Honors Algebra 2 Final Exam Flashcards

Questions and Answers

What are natural numbers?

Positive integers and 0 (0, 1, 2, 3...)

Numbers that can be expressed as p/q where p and q are integers and q is not 0

Negative whole numbers, positive whole numbers, and zero (-2, -1, 0, 1, 2...)

Positive integers (1, 2, 3...) (correct)

What are whole numbers?

Negative whole numbers, positive whole numbers, and zero (-2, -1, 0, 1, 2...)

Positive integers (1, 2, 3...)

Positive integers and 0 (0, 1, 2, 3...) (correct)

Numbers that can be expressed as p/q where p and q are integers and q is not 0

What defines integers?

Positive integers (1, 2, 3...)

Positive integers and 0 (0, 1, 2, 3...)

Positive whole numbers, negative whole numbers, and zero (-2, -1, 0, 1, 2...) (correct)

Numbers whose decimal part does not terminate or repeat

What does a rational number look like?

p/q where p and q are integers and q is not 0 Signup and view all the answers

Identify an irrational number.

A number whose decimal part does not terminate or repeat Signup and view all the answers

What defines real numbers?

All rational and irrational numbers Signup and view all the answers

What does it mean if a system of equations is consistent and independent?

It has a unique solution. Signup and view all the answers

What is the purpose of the horizontal line test?

To determine if a function is invertible Signup and view all the answers

What does the vertical line test determine?

If a graph is a function Signup and view all the answers

What is the definition of an inconsistent system of equations?

It has no solution. Signup and view all the answers

What is an identity matrix?

A square matrix Signup and view all the answers

What is an augmented matrix?

Contains the coefficient matrix with an extra column for constants Signup and view all the answers

What does the zero-product property state?

If a product is zero, at least one factor must be zero. Signup and view all the answers

What is contained in the vertex form of a quadratic function?

y = a(x-h)^2 + k Signup and view all the answers

What is the standard form of a quadratic function?

y = ax^2 + bx + c Signup and view all the answers

What is the quadratic formula used for?

To find the roots of a quadratic equation Signup and view all the answers

What does the axis of symmetry represent?

The line that divides the parabola into two symmetrical halves Signup and view all the answers

What is the standard form of complex numbers?

a + bi Signup and view all the answers

What are imaginary numbers?

Numbers in which i = √-1 Signup and view all the answers

What is the conjugate of the complex number a + bi?

a - bi Signup and view all the answers

What characterizes an exponential expression?

The variable is the exponent Signup and view all the answers

What does 'log' represent?

The inverse of an exponent Signup and view all the answers

What are inverse functions?

Functions that are reflections over y = x Signup and view all the answers

What is the value of e approximately equal to?

2.718 Signup and view all the answers

What is the natural log?

The inverse function of a natural exponential function Signup and view all the answers

What is the inverse relationship between y = b^x and x = logb(y)?

logarithmic and exponential functions Signup and view all the answers

What does it mean for a degree of the numerator to be greater than the degree of the denominator?

Oblique Signup and view all the answers

What does it mean for the degree of the numerator to be equal to the degree of the denominator?

Horizontal Signup and view all the answers

What does it mean for the degree of the numerator to be less than the degree of the denominator?

Zero Signup and view all the answers

What are vertical asymptotes?

They occur at every number that is a zero of the denominator but not the numerator Signup and view all the answers

What is a hole in a graph?

Occurs at every number that is a zero of the numerator and denominator Signup and view all the answers

What defines a radical equation?

Contains at least one radical expression with a variable under the radical symbol Signup and view all the answers

What is a sequence?

An ordered list of numbers called terms Signup and view all the answers

What is a finite sequence?

A sequence with a last term Signup and view all the answers

What is an infinite sequence?

A sequence that continues without end Signup and view all the answers

What is an explicit formula?

A formula that defines the nth term of a sequence Signup and view all the answers

What is a recursive formula?

A formula based solely on previous terms Signup and view all the answers

What does a series indicate?

The sum of terms of a sequence Signup and view all the answers

What does summation notation represent?

A way to express a series using sigma Signup and view all the answers

What is an arithmetic sequence?

A sequence where each term differs by a set amount, d Signup and view all the answers

What is an arithmetic series?

An expression that indicates the sum of terms of an arithmetic sequence Signup and view all the answers

What is a geometric series?

The indicated sum of the terms of a geometric sequence Signup and view all the answers

What does it mean to converge?

As n values grow, the sum approaches a fixed number |r| < 1 Signup and view all the answers

What does it mean to diverge?

The sum does not approach a fixed number |r| ≥ 1 Signup and view all the answers

What is Pascal's Triangle used for?

Expanding polynomials Signup and view all the answers

Study Notes

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.

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Prepare for your Honors Algebra 2 final exam with these essential flashcards. Each card focuses on key mathematical terms and their definitions, ranging from natural numbers to irrational numbers. Use this resource to strengthen your understanding and improve your exam readiness.