Questions and Answers
What is a relation?
Set of ordered pairs
What are the coordinates of a point on the coordinate plane?
(x,y)
What is a coordinate plane?
A plane formed by 2 perpendicular lines called axes
What is a function?
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What does a Mapping Diagram represent?
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What is a Table in mathematics?
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What is the domain in a function?
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What is the range in a function?
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What is a variable?
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What is an independent variable?
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What is a dependent variable?
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What is the vertical line test?
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What does the slope represent?
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In the equation y = mx + b, 'm' stands for __________.
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In the equation y = mx + b, 'b' stands for __________.
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How do you combine like terms?
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What is the difference between a whole number and an integer?
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The slopes of parallel lines are different.
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What is the solution of a system of equations?
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What do you call a data point that does not fit in with the rest of the data?
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What is the maximum or minimum in a box and whisker plot?
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What is the geometric sequence?
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What is the arithmetic sequence?
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When multiplying fractions, you should __________.
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How do you convert an improper fraction to a mixed number?
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Study Notes
Algebraic Concepts and Definitions
- Relation: A set of ordered pairs.
- Ordered Pair: Represents coordinates of a point in the coordinate plane, denoted as (x, y).
- Coordinate Plane: Formed by two perpendicular lines called axes; x-axis (horizontal) and y-axis (vertical).
- Function: A specific relation where each x-value is linked to only one y-value; it must pass the vertical line test.
- Mapping Diagram: Visual representation where bubbles represent corresponding x-values and y-values.
Key Components
- Domain: The set of all possible x-values (inputs) in a function.
- Range: The set of all possible y-values (outputs) in a function.
- Variable: A letter or symbol representing a number; not a fixed number.
- Independent Variable: The input in a function, often represented as x; controlled by the user.
- Dependent Variable: The output in a function, represented as y; cannot be controlled by the user.
- Other Names: x can be referred to as domain, independent variable, or input; y can be known as range, dependent variable, or output.
Functions and Tests
- Vertical Line Test: A graphical method for determining if a relation is a function; a vertical line must intersect the graph at most once.
- Discrete Function: Data represented by individual points on a graph; cannot be broken down further.
- Examples of Functions: Linear functions, quadratic functions, and inverse functions.
Slope and Intercepts
- Slope (m): Indicates the steepness of a line; calculated as the change in y (rise) divided by the change in x (run).
- Y-intercept (b): The point where a line crosses the y-axis, represented as (0, y).
- Slope of Horizontal Line: Always equal to 0.
- Slope of Vertical Line: Undefined.
Equations and Inequalities
- Slope-Intercept Form: Represents a line as y = mx + b.
- Linear Inequality: Similar to linear equations but includes symbols like <, > for inequalities.
- System of Equations: Two or more equations graphed on the same plane; can have no solution, one solution, or infinitely many solutions.
Special Terms and Properties
- Factoring: Breaking down expressions into simpler factors.
- Like Terms: Terms in an expression that have the same variables raised to the same exponents.
- Combining Like Terms: Involves adding their coefficients.
- Associative, Distributive, and Commutative Properties: Rules governing operations in math.
Data and Statistics
- Mean (Average): Total of data points divided by the number of points.
- Median: Middle value when data is ordered; average of two middle values if needed.
- Mode: The most frequently occurring number in a data set.
- Range: Difference between the largest and smallest value in a data set.
Fraction and Decimal Operations
- Adding/Subtracting Fractions: Requires a common denominator.
- Multiplying Fractions: Multiply numerators together and denominators together, then simplify if possible.
- Dividing Fractions: Use the "Keep, Change, Flip" method.
- Converting Between Fractions and Decimals: Divide numerator by the denominator or recognize decimal places.
Graphs and Visuals
- Histograms: Bar graph showing frequency distribution across value ranges.
- Box and Whisker Plots: Visual representation showing median, quartiles, and potential outliers.
Miscellaneous Concepts
- Maximum/Minimum: Highest and lowest values in data representation like box plots.
- Percent Conversion: Understanding how to convert between decimal, fraction, and percentage forms.
- Perfect Squares: Results of integers multiplied by themselves. Examples include 1, 4, 9, 16, etc.
Final Notes
- Solving Proportions: Involves cross-multiplication.
- Radicals: Refers to square roots; methods of simplifying need careful attention to detail.
- Standard Form of a Line: Written as Ax + By = C; requires no fractions or decimals with A positive.
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Review essential algebra concepts with these flashcards. Each card includes a term related to relations, ordered pairs, the coordinate plane, and functions. Enhance your understanding and prepare effectively for the EOC exam!