Question 1

Let U be the set of all colors and S be the subset {red, orange, yellow, green, blue, violet}. Place the appropriate symbol in the blank: ​ {orange} _____ U ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 2

Place the appropriate symbol in the blank: ​ { 2 } ____ { 1, 2, 3, 4, 5 } ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 3

Rewrite the following statement using mathematical symbols. ​ The set D is a subset of the set C . ​

Accepted Answer

A)  D ⊄ C 
B)  C ⊆ D 
C)  D ⊆ C 
D)  D ⊇ C 
E)  D ∈ C 
A)  D ⊄ C 
B)  C ⊆ D 
C)  D ⊆ C 
D)  D ⊇ C 
E)  D ∈ C

Question 4

An elementary teacher has asked her students to place their names in the region that represents their answers to the question "Which pets live in your home?" D = the set of students who have at least one dog C = the set of students who have at least one cat O = the set of students who have a pet that is not a dog or a cat Describe the following set with a Venn diagram. Students who have at least one dog but do not have any cats.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 5

Below is a magic square. ​   ​ Describe a pattern(s) you see in this magic square. ​

Accepted Answer

A)  The sum of any row is 65. 
B)  The sum of any row or column is 65. 
C)  The sum of either center diagonal is 65. 
D)  The sum of any column is 65. 
E)  All of the above 
A)  The sum of any row is 65. 
B)  The sum of any row or column is 65. 
C)  The sum of either center diagonal is 65. 
D)  The sum of any column is 65. 
E)  All of the above

Question 6

Examine the magic triangle below. ​   ​ Describe a pattern(s) you see in the triangle. ​

Accepted Answer

A)  The smallest number of each side lies in the middle. 
B)  The largest number of each side lies on a corner. 
C)  The product of each side is 15. 
D)  The sum of each side is 9. 
E)  All of the above 
A)  The smallest number of each side lies in the middle. 
B)  The largest number of each side lies on a corner. 
C)  The product of each side is 15. 
D)  The sum of each side is 9. 
E)  All of the above

Question 7

At the beginning of the month, Jack and Jill had $ 629 in a checking account. During the month, they wrote checks for $ 23 , $ 57 , and $ 58 . They made a withdrawal of $ 61 from the automatic teller machine, and they made deposits of $ 153 and $ 70 . How much money did they have at the end of the month? ​

Accepted Answer

A)  $ 430 
B)  $ 644 
C)  $ 653 
D)  $ 605 
E)  $ 711 
A)  $ 430 
B)  $ 644 
C)  $ 653 
D)  $ 605 
E)  $ 711

Question 8

The Lewis and Clark expedition between 1804 and 1806 covered almost 8000 miles. If you can drive 280 miles per day, about how many days will it take you to drive the same distance? Round your answer to the nearest day. ​

Accepted Answer

A)  21 days 
B)  30 days 
C)  26 days 
D)  34 days 
E)  29 days 
A)  21 days 
B)  30 days 
C)  26 days 
D)  34 days 
E)  29 days

Question 9

Place the appropriate symbol in the blank: ​ 2 ____ { 1, 2, 3, 4, 5 } ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 10

A farmer needs to fence a rectangular piece of land. She wants the length of the field to be 80 feet longer than the width. If she has 1160 feet of fencing material, what should be the length and the width of the field? ​

Accepted Answer

A)  length = 330 feet; width = 250 feet 
B)  length = 280 feet; width = 200 feet 
C)  length = 380 feet; width = 300 feet 
D)  length = 430 feet; width = 350 feet 
E)  length = 230 feet; width = 150 feet 
A)  length = 330 feet; width = 250 feet 
B)  length = 280 feet; width = 200 feet 
C)  length = 380 feet; width = 300 feet 
D)  length = 430 feet; width = 350 feet 
E)  length = 230 feet; width = 150 feet

Question 11

On a digital clock, how many times in one day will the numbers be equal digits as they are, for example in 1:11? ​

Accepted Answer

A)  3 
B)  7 
C)  5 
D)  4 
E)  6 
A)  3 
B)  7 
C)  5 
D)  4 
E)  6

Question 12

Let U = { x | x is an American}, F = { x | x is a female} , S = { x | x is a smoker} , P = { x | x has a health problem}. ​ Convert the following symbols into everyday English. ​ S ∩ F ∩ P ​

