Algebra 2: Part 1 Flashcards

Questions and Answers

What is the first step in writing an algebraic expression for a real-world situation?

Identify any unknown values and assign variables to them.

Identify the variable(s), coefficient(s), and constant(s) in the expression -13x + 45.

Variable: x, Coefficient: -13, Constant: 45

What is the expression for the total number of runners competing in a tournament with n schools?

12n

Write the expression that represents the amount of money Anna earns from selling pies and cupcakes.

$10p + $2c Signup and view all the answers

What is the total amount Ben spent at the fair if he rode r rides?

$3r + $10 Signup and view all the answers

What does it mean to have the simplified form of an expression?

An equivalent expression that's easier to use than the original expression. Signup and view all the answers

The first step in the order of operations is to simplify inside any ______ or grouping symbols.

parentheses Signup and view all the answers

What is the first operation applied to the expression 2(x + 3) + 4(x - 1)?

Multiplication using the distributive property. Signup and view all the answers

What is the result of simplifying the expression 2(x + 3) + 4(x - 1)?

6x + 2 Signup and view all the answers

What is the first step in simplifying the expression 3(x + 2x) + 4(x + 1)?

Simplify inside the first parentheses. Signup and view all the answers

Study Notes

Writing Algebraic Expressions

Identify unknown values in real-world situations and assign variables.
Determine necessary operations to accurately describe the situation.

Coefficients, Variables, and Constants

Expression: -13x + 45
- Variable: x
- Coefficient: -13
- Constant: 45
Expression: 12 - y
- Variable: y
- Coefficient: -1
- Constant: 12
Expression: 2y + 3x - 6
- Variables: x, y
- Coefficients: 2, 3
- Constant: -6
Expression: 24 - 56m + 103
- Variable: m
- Coefficient: -56
- Constants: 24, 103
Expression: 3.25 + 0.5p
- Variable: p
- Coefficient: 0.5
- Constant: 3.25

Total Number of Runners

Unknown value for number of schools competing: n.
Total runners expression: 12n (12 runners per school).

Earnings from Bake Sale

Variables for unknowns: p (pies sold), c (cupcakes sold).
Earnings from pies: $10p; from cupcakes: $2c.
Total earnings expression: $10p + $2c.

Expenses at the Fair

Variable for rides: r.
Cost for rides: $3r; entrance fee is $10.
Total spending expression: $3r + $10.

Simplifying Expressions

Simplification results in equivalent expressions that are often shorter and easier to use.
May involve combining like terms and applying the distributive property.
Example simplification: 2(x+3) + 4(x-1) requires distributive property and combining like terms.

Order of Operations

Step 1: Simplify inside parentheses.
Step 2: Evaluate exponents.
Step 3: Perform multiplication and division from left to right.
Step 4: Perform addition and subtraction from left to right.

Example of Expression Simplification

Example: Simplify 2(x + 3) + 4(x - 1).
- Apply distributive rule: 2x + 6 + 4x - 4.
- Combine like terms: (2 + 4)x + 2 leads to 6x + 2.

Another Example of Simplification

Example: Simplify 3(x + 2x) + 4(x + 1).
- Simplify first parentheses: 3(3x) + 4(x + 1).
- Apply distributive rule: 9x + 4x + 4.

Description

Test your understanding of algebraic expressions with our flashcards on identifying coefficients, variables, and constants. Learn how to assign variables to real-world situations and the operations needed to create expressions. Perfect for Algebra 2 students preparing for exams.