# Expressions, Equations, Functions, & Relations

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The "Expressions, Equations, Functions, & Relations Quiz" is an educational tool designed to assess individuals' understanding of key mathematical concepts in the realm of algebra and beyond. This comprehensive quiz covers a wide range of topics, from basic arithmetic expressions to more complex equations and functions.
You are presented with a series of questions that challenge your ability to differentiate between expressions and equations, identify variables, coefficients, and constants, and solve various types of mathematical problems. Additionally, the quiz delves into the concept of functions and relations, exploring how inputs and outputs are related and how mathematical relationships can Read morebe represented graphically and symbolically.
One of the strengths of this quiz is its ability to cater to learners of all levels. Whether you're a beginner seeking to grasp the basics or an advanced student looking to refine your skills, the quiz offers questions of varying difficulty to accommodate different levels of proficiency.

## Expressions, Equations, Functions, & Relations Questions and Answers

• 1.

### Brett got on an elevator and rode up 10 floors.  Next he rode down 7 floors.  After that he went up 4 floors.  Finally he went down 6 floors.  When he got off the elevator he was on the 11th floor.  What floor was he on when he started his ride?

• A.

8th floor

• B.

9th floor

• C.

10th floor

• D.

12th floor

C. 10th floor
Explanation
If Brett started on the 10th floor and went up 10 floors, he would be on the 20th floor. Then, if he went down 7 floors, he would be on the 13th floor. Going up 4 floors would bring him to the 17th floor, and going down 6 floors would bring him to the 11th floor. Therefore, he must have started on the 10th floor.

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• 2.

### Sara and Kim together have  15 pencils.  Sara has 9  pencils. Mark and Kim together have 10 pencils.  How many pencils does Mark have?

• A.

5

• B.

34

• C.

8

• D.

4

D. 4
Explanation
Since Sara has 9 pencils and Sara and Kim together have 15 pencils, it means Kim has 15 - 9 = 6 pencils.
Also, Mark and Kim together have 10 pencils, so if Kim has 6 pencils, Mark must have 10 - 6 = 4 pencils.

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• 3.

### What is the algebraic expression for "a number f decreased by 18"?

• A.

18f

• B.

F + 18

• C.

F - 18

• D.

18 + f

C. F - 18
Explanation
The algebraic expression for "a number f decreased by 18" is f - 18. This is because the phrase "decreased by" indicates subtraction, and the number being decreased is represented by the variable f. Therefore, f - 18 represents the value of f with 18 subtracted from it.

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• 4.

### The coefficient of x when you have 1.55x is.....

• A.

1.00

• B.

0.55

• C.

1.55

• D.

155

C. 1.55
Explanation
The coefficient of x is the number multiplied by x. In this case, the coefficient of x is 1.55 because 1.55x means that x is being multiplied by 1.55.

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• 5.

### The coefficient of y when you have 22y/9 is.....

• A.

1/9

• B.

22/9

• C.

22

B. 22/9
Explanation
The given expression is 22y/9. In this expression, the coefficient of y is 22/9. This is because the coefficient of a variable is the number that multiplies the variable. In this case, the variable y is being multiplied by 22/9. Therefore, the coefficient of y is 22/9.

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• 6.

### The PURPOSE of a Function and Relation is to explain how something works and what is happening! It describes what is happening using NUMBERS (that don't change) and VARIABLES (that can change).

• A.

True

• B.

False

A. True
Explanation
The purpose of a function and relation is indeed to explain how something works and what is happening. Functions and relations use numbers and variables to describe what is happening, with numbers representing fixed values and variables representing values that can change. This statement accurately describes the purpose of functions and relations, making the answer true.

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• 7.

### Which (variable) do MATH BOOKS often use instead of "f(x)"? This (variable) and f(x) mean the same thing!!!Example: f(x) = x + 6  can also be written as (variable) = x + 6

y
Y
Explanation
Math books often use the variable "y" instead of "f(x)". In this case, "y" and "f(x)" are used interchangeably to represent the same thing. For example, the equation "f(x) = x + 6" can also be written as "y = x + 6".

