Questions and Answers
What is a variable?
What is a constant?
A number that has a set value and is not next to a variable.
What is a coefficient?
A number that is next to a variable.
What does distribution refer to in mathematics?
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What does combining like terms mean?
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What is the independent variable represented by in equations?
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What does Y represent in functions?
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An inequality is a mathematical sentence that contains less than or greater than.
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What does 'greater than' signify in a graph?
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What does 'less than or equal to' indicate?
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What is the definition of a function?
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What is a linear function?
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What is the quadratic function?
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What is the Quadratic Formula?
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What does radical mean in mathematics?
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What is the meaning of 'tangent'?
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Study Notes
Algebra Concepts
- Variables: Represent numbers that change, commonly denoted as x, y, or other letters.
- Constants: Fixed values, not associated with variables.
- Coefficients: Numbers directly adjacent to variables, indicating multiplication.
Operations and Functions
- Distribution: A process where a number outside parentheses multiplies all terms within the parentheses.
- Combining Like Terms: The method of simplifying algebraic expressions by grouping similar terms.
- Independent Variable (X): Represents inputs in equations; can vary independently.
- Dependent Variable (Y): Represents outputs in equations; changes in response to the independent variable.
Inequalities and Relations
- Inequality: A statement involving less than, greater than, or equivalent expressions.
- Greater Than and Less Than: Represented with open circles on a number line.
- Greater Than or Equal To & Less Than or Equal To: Indicated with closed circles, showing inclusive limits.
Graphing and Functions
- Relation: Composed of ordered pairs; includes an independent and a dependent variable.
- Function: A special relation where each X value corresponds to only one Y value, tested using the vertical line test.
- Ordered Pair: Coordinates used to designate points in a coordinate plane.
Types of Functions
- Linear Function: Graph results in a straight line, expressed as Y = MX + B.
- Quadratic Function: Formed as y = x², typically creating a parabolic shape.
- Solutions to a Quadratic: Referred to as roots, x-intercepts, or zeros.
Systems and Equations
- System of Linear Equations: Involves two or more linear functions that may have zero, one, or infinitely many solutions.
Special Terms in Algebra
- Radical: Equivalent to taking the square root of a number.
- Axis of Symmetry: A line that divides a shape or graph into two mirrored halves.
- Vertex: The point at which a quadratic function achieves its maximum or minimum value.
Advanced Concepts
- Binomial Theorem: Provides the coefficients of terms in polynomial expansions.
- Quadratic Formula: Used for solving quadratic equations, represented as b ± √(b² - 4ac) / 2a.
- FOIL Method: A technique for multiplying two binomials, standing for First, Outer, Inner, Last.
- Difference of Squares: An algebraic identity defined as b² = (a - b)(a + b).
Trigonometric Functions
- Imaginary Number: Indicated by a cursive i, used within square root expressions.
- Tangent: Defined as opposite side over adjacent side in a right triangle.
- Cosine: Ratio of the adjacent side over the hypotenuse.
- Sine: Ratio of the opposite side over the hypotenuse.
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Description
Test your knowledge of key algebraic concepts with these flashcards designed for ABEKA Algebra 2. Each card contains a definition and example of important terms such as variables, constants, coefficients, and distribution. Perfect for reinforcing your understanding before exams.