Honors Algebra 2 Final Exam Flashcards

Natural Numbers

• Defined as positive integers: 1, 2, 3, ...

Whole Numbers

• Includes positive integers and zero: 0, 1, 2, 3, ...

Integers

• Comprises positive whole numbers, negative whole numbers, and zero: -2, -1, 0, 1, 2, ...

Rational Numbers

• Expressed in form p/q where p and q are integers, with q ≠ 0.

Irrational Numbers

• Numbers with decimal parts that do not terminate or repeat.

Real Numbers

• Encompasses all rational and irrational numbers.

Consistent and Independent Systems

• A system of equations with exactly one solution.

Horizontal Line Test

• A function is invertible if every horizontal line intersects its graph at most once.

Vertical Line Test

• A graph represents a function if every vertical line intersects it at no more than one point.

Consistent and Dependent Systems

• A system of equations with infinitely many solutions.

Inconsistent Systems

• A system of equations with no solution.

Identity Matrix

• Defined as a square matrix that acts as the multiplicative identity in matrix operations.

Augmented Matrix

• Used for solving systems of equations; contains the coefficient matrix along with an additional column for constant terms.

Zero-Product Property

• States that if pq = 0, then either p = 0 or q = 0.

Vertex Form

• A specific way to express quadratic functions, though not defined here.

X-Intercept Form

• Expressed as y = a(x - s)(x - t), where s and t are x-intercepts.

Standard Form

• Another expression for quadratic functions, currently undefined.

Quadratic Formula

• A method to find the roots of quadratic equations, details are not provided here.

Axis of Symmetry

• A vertical line that divides a parabola into two mirror-image halves, specifics are not noted here.

Complex Numbers

• Represented in standard form as a + bi, where a and b are real numbers.

Imaginary Numbers

• Defined by i = √-1, used to represent numbers that have no real solutions.

Conjugate

• The form a + bi becomes a - bi, used for simplifying complex expressions.

Exponential Expression

• Involves a fixed base with a variable exponent.

Logarithm

• Serves as the inverse operation to exponentiation.

Inverse Functions

• Two functions that reflect over the line y = x.

Euler’s Number (e)

• Approximately equal to 2.718, important in calculus and exponential growth.

Natural Logarithm

• The inverse function of natural exponential functions.

Inverse Relationship Between Exponential and Logarithmic Functions

• y = b^x is the inverse of x = logb(y).

Oblique Asymptote

• Arises when the degree of the numerator exceeds that of the denominator.

Horizontal Asymptote

• Occurs when the degree of the numerator equals that of the denominator.

Vertical Asymptote

• Found at values where the denominator equals zero, provided the numerator does not equal zero at those points.

Holes in Graphs

• Occur where both the numerator and denominator are zero, typically resolved by canceling factors.

Radical Equations

• Equations containing at least one radical expression with a variable under the radical.

Sequence

• An ordered set of numbers termed "terms".

Finite Sequence

• A sequence that has a definitive last term.

Infinite Sequence

• A sequence that continues indefinitely without termination.

Explicit Formula

• Provides a direct formula to calculate the nth term of a sequence.

Recursive Formula

• A formula relying on one or more preceding terms to generate subsequent terms.

Series

• Represents the sum of terms from a sequence.

Summation Notation

• Denoted by sigma (Σ), used to express series compactly.

Arithmetic Sequence

• A sequence where each term changes by a fixed amount, known as d.

Arithmetic Series

• The sum of terms in an arithmetic sequence.

Geometric Series

• The sum of terms in a geometric sequence.

Convergence

• Refers to a scenario where, as n approaches infinity, the sum approaches a fixed value, typically where |r| < 1.

Divergence

• When the sum fails to converge to a fixed number, occurring when |r| ≥ 1.

Pascal's Triangle

• A triangular array used for uncomplicated binomial expansion to a power.