Questions and Answers
What is the highest power of the variable in a quadratic equation?
What is the purpose of graphing an equation on a coordinate plane?
What is an example of an inequality?
What is the method of solving equations by finding common factors?
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What is the notation for a function?
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What is the definition of a polynomial?
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What is the method of solving systems of equations by replacing one equation with the expression from another equation?
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What is the purpose of variables in algebra?
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Study Notes
Algebra
What is Algebra?
- A branch of mathematics that deals with the study of variables and their relationships
- Uses symbols, equations, and formulas to solve problems
Key Concepts:
Variables and Expressions
- Variables: letters or symbols that represent unknown values
- Expressions: combinations of variables, constants, and mathematical operations
- Example: 2x + 5 is an expression, where x is a variable and 2 and 5 are constants
Equations and Inequalities
- Equations: statements that two expressions are equal
- Inequalities: statements that one expression is greater than, less than, or equal to another
- Examples:
- Equation: 2x + 3 = 5
- Inequality: 2x - 4 > 3
Solving Equations and Inequalities
- Linear equations: equations in which the highest power of the variable is 1
- Quadratic equations: equations in which the highest power of the variable is 2
- Methods for solving equations:
- Addition/Subtraction
- Multiplication/Division
- Factoring
- Quadratic Formula
Graphing
- Graphing equations on a coordinate plane
- x-axis: horizontal axis
- y-axis: vertical axis
- Points on the graph represent solutions to the equation
- Example: graphing the equation y = 2x - 3
Functions
- Relations between a set of inputs (domain) and a set of possible outputs (range)
- Notation: f(x) = output
- Example: f(x) = 2x + 1, where x is the input and 2x + 1 is the output
Systems of Equations
- Sets of two or more equations that must be true at the same time
- Methods for solving systems:
- Substitution
- Elimination
- Graphing
Polynomials
- Expressions consisting of variables and coefficients combined using only addition, subtraction, and multiplication
- Examples: x^2 + 3x - 4, 2x^3 - 5x^2 + x - 1
Algebra
Definition and Scope
- Algebra is a branch of mathematics that studies variables and their relationships
- It uses symbols, equations, and formulas to solve problems
Variables and Expressions
- Variables represent unknown values and are denoted by letters or symbols
- Expressions are combinations of variables, constants, and mathematical operations
- Example: 2x + 5 is an expression, where x is a variable and 2 and 5 are constants
Equations and Inequalities
- Equations are statements that two expressions are equal
- Inequalities are statements that one expression is greater than, less than, or equal to another
- Examples:
- Equation: 2x + 3 = 5
- Inequality: 2x - 4 > 3
Solving Equations and Inequalities
- Linear equations have the highest power of the variable as 1
- Quadratic equations have the highest power of the variable as 2
- Methods for solving equations include:
- Addition/Subtraction
- Multiplication/Division
- Factoring
- Quadratic Formula
Graphing
- Graphing equations on a coordinate plane with x-axis (horizontal) and y-axis (vertical)
- Points on the graph represent solutions to the equation
- Example: graphing the equation y = 2x - 3
Functions
- Relations between a set of inputs (domain) and a set of possible outputs (range)
- Notation: f(x) = output
- Example: f(x) = 2x + 1, where x is the input and 2x + 1 is the output
Systems of Equations
- Sets of two or more equations that must be true at the same time
- Methods for solving systems include:
- Substitution
- Elimination
- Graphing
Polynomials
- Expressions consisting of variables and coefficients combined using addition, subtraction, and multiplication
- Examples: x^2 + 3x - 4, 2x^3 - 5x^2 + x - 1
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Description
Get familiar with the fundamentals of algebra, including variables, expressions, equations, and inequalities. Learn how to solve problems using symbols, equations, and formulas.