Algebra-1B Key Terms Quiz

Number Types

• Perfect squares: Numbers with integer square roots.
• Rational numbers: Can be expressed as a fraction of two integers; in decimal form, they are either terminating or repeating.
• Natural numbers: The set of counting numbers, excluding zero.
• Whole numbers: Non-negative integers, including zero.
• Integers: Whole numbers that include negative values.
• Irrational numbers: Cannot be expressed as a ratio of integers; their decimal representation is nonterminating and nonrepeating.
• Real numbers: Comprised of both rational and irrational numbers.

Algebraic Concepts

• Inequality: Compares two expressions with inequality symbols; graphically represented by open or closed circles.
• Distributive property: Describes how to remove parentheses in expressions: a(b + c) = ab + ac.
• Constant: A term without a variable factor.
• Coefficient: The numerical factor in a term with a variable.
• Term: May be a number, variable, or a combination of both.
• Like terms: Terms with the same variable and exponent, which can be combined.
• Unlike terms: Terms with different variables or exponents that cannot be combined.

Solutions in Equations

• Solution of an equation (one variable): Values that satisfy the equation.
• Solution of an equation (two variables): Ordered pairs that make the equation true.
• Radical: Another term for square root.

Geometry

• Parallel lines: Lines that never intersect and remain equidistant.
• Perpendicular lines: Lines that intersect at a 90-degree angle.
• Slope: The rate of change of a line; calculated as (y2 - y1) / (x2 - x1).

Equation Forms

• Point-slope form: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point.
• Slope-intercept form: y = mx + b, with m as the slope and b as the y-intercept.
• Standard form: Ax + By = C; useful for finding intercepts.

Systems of Equations

• System of linear equations: Two or more equations combined, with potential solutions as intersections of their graphs.
• Common methods to solve:
  • Graphing: Plot the equations to find can intersect points.
  • Substitution: Solve one equation for a variable and substitute into the other.
  • Elimination: Manipulate equations to eliminate one variable.

Exponents

• Exponent basics: Notation indicating repeated multiplication; rules for multiplying, dividing, and raising powers summarized:
  • Multiplying: Add exponents.
  • Dividing: Subtract exponents.
  • Raising a power to a power: Multiply exponents.
• An exponent of zero equals one, regardless of the base.

Factoring and Polynomials

• Polynomial: An expression with one or more terms.
• Factoring techniques:
  • Greatest common factor (GCF): Identifying and factoring out shared factors.
  • Difference of squares: a² - b² = (a + b)(a - b).
  • Factoring quadratics: Rewrite quadratic as (x - r)(x - s), finding roots.

Quadratic Functions

• Quadratic equation: y = ax² + bx + c; graphed as a parabola.
• Vertex: The highest or lowest point on the parabola, calculated as -(b/2a).
• Roots: Number of solutions varies: two roots for two intercepts, one for a single intercept, none for no intercepts.

Solving Quadratic Equations

• Methods:
  • Graphing: Find x-intercepts where the graph crosses the x-axis.
  • Factoring: Create two binomials and set each equal to zero.
  • Completing the square: Transform the equation into a perfect square trinomial.
  • Quadratic formula: Always applicable for finding solutions.

Additional Points

• Accounts for the behavior of exponents with positive/negative bases and the impact of zero and negative exponents.
• Proper notation involves using the "±" sign for roots when applicable.