Algebra 1 Honors EOC Review Flashcards

Study Notes

Linear Equations

Slope-Intercept Form: Y=mx+b, where m represents the slope and b is the y-intercept.
Slope: Measures steepness, calculated as "rise over run" or m=(y2-y1)/(x2-x1).
Negative Slope: Indicates a downward slope from left to right; one variable increases while the other decreases.
Direct Variation: A proportional relationship where the line passes through the origin; eq. examples include y=2x.

Geometric Concepts

Cartesian Plane: Divided into four quadrants—Quadrant 1 (upper right), Quadrant 2 (upper left), Quadrant 3 (bottom left), Quadrant 4 (bottom right), noted counter-clockwise.
Triangle Angles: The sum of internal angles in a triangle is always 180°.
Circle Angles: A full circle measures 360°.
Angles: Include types such as supplementary, complementary, vertical, alternate interior, and corresponding angles.

Exponents and Scientific Notation

Laws of Exponents:
- Product Law: For same bases, multiply by adding exponents.
- Quotient Law: For same bases, divide by subtracting exponents.
- Power Law: Emergences when raising an exponent to another exponent, e.g. (a³)⁵ = a¹⁵.
Negative Bases: Even exponents yield a positive outcome; odd exponents yield a negative outcome.
Scientific Notation: Expresses values as a product of a number (1 to 10) and a power of 10.

Algebraic Operations and Properties

Combining Like Terms: Requires both variable and exponent to be the same for addition or subtraction.
Distribution Property: External terms apply to all elements within parentheses.
Foil Method: Technique for multiplying two binomials: First, Outside, Inside, Last.

Probability Concepts

Sample Space: Represents all possible outcomes, often illustrated as lists or tree diagrams.
Probability: Likelihood of an event occurring, represented as a fraction, decimal, or percentage between 0%-100%.
Compound Probability: The product of individual probabilities for independent events.
Permutations: Specific arrangements of values, using factorial notation e.g., 5! = 5×4×3×2×1.

Quadratic Functions

Quadratic Equation Form: General form is Ax² + Bx + C, where A cannot be zero.
Parabola: The graph shape of a quadratic equation.
Vertex: The highest or lowest point of a parabola located at the axis of symmetry, calculated by -b/2a.
Axis of Symmetry: Divides the parabola into two mirror-image halves.

Systems of Equations

Graphing Method: Finding solutions by graphing both equations; solution is the intersection point.
Substitution Method: Solving one equation for a variable and substituting it into the other equation.
Elimination Method: Adding or subtracting entire equations to eliminate a variable, making it easier to find solutions.

Symmetry and Transformations

Line of Symmetry: A line that divides a figure into two mirrored parts.
Rotation Symmetry: A figure that can be rotated around a point to match its original position, defined by the smallest angle of rotation.
Translation: Movement of a figure without rotation; represented with vectors indicating direction and distance.

Miscellaneous

Percentage Calculations: Solve using proportions, ensuring that the number '100' goes on the lower left in proportion problems.
Percent Change: Calculated by dividing the change amount by the original value; consecutive percentage changes require careful calculation as they do not simply accumulate.
Fundamental Counting Principle: Total number of options derived by multiplying the number of choices in each category.

Description

This set of flashcards is designed to help students review key concepts in Algebra 1, specifically for the end-of-course (EOC) assessment. Each card includes critical definitions and formulas such as the slope-intercept form and the concept of slope. Perfect for quick revision before exams!