Accepted Answer

A)  An American female who is a smoker or has a health problem. 
B)  An American female who is not a smoker and has a health problem. 
C)  An American smoker who is a female or has a health problem. 
D)  An American female who is a smoker and has a health problem. 
E)  An American female who does not have a health problem. 
A)  An American female who is a smoker or has a health problem. 
B)  An American female who is not a smoker and has a health problem. 
C)  An American smoker who is a female or has a health problem. 
D)  An American female who is a smoker and has a health problem. 
E)  An American female who does not have a health problem.

Question 13

Describe the following set using set-builder notation. ​ The set of prime numbers less than 131 . ​

Accepted Answer

A)  { x | x is a number less than 131 } 
B)  { 2, 3, 5, 7, 11, 13,..., 131 } 
C)  { 2, 131 } 
D)  [ 0, 131 ) 
E)  { x | x is a prime number less than 131 } 
A)  { x | x is a number less than 131 } 
B)  { 2, 3, 5, 7, 11, 13,..., 131 } 
C)  { 2, 131 } 
D)  [ 0, 131 ) 
E)  { x | x is a prime number less than 131 }

Question 14

A special rubber ball is dropped from the top of a wall that is 652 m high. Each time the ball bounces, it rises half as high as the distance it fell. The ball is caught when it bounces 40.75 m high. How many times did the ball bounce? ​

Accepted Answer

A)  9 
B)  7 
C)  8 
D)  6 
E)  4 
A)  9 
B)  7 
C)  8 
D)  6 
E)  4

Question 15

Martha planted 13 rows of apple trees, and each row had 26 trees. If each tree yielded an average of 220 apples, how many apples grew in her orchard? ​

Accepted Answer

A)  2,860 
B)  37,180 
C)  148,720 
D)  74,360 
E)  5,720 
A)  2,860 
B)  37,180 
C)  148,720 
D)  74,360 
E)  5,720

Question 16

Palindromes are numbers whose value is the same backwards as forwards. For example, 1331 is a palindrome. Most children love explorations with palindromes because they find the patterns fun and the investigations are so mathematically rich. How many palindromes can you find between 100 and 799? ​

Accepted Answer

A)  14 
B)  35 
C)  70 
D)  77 
E)  63 
A)  14 
B)  35 
C)  70 
D)  77 
E)  63

Question 17

At a bicycle store, there were a bunch of bicycles and tricycles. If there were 38 seats and 88 wheels, how many bicycles and how many tricycles were there? ​

Accepted Answer

A)  24 bicycles and 26 tricycles 
B)  12 bicycles and 26 tricycles 
C)  14 bicycles and 24 tricycles 
D)  52 bicycles and 36 tricycles 
E)  26 bicycles and 12 tricycles 
A)  24 bicycles and 26 tricycles 
B)  12 bicycles and 26 tricycles 
C)  14 bicycles and 24 tricycles 
D)  52 bicycles and 36 tricycles 
E)  26 bicycles and 12 tricycles

Question 18

Let U = { x | x is an American}, F = { x | x is a female} , S = { x | x is a smoker} , P = { x | x has a health problem} . Represent the following description with a Venn diagram. ​ An American female or an American smoker. ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 19

The table below shows the hourly wages of four different job classifications at a small construction company:   Carlos Vasquez, a plumbing contractor, hires 5 plumbers from this company at the hourly wage given in the table. If each plumber works 30 hours, what are the total wages paid by Carlos?

Accepted Answer

A)  $ 4,380 
B)  $ 4,379 
C)  $ 4,370 
D)  $ 4,350 
E)  .$ 4,380 
A)  $ 4,380 
B)  $ 4,379 
C)  $ 4,370 
D)  $ 4,350 
E)  .$ 4,380

Question 20

A special rubber ball is dropped from the top of a wall that is 512 feet high. Each time the ball bounces, it rises half as high as the distance it fell. The ball is caught when it bounces 1 foot high. How many times did the ball bounce? ​

Accepted Answer

A)  256 
B)  10 
C)  18 
D)  9 
E)  512 
A)  256 
B)  10 
C)  18 
D)  9 
E)  512

Let U be the set of all colors and S be the subset {red, orange, yellow, green, blue, violet}. Place the appropriate symbol in the blank: {orange} _____ U

Place the appropriate symbol in the blank: { 2 } ____ { 1, 2, 3, 4, 5 }

Rewrite the following statement using mathematical symbols. The set D is a subset of the set C .

