing the combination of different sets. The intersection of two or more sets is the set of elements being shared by those sets.

For example:

  • If set S = {2, 3, 4, 5} and set T = {4, 5, 6}, then the intersection of sets S and T (which is written S T) is the set {4, 5}.
  • If set R = {1, 2, 3, 4} and set P = {5, 6, 7, 8}, then the intersection of sets R and P contains no elements. This set is called the empty set or null set (which is written with the symbol ).

Practice:

Given set W = {2, 4, 5, 8} and set Z = {2, 3, 5, 7} and set Q is W Z.

  1. Give one element of set Q.
  1. How many elements are in set Q?

Given set P is the set of all prime numbers and set E is the set of all even numbers.

  1. Find the elements of P E.

Given set O is the set of all odd numbers and set E is the set of all even numbers.

4. Find O E.

Set Theory Sheet 4

Sets A and B are represented with the Venn diagrams below.

Practice:

  1. Shade the region representing A B in the diagram below.

AB

  1. In the diagram below, shade the region represented by the elements in set A that are not in set B.

A B

  1. Shade the region representing A B in the diagram below.

A B

Set Theory Sheet 5

Sets A, B, and C are represented with the Venn diagram below.

A B

C

Practice:

  1. Shade the region representing A C in the diagram below.

A B

C

  1. Shade the region representing B C in the diagram below.

A B

C

  1. In the diagram below, shade the region representing A B C (the elements being shared in sets A, B, and C)

A B

C

  1. In the diagram below, shade the region representing elements in set A B that are not in set C.

A B C

Set Theory Sheet 6

Practice:

Given L = {2, 3, 6, 8, 9} and M = {0, 1, 2, 4, 6, 9, 10}.

  1. Place the elements of sets L and M in the Venn diagram below.

L M

Given set A = {the set of all the factors of 12} and set B = {the set of

all factors of 16}.

  1. Place the elements of sets A and B in the diagram below.

A B

  1. List all the elements in A B.
  1. List all the elements in A B.
  1. How many elements are in the set A that are not in set B?

Given set C is the set of all multiples of 5 and D is the set of

all multiples of 4.

C D

  1. Give an element in C D.
  1. Give an element in set D that is not in set C.
  1. Give an example of 2 numbers whose intersection of prime factors would be the empty set.
Set Theory Sheet 7

Practice:

1. Given A = {1, 2, 3, 4, 5, 6, 7, 8}

B = {2, 4, 6, 8, 10, 12}

C = A B

What is the mean of set C?

  1. 1.25
  2. 5.00
  3. 5.50
  4. 6.25
  5. 7.33

2. Given D = {1, 2, 3, 4, 5, 6, 7, 8}

E = {2, 4, 6, 8, 10, 12}

F = D E

What is the mean of set F?

  1. 1.25
  2. 5.00
  3. 5.80
  4. 6.25
  5. 7.33

3. Given G = {3, 4, 5, 6, 7, 8}

H = {-3, 1, 11, 15, x}

G H =

Which of the following could not be the mean of set H?

  1. 4.00
  2. 4.80
  3. 5.20
  4. 6.20
  5. 12.60

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Algebra 2 SAT Resource - 7.06