Questions and Answers
What does the equation $Y=mx+b$ represent?
What is the formula for slope?
m = (y2 - y1) / (x2 - x1)
A negative slope means the line goes uphill when viewed from left to right.
False
What does 'direct variation' imply?
Signup and view all the answers
What does 'method of constant differences' allow you to determine?
Signup and view all the answers
What are the four quadrants of the Cartesian plane?
Signup and view all the answers
A ____ is the line that captures the general trend of a group of data points.
Signup and view all the answers
The sum of angles in a triangle is 90 degrees.
Signup and view all the answers
What are complementary angles?
Signup and view all the answers
How do you define 'exponential growth'?
Signup and view all the answers
What is the formula for a quadratic equation?
Signup and view all the answers
What does the axis of symmetry of a parabola represent?
Signup and view all the answers
Probability is the likelihood that a particular ____ will occur.
Signup and view all the answers
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.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
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!