Below is a magic square. Describe a pattern(s) you see in this magic square.

Examine the magic triangle below. Describe a pattern(s) you see in the triangle.

The Lewis and Clark expedition between 1804 and 1806 covered almost 8000 miles. If you can drive 280 miles per day, about how many days will it take you to drive the same distance? Round your answer to the nearest day.

Place the appropriate symbol in the blank: 2 ____ { 1, 2, 3, 4, 5 }

A farmer needs to fence a rectangular piece of land. She wants the length of the field to be 80 feet longer than the width. If she has 1160 feet of fencing material, what should be the length and the width of the field?

On a digital clock, how many times in one day will the numbers be equal digits as they are, for example in 1:11?

Let U = { x | x is an American}, F = { x | x is a female} , S = { x | x is a smoker} , P = { x | x has a health problem}. Convert the following symbols into everyday English. S ∩ F ∩ P

Describe the following set using set-builder notation. The set of prime numbers less than 131 .

A special rubber ball is dropped from the top of a wall that is 652 m high. Each time the ball bounces, it rises half as high as the distance it fell. The ball is caught when it bounces 40.75 m high. How many times did the ball bounce?

Martha planted 13 rows of apple trees, and each row had 26 trees. If each tree yielded an average of 220 apples, how many apples grew in her orchard?

Palindromes are numbers whose value is the same backwards as forwards. For example, 1331 is a palindrome. Most children love explorations with palindromes because they find the patterns fun and the investigations are so mathematically rich. How many palindromes can you find between 100 and 799?

At a bicycle store, there were a bunch of bicycles and tricycles. If there were 38 seats and 88 wheels, how many bicycles and how many tricycles were there?

Let U = { x | x is an American}, F = { x | x is a female} , S = { x | x is a smoker} , P = { x | x has a health problem} . Represent the following description with a Venn diagram. An American female or an American smoker.

The table below shows the hourly wages of four different job classifications at a small construction company: Carlos Vasquez, a plumbing contractor, hires 5 plumbers from this company at the hourly wage given in the table. If each plumber works 30 hours, what are the total wages paid by Carlos?

A special rubber ball is dropped from the top of a wall that is 512 feet high. Each time the ball bounces, it rises half as high as the distance it fell. The ball is caught when it bounces 1 foot high. How many times did the ball bounce?

The Number System

Understanding Addition and Subtraction

Understanding Multiplication and Division

Proportional Reasoning

Algebraic Thinking

Understanding Statistics and Probability

Geometry As Shape

Geometry As Measurement

Geometry As Transforming Shapes

Filters

Exam 1: Foundations for Learning Mathematics

Let U be the set of all colors and S be the subset {red, orange, yellow, green, blue, violet}. Place the appropriate symbol in the blank: ​ {orange} _____ U ​

Place the appropriate symbol in the blank: ​ { 2 } ____ { 1, 2, 3, 4, 5 } ​

Rewrite the following statement using mathematical symbols. ​ The set D is a subset of the set C . ​

Below is a magic square. ​ ​ Describe a pattern(s) you see in this magic square. ​

Examine the magic triangle below. ​ ​ Describe a pattern(s) you see in the triangle. ​

The Lewis and Clark expedition between 1804 and 1806 covered almost 8000 miles. If you can drive 280 miles per day, about how many days will it take you to drive the same distance? Round your answer to the nearest day. ​

Place the appropriate symbol in the blank: ​ 2 ____ { 1, 2, 3, 4, 5 } ​

A farmer needs to fence a rectangular piece of land. She wants the length of the field to be 80 feet longer than the width. If she has 1160 feet of fencing material, what should be the length and the width of the field? ​

On a digital clock, how many times in one day will the numbers be equal digits as they are, for example in 1:11? ​

Let U = { x | x is an American}, F = { x | x is a female} , S = { x | x is a smoker} , P = { x | x has a health problem}. ​ Convert the following symbols into everyday English. ​ S ∩ F ∩ P ​