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• 8.

### Is this true or false?A FUNCTION is a SPECIAL TYPE of RELATION. A RELATION is not always a FUNCTION.

• A.

True

• B.

False

A. True
Explanation
A function is a special type of relation because it assigns exactly one output value to each input value. In other words, for every input, there is only one corresponding output. However, a relation is not always a function because it can have multiple output values for a single input value. Therefore, the statement that a function is a special type of relation and a relation is not always a function is true.

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• 9.

### The expression "four less than a number" is the same as which of the following?

• A.

4-x

• B.

X-4

B. X-4
Explanation
The expression "four less than a number" implies that we are subtracting 4 from the number. In the expression x-4, we are subtracting 4 from x, which aligns with the given expression. Therefore, x-4 is the correct answer.

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• 10.

### Four times the sum of nine and a number can be expressed as -

• A.

4(9 + n)

• B.

4 x 9 + n

• C.

4 + n + 9

• D.

4n + 9

A. 4(9 + n)
Explanation
The sum means to add. You want to add the two numbers AND then multiply it by four.

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• 11.

### Three times Cassie's age increased by nine is twelve. This can be expressed as -

• A.

3x+12 - 9

• B.

3x + 9=12

• C.

3x + 12 = 9

• D.

3x + 5

B. 3x + 9=12
Explanation
The given equation is trying to express a relationship between Cassie's age and a certain value. The equation states that three times Cassie's age increased by nine is equal to twelve. By solving the equation, we find that the expression 3x + 9, where x represents Cassie's age, is equal to 12.

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• 12.

### Steve had x dollars in his bank account and then he deposited \$10 each week for 3 weeks.  His total amount of money in the bank is now \$70.  What is x? ( How much money did he have to start?)

• A.

\$60

• B.

\$20

• C.

\$40

C. \$40
Explanation
Steve deposited \$10 each week for 3 weeks, which means he added a total of \$30 to his account. His total amount of money in the bank is now \$70. To find out how much money he had to start with (x), we need to subtract the amount he deposited (\$30) from the total amount in the bank (\$70). Therefore, x = \$70 - \$30 = \$40.

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• 13.

### What is the difference between an expression and an equation? Pick ONE answer-

• A.

They are the same thing.

• B.

An equation has an equal sign, but an expression does not.

• C.

An equation has more numbers and an expression has more variables.

B. An equation has an equal sign, but an expression does not.
Explanation
An equation and an expression are different in that an equation always contains an equal sign, while an expression does not. An equation represents a mathematical relationship between two or more quantities, indicating that they are equal. On the other hand, an expression is a combination of numbers, variables, and mathematical operations, but it does not show equality. Therefore, the correct answer is that an equation has an equal sign, but an expression does not.

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• 14.

### What does 25k mean?

• A.

• B.

The difference between k and 25.

• C.

The product of 25 and k.

C. The product of 25 and k.
Explanation
The correct answer is "the product of 25 and k". In mathematical terms, "the product" refers to the result of multiplying two numbers together. Therefore, when we say "the product of 25 and k", it means that we are multiplying the value of 25 with the value of k.

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• 15.

### The sum of three and twenty-two, divided by the number 'a' can also be expressed as -

• A.

(3 + 22) / a

• B.

A / (3 + 22)

• C.

3 + 22 / a

A. (3 + 22) / a
Explanation
The correct answer is (3 + 22) / a. This is because the given expression states that the sum of three and twenty-two is divided by the number a. Therefore, we need to add three and twenty-two first, and then divide the sum by a.

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• 16.

### Fill in the blank with the correct word! A _________ is a letter that represents a number(of something). Hint: the answer has 8 letters

variable, VARIABLE , Variable
Explanation
A variable is a letter that represents a number (of something). In programming and mathematics, variables are used to store and manipulate data. They can hold different values at different times, allowing for flexibility and dynamic calculations. The hint provided indicates that the answer has 8 letters, which matches with the word "variable".

