FLVS Algebra 1 Module 1 Flashcards

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is an algebraic expression?

A mathematical sentence containing numbers, variables, constants and operations. (correct)

An equation with an equal sign.

A single constant.

A number with no variables.

What are like terms?

Like terms are terms that have the same variables and powers but can have different coefficients.

What is a variable?

A letter used to stand for a number.

What are operations in mathematics?

Operations include parenthesis, exponents, multiplication, division, addition, and subtraction. Signup and view all the answers

What are terms in an algebraic expression?

Terms are things that are added or subtracted in an expression. Signup and view all the answers

What are factors?

Factors are things being multiplied in each term. Signup and view all the answers

What are coefficients?

Coefficients are the numerical parts of terms that have variables. Signup and view all the answers

What is a constant in an expression?

A constant is a term in the expression that contains only numbers. Signup and view all the answers

What is a base in exponentiation?

The base is the quantity being raised to a power. Signup and view all the answers

What is an exponent?

An exponent is the number of times the base is multiplied by itself. Signup and view all the answers

When simplifying expressions, you should follow the order of operations.

True Signup and view all the answers

You can substitute the value of a variable in an algebraic equation.

True Signup and view all the answers

What parts make up an algebraic expression?

Numbers, variables, and operations. Signup and view all the answers

How can algebraic expressions be rewritten?

By simplifying them using mathematical operations. Signup and view all the answers

How do you evaluate algebraic expressions using substitution?

By substituting known values for variables and performing operations. Signup and view all the answers

How are algebraic expressions created from words and phrases?

By breaking them into pieces and translating the key terms into mathematical symbols. Signup and view all the answers

How are algebraic expressions interpreted in context?

By using the WHAT acronym to identify known values, key terms, and to translate them. Signup and view all the answers

What is the process to solve equations with variables on both sides?

Simplify and get the variable on one side. Signup and view all the answers

What are the steps used to solve a one-variable equation?

<ol> <li>Simplify each side, 2. Use properties to move variable terms, 3. Multiply/divide, 4. Check your answer.</li> </ol> Signup and view all the answers

How do you solve equations that contain fractions and decimal numbers?

Multiply by the least common denominator (LCD). Signup and view all the answers

What determines if a one-variable equation has more than one solution?

They can have infinite solutions if both sides are equal. Signup and view all the answers

What is a constraint in mathematics?

A condition set in a situation, often expressed in a mathematical statement. Signup and view all the answers

How are one-variable equations created for real-world questions?

Using the SELFIE framework to identify important information and unknowns. Signup and view all the answers

What does it mean when solutions are interpreted as viable or nonviable?

Viable solutions are possible, while nonviable solutions are impossible. Signup and view all the answers

What is an inequality?

A problem with many solutions that either exceed or are less than a variable's value. Signup and view all the answers

What happens when you multiply or divide an inequality by a negative number?

False Signup and view all the answers

What should you remember when solving word problems?

Use the SELFIE method to guide the problem-solving process. Signup and view all the answers

How can you solve inequalities in one-variable?

Start with the SELFIE method and remember to flip the symbol if dividing by a negative number. Signup and view all the answers

How can you create inequalities in one-variable?

Use the SELFIE method to identify unknowns and set up the equations. Signup and view all the answers

What do solutions for compound inequalities look like?

Solutions may include 'and' or 'or'. Signup and view all the answers

How can you solve compound inequalities and one-variable equations?

By using 'and' for conjunctions. Signup and view all the answers

What is a conjunction?

'And' is a conjunction in logic. Signup and view all the answers

What is a disjunction?

'Or' is a disjunction in logic. Signup and view all the answers

How are absolute value inequalities rewritten as compound inequalities?

<ol> <li>Drop absolute value bars for the first inequality. 2. Flip the symbol for the second. 3. Insert 'and' or 'or' between them.</li> </ol> Signup and view all the answers

How are one-variable compound inequalities created to model constraints?

Use the SELFIE method, paying attention to words like 'between' and 'within'. Signup and view all the answers

How is rearranging formulas similar to solving equations?

You can manipulate any equation as long as you keep it balanced. Signup and view all the answers

How are units of measurement chosen in formulas?

Small units for small measurements and large units for large measurements. Signup and view all the answers

How are literal equations rearranged with coefficients represented by letters?

You must reverse the order of operations to solve for the desired variable. Signup and view all the answers

How do you solve a literal equation for a specific variable?

Solve the formula for the specific variable. Signup and view all the answers

How do you solve problems that involve converting units of measure?

Convert using the same units in the numerator and denominator. Signup and view all the answers

Study Notes

Algebraic Expressions

Algebraic expressions consist of numbers, variables (like x, y), constants, and operations (addition, subtraction, etc.).
They lack an equal sign and can be formed from verbal phrases, translating language into mathematical symbols.
Example: The expression 3x + 2 translates to “three times x plus two.”

Like Terms

Like terms share identical variables and powers but may have different coefficients, allowing for simplification in expressions.

Variables and Constants

A variable is represented by a letter (e.g., x) and stands in for unknown numbers.
Constants are numerical terms in an expression without variables.

Operations and Terms

Fundamental operations include parentheses, exponents, multiplication, division, addition, and subtraction, often remembered by the acronym PEMDAS.
Terms are components being added or subtracted in an expression.

Factors and Coefficients

Factors are quantities being multiplied within terms; for instance, in 7xy, both 7 and xy are factors.
Coefficients are numeric parts of variable terms. For example, in 4x, 4 is the coefficient.

Exponents and Bases

The base is the number being raised in an expression using exponents, while the exponent indicates how many times to multiply the base.
In the term eight squared, 8 is the base and 2 is the exponent.

Simplifying and Evaluating Expressions

Simplification adheres to order of operations (PEMDAS), working left to right.
Substituting known variable values into expressions allows for evaluation and checking of answers.

Creating and Interpreting Expressions

Algebraic expressions can be formulated from words by following translation techniques and using key acronyms like WHAT for context.
The SELFIE method is effective for problem-solving: Search for information, Express unknowns, Look for equal quantities, Find solutions, Interpret, and Explain answers.

One-Variable Equations

Equations can have variables on both sides; simplification is key to isolate the variable.
Solutions may vary: there can be infinite solutions (e.g., 3 = 3) or no solution (e.g., 2x - 6 = 2).
The process for solving involves simplification, applying mathematical properties, and checking answers for correctness.

Constraints and Inequality

Constraints specify conditions in math problems, much like those employed in real-world scenarios.
Inequalities describe a range of solutions using terms like "greater than" and "less than."
When multiplying or dividing by a negative in inequalities, remember to flip the inequality symbol.

Compound Inequalities

Solutions for compound inequalities are indicated by "and" or "or" based on the conditions set.
You can model real-world situations using compound inequalities by recognizing words that signify ranges.

Formulas and Literal Equations

Rearranging formulas adheres to maintaining balance, similar to solving equations.
Choosing appropriate units is crucial; use smaller units for small measurements and larger ones for extensive measurements.
Converting units requires consistent units in both the numerator and denominator for accurate calculations.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

Explore essential concepts in Algebra 1 Module 1 through these flashcards. Learn key definitions such as algebraic expressions and like terms, and enhance your mathematical understanding. Perfect for students preparing for exams or needing a quick review.