Describe the following set using set-builder notation. ​ The set of prime numbers less than 131 . ​

A special rubber ball is dropped from the top of a wall that is 652 m high. Each time the ball bounces, it rises half as high as the distance it fell. The ball is caught when it bounces 40.75 m high. How many times did the ball bounce? ​

Martha planted 13 rows of apple trees, and each row had 26 trees. If each tree yielded an average of 220 apples, how many apples grew in her orchard? ​

Palindromes are numbers whose value is the same backwards as forwards. For example, 1331 is a palindrome. Most children love explorations with palindromes because they find the patterns fun and the investigations are so mathematically rich. How many palindromes can you find between 100 and 799? ​

At a bicycle store, there were a bunch of bicycles and tricycles. If there were 38 seats and 88 wheels, how many bicycles and how many tricycles were there? ​

Let U = { x | x is an American}, F = { x | x is a female} , S = { x | x is a smoker} , P = { x | x has a health problem} . Represent the following description with a Venn diagram. ​ An American female or an American smoker. ​

The table below shows the hourly wages of four different job classifications at a small construction company: Carlos Vasquez, a plumbing contractor, hires 5 plumbers from this company at the hourly wage given in the table. If each plumber works 30 hours, what are the total wages paid by Carlos?

A special rubber ball is dropped from the top of a wall that is 512 feet high. Each time the ball bounces, it rises half as high as the distance it fell. The ball is caught when it bounces 1 foot high. How many times did the ball bounce? ​

The Number System

Understanding Addition and Subtraction

Understanding Multiplication and Division

Proportional Reasoning

Algebraic Thinking

Understanding Statistics and Probability

Geometry As Shape

Geometry As Measurement

Geometry As Transforming Shapes

Filters

Let U be the set of all colors and S be the subset {red, orange, yellow, green, blue, violet}. Place the appropriate symbol in the blank: {orange} _____ U

Place the appropriate symbol in the blank: { 2 } ____ { 1, 2, 3, 4, 5 }

Rewrite the following statement using mathematical symbols. The set D is a subset of the set C .

Below is a magic square. Describe a pattern(s) you see in this magic square.

Examine the magic triangle below. Describe a pattern(s) you see in the triangle.

The Lewis and Clark expedition between 1804 and 1806 covered almost 8000 miles. If you can drive 280 miles per day, about how many days will it take you to drive the same distance? Round your answer to the nearest day.

Place the appropriate symbol in the blank: 2 ____ { 1, 2, 3, 4, 5 }

A farmer needs to fence a rectangular piece of land. She wants the length of the field to be 80 feet longer than the width. If she has 1160 feet of fencing material, what should be the length and the width of the field?

On a digital clock, how many times in one day will the numbers be equal digits as they are, for example in 1:11?

Let U = { x | x is an American}, F = { x | x is a female} , S = { x | x is a smoker} , P = { x | x has a health problem}. Convert the following symbols into everyday English. S ∩ F ∩ P

Describe the following set using set-builder notation. The set of prime numbers less than 131 .

A special rubber ball is dropped from the top of a wall that is 652 m high. Each time the ball bounces, it rises half as high as the distance it fell. The ball is caught when it bounces 40.75 m high. How many times did the ball bounce?

Martha planted 13 rows of apple trees, and each row had 26 trees. If each tree yielded an average of 220 apples, how many apples grew in her orchard?

Palindromes are numbers whose value is the same backwards as forwards. For example, 1331 is a palindrome. Most children love explorations with palindromes because they find the patterns fun and the investigations are so mathematically rich. How many palindromes can you find between 100 and 799?

At a bicycle store, there were a bunch of bicycles and tricycles. If there were 38 seats and 88 wheels, how many bicycles and how many tricycles were there?

Let U = { x | x is an American}, F = { x | x is a female} , S = { x | x is a smoker} , P = { x | x has a health problem} . Represent the following description with a Venn diagram. An American female or an American smoker.

A special rubber ball is dropped from the top of a wall that is 512 feet high. Each time the ball bounces, it rises half as high as the distance it fell. The ball is caught when it bounces 1 foot high. How many times did the ball bounce?