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?
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What does 'method of constant differences' allow you to determine?
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What are the four quadrants of the Cartesian plane?
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A ____ is the line that captures the general trend of a group of data points.
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The sum of angles in a triangle is 90 degrees.
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What are complementary angles?
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How do you define 'exponential growth'?
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What is the formula for a quadratic equation?
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What does the axis of symmetry of a parabola represent?
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Probability is the likelihood that a particular ____ will occur.
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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
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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.
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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!