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Questions and Answers
What is algebra?
Algebra is based on the operations of arithmetic and on the concept of an unknown quantity, or variable.
How do you multiply an algebraic equation by another algebraic equation?
Multiply each term in one equation by each term in the other equation. E.g. FOIL - (x + 1)(x + 2) = x^2 + 3x + 2.
What is a term in algebra?
A term is either a constant, a variable, or the product of one or more constants and/or variables.
What is a constant?
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What is an algebraic expression?
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What types of triangles does the Pythagorean Theorem apply to?
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What is a polynomial?
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What are solutions (roots) in an algebraic equation?
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What are equivalent equations?
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What is a linear equation?
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What is a linear equation with one unknown?
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What is a linear equation with two unknowns?
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How do you solve a linear equation with one unknown?
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What is the difference between fractions and ratios?
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How do you solve two linear equations with two unknowns using substitution?
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What is a coefficient?
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How do you solve two linear equations with two unknowns using elimination?
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Why does setting equations equal to zero help in finding solutions?
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Study Notes
Algebra Fundamentals
- Algebra combines arithmetic operations with the concept of variables, representing unknown quantities (e.g. 3x² + 3x + 3).
- Numerical expressions symbolize known quantities called constants.
Operations in Algebra
- Multiplication of algebraic equations involves distributing each term in one equation by each term in the other (e.g. FOIL method).
- An algebraic expression consists of variables, constants, and arithmetic operations.
Components of Algebra
- A term can be a constant, a variable, or a product of constants and/or variables, functioning as a single input in functions.
- A polynomial is characterized by:
- Being a sum of terms,
- Having nonnegative integer powers for variables,
- Possibly containing multiple variables or a single term (monomial).
Equation Characteristics
- Solutions or roots of an equation are value assignments to variables that satisfy the equation.
- Equivalent equations share the same solutions, maintain their integrity despite algebraic manipulation.
Linear Equations
- Linear equations feature linear polynomials, with variables having an exponent of 1.
- Types include:
- One unknown: involves isolating the variable to find its value.
- Two unknowns: consist of linear equations with two variables, solvable through substitution or elimination methods.
Solving Linear Equations
- Substitution method:
- Express one unknown in terms of another, substitute into the second equation, and solve for the unknown.
- Elimination method:
- Adjust equations to align coefficients of one variable; add or subtract to eliminate it and solve for the other.
Ratios and Fractions
- Fractions represent a part over a whole, while ratios compare parts against each other (e.g. part:part or part:whole).
Finding Solutions
- Setting equations to zero allows for determining inputs that satisfy the equation, essential for solving algebraic representations.
Studying That Suits You
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Description
Test your knowledge of basic algebra principles with these flashcards. Each card provides a definition or explanation about fundamental algebraic concepts. Perfect for students looking to strengthen their understanding of algebraic operations and equations.