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• 17.

### Please fill in the answer below... The ____________ of a variable is the number in front of the variable. Hint: the answer has 11 letters

coefficient, COEFFICIENT, Coefficient
Explanation
The coefficient of a variable is the number in front of the variable. In algebraic expressions, variables are often multiplied by numbers, and the coefficient represents that number. It helps determine the scale or magnitude of the variable's impact on the expression. In this case, "coefficient" is the correct answer, and it has 11 letters.

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• 18.

### Translate from an English expression into an Algebraic expression: a decreased by 17 (answer with NO SPACES  Example: x+5)

a-17, A-17
Explanation
The correct answer is a-17 or A-17. This represents the English expression "a decreased by 17" translated into an algebraic expression. The variable "a" is being subtracted by 17.

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• 19.

### Translate from an English expression into an Algebraic expression: The ratio of m and n (answer with NO SPACES- Example: x+5)

m/n, M/N
Explanation
The given question asks for the translation of the English expression "the ratio of m and n" into an algebraic expression. The correct answer is "m/n" or "M/N" as both expressions represent the ratio of m to n, where m is the numerator and n is the denominator.

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• 20.

### Translate from an English expression into an Algebraic expression: 8 less than the sum of a and b (answer with NO SPACES-  Example: x+5) HINT - don't forget the ()

(a+b)-8, (A+B)-8
Explanation
The given expression translates from an English expression into an Algebraic expression as (a+b)-8 or (A+B)-8. This means that you take the sum of a and b (or A and B) and then subtract 8 from it.

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• 21.

### A FUNCTION is a "special" type of ____________.

relationship, RELATIONSHIP, Relationship, Relation, relation, RELATION
Explanation
A function is a "special" type of relationship. In mathematics, a function relates each input value to exactly one output value, which differentiates it from other types of relationships where one input can have multiple outputs.

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• 22.

### Why is a Function so useful when you are trying to understand a situation?

• A.

A Function gives us an "EXACT" answer for every input!

• B.

A Function describes what is happening using "numbers" that don't change and "variables" for the things that can change.

• C.

Both of the above answers are CORRECT!

C. Both of the above answers are CORRECT!
Explanation
A function is useful when trying to understand a situation because it provides an exact answer for every input and describes what is happening using numbers that don't change and variables for the things that can change. This allows for a comprehensive understanding of the situation and the ability to analyze different scenarios and variables.

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• 23.

### If you have the Function -  Juggling (S) = 3 balls X _____  , where S =  # of seconds What variable should you put in the blank?!?

s, S
Explanation
The variable that should be put in the blank is "s" or "S". The function "Juggling (S) = 3 balls X _____" suggests that the number of seconds, represented by "s" or "S", is the variable that determines the number of balls being juggled.

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• 24.

### Check ALL the answers that are TRUE! What were the reasons behind your classmates engaging in weightlifting and Mr. Morehead juggling balls during class?

• A.

So I could learn how to "describe a situation" using numbers and variables.

• B.

To help me understand the Purpose of a Function is to explain how something works!

• C.

So I could decide what INPUT, OUTPUT, and VARIABLES to use so my Function is easy to understand.

• D.

Because Mr. Morehead used to be in a juggling circus.

A. So I could learn how to "describe a situation" using numbers and variables.
B. To help me understand the Purpose of a Function is to explain how something works!
C. So I could decide what INPUT, OUTPUT, and VARIABLES to use so my Function is easy to understand.
Explanation
The correct answers are all related to the purpose and benefits of weight lifting and juggling balls in class. By doing weight lifting and juggling, students can learn how to "describe a situation" using numbers and variables, understand the purpose of a function in explaining how something works, and decide what input, output, and variables to use in order to make their function easy to understand. These activities provide practical examples and applications of mathematical concepts, helping students develop problem-solving skills and apply mathematical principles in real-life situations.

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• Current Version
• Feb 14, 2024
Quiz Edited by
ProProfs Editorial Team
• Jun 18, 2014
Quiz Created by
David

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