Algebra 1.1 Assignment: Variables and Expressions

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Questions and Answers

What is an algebraic expression?

A mathematical phrase that cannot be determined true or false

A numerical value

A mathematical expression containing one or more variables (correct)

A letter or symbol used to represent an unknown

What is the definition of a coefficient?

The constant preceding the variables in a product (correct)

An unknown quantity

A mathematical phrase

A constant value

What is a constant?

A numerical value

What is an expression?

A mathematical phrase that cannot be determined true or false Signup and view all the answers

What is a variable?

A letter or symbol used to represent an unknown Signup and view all the answers

If x is 5, then 6x = _____.

30 Signup and view all the answers

What is the expression for the sum of n and five?

n + 5 Signup and view all the answers

What is the expression for five subtracted from n?

n - 5 Signup and view all the answers

What is the expression for eight added to x?

x + 8 Signup and view all the answers

What is the expression for eight subtracted from x?

x - 8 Signup and view all the answers

What is the expression for eight minus x?

8 - x Signup and view all the answers

What is the expression for five minus n?

5 - n Signup and view all the answers

What is the expression for x added to the sum of five and seven?

x + (5 + 7) Signup and view all the answers

What is the expression for the sum of eight and two, subtracted from x?

x - (8 + 2) Signup and view all the answers

What is the expression for the difference of eight and two, added to x?

x + (8 - 2) Signup and view all the answers

What is the expression for the sum of x and itself?

x + x Signup and view all the answers

Which expression does not represent 'the sum of n and 6'?

6n Signup and view all the answers

Which of the following expressions represents 'the difference of 8 and n'?

8 - n Signup and view all the answers

Which of the following expressions does not represent 'four more than one-third x'?

1/4x + 3 Signup and view all the answers

Which of the following expressions represents 'twelve diminished by six times a number'?

12 - 6n Signup and view all the answers

Which of the following expressions represents 'three times the difference between t and y'?

3(t - y) Signup and view all the answers

Which of the following expressions represents 'the quotient of nine times a number and seven'?

9n ÷ 7 Signup and view all the answers

Which of the following expressions represents 'the sum of n and the sum of 8 and 6'?

n + (8 + 6) Signup and view all the answers

The coefficient of 6x is _____.

6 Signup and view all the answers

The coefficient of 8 + 2N is _____.

16 Signup and view all the answers

The coefficient of 9(14)P is _____.

126 Signup and view all the answers

The coefficient of 2(3)(6)Q is _____.

36 Signup and view all the answers

Look at each expression. Is it equivalent to 'the quotient of 10 plus x and y minus 3'?

(10+x)/(y-3) Signup and view all the answers

For 3x^2 - 4x + 1, match the following:

x = Variable 3 = Coefficient 1 = Constant 3x^2 - 4x + 1 = Algebraic Expression 2 = Degree Signup and view all the answers

Study Notes

Key Definitions

Algebraic Expression: A mathematical expression that includes one or more variables.
Coefficient: The constant factor that multiplies a variable in an expression.
Constant: A fixed numerical value not affected by variables.
Expression: A mathematical phrase that represents a value but cannot be classified as true or false.
Variable: A symbol or letter that stands for an unknown number.

Mathematical Operations with Variables

Example when x = 5: Substituting gives ( 6x = 30 ).
The sum of ( n ) and five: Written as ( n + 5 ).
Five subtracted from ( n ): Written as ( n - 5 ).
Eight added to ( x ): Expressed as ( x + 8 ).
Eight subtracted from ( x ): Expressed as ( x - 8 ).
Eight minus ( x ): Presented as ( 8 - x ).
Five minus ( n ): Expressed as ( 5 - n ).
( x ) added to the sum of five and seven: Written as ( x + (5 + 7) ).
The sum of eight and two, subtracted from ( x ): Written as ( x - (8 + 2) ).
The difference of eight and two, added to ( x ): Expressed as ( x + (8 - 2) ).
The sum of ( x ) and itself: Written as ( x + x ).

Expression Evaluation and Identification

Incorrect representation of "the sum of ( n ) and 6": ( 6n ) (not ( 6 + n ) or ( n + 6 )).
Correct representation of "the difference of 8 and ( n )": ( 8 - n ) (not ( n - 8 ) or (-8n)).
Incorrect option for "four more than one-third ( x )": ( 1/4x + 3 ).
Correct representation of "twelve diminished by six times a number": ( 12 - 6n ).

Coefficient Analysis

Coefficient of ( 6x ): 6.
Coefficient of ( 8 + 2N ): 16 (from multiplying 8 and 2).
Coefficient of ( 9(14)P ): 126 (product of 9 and 14).
Coefficient of ( 2(3)(6)Q ): 36 (product of 2, 3, and 6).

Expression Equivalence

For expression ( \frac{10 + x}{y - 3} ):
- ( \frac{10+x}{y} ): No
- ( \frac{10+x}{y-3} ): Yes
- ( 10 + \frac{x}{y} - 3 ): No
- ( \frac{10 + x - 3}{y} ): No

Properties of Algebraic Expressions

For the expression ( 3x^2 - 4x + 1 ):
- Variable: ( x ).
- Coefficient: 3 (of the term ( 3x^2 )).
- Constant: 1 (the standalone integer).
- Algebraic Expression: ( 3x^2 - 4x + 1 ).
- Degree: 2 (highest power of variable ( x )).

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Test your knowledge on key concepts of algebra with these flashcards focused on variables and expressions. This assignment will help reinforce definitions such as algebraic expressions, coefficients, constants, and more. Perfect for students looking to solidify their understanding of fundamental algebra topics.