Algebra 1 EOC Review Flashcards
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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?

<p>A special relation where each x-value is paired with only one y-value.</p> Signup and view all the answers

What does a Mapping Diagram represent?

<p>Bubbles that represent the x-values and the y-values.</p> Signup and view all the answers

What is a Table in mathematics?

<p>A way to represent ordered pairs.</p> Signup and view all the answers

What is the domain in a function?

<p>Set of all of the possible x-values.</p> Signup and view all the answers

What is the range in a function?

<p>Set of all the possible y-values.</p> Signup and view all the answers

What is a variable?

<p>Not a number; a letter or symbol that stands for a number.</p> Signup and view all the answers

What is an independent variable?

<p>The input or cause in a situation or problem.</p> Signup and view all the answers

What is a dependent variable?

<p>The output or result in a situation or problem.</p> Signup and view all the answers

What is the vertical line test?

<p>A relation is a function if a vertical line drawn through the graph touches the graph only once.</p> Signup and view all the answers

What does the slope represent?

<p>The steepness of a line.</p> Signup and view all the answers

In the equation y = mx + b, 'm' stands for __________.

<p>slope</p> Signup and view all the answers

In the equation y = mx + b, 'b' stands for __________.

<p>the y-intercept</p> Signup and view all the answers

How do you combine like terms?

<p>Add their coefficients.</p> Signup and view all the answers

What is the difference between a whole number and an integer?

<p>Whole numbers start at 0 while integers include all positive and negative numbers.</p> Signup and view all the answers

The slopes of parallel lines are different.

<p>False</p> Signup and view all the answers

What is the solution of a system of equations?

<p>Where the lines touch or cross.</p> Signup and view all the answers

What do you call a data point that does not fit in with the rest of the data?

<p>Outlier</p> Signup and view all the answers

What is the maximum or minimum in a box and whisker plot?

<p>The largest and smallest numbers shown.</p> Signup and view all the answers

What is the geometric sequence?

<p>A pattern in which you multiply or divide by a common number.</p> Signup and view all the answers

What is the arithmetic sequence?

<p>A pattern in which you add a number each time.</p> Signup and view all the answers

When multiplying fractions, you should __________.

<p>Cancel or reduce if possible, then multiply straight across.</p> Signup and view all the answers

How do you convert an improper fraction to a mixed number?

<p>Determine how many times the denominator goes into the numerator, then note the remainder.</p> Signup and view all the answers

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!

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