Algebra 2 Regents Flashcards

Questions and Answers

What is a sequence?

An ordered list of numbers, formally defined as a function with the set of positive integers as its domain.

What does f(1) or a₁ represent?

Common difference

2nd term

3rd term

1st term (correct)

What is the previous term in sequences?

The term that comes before the current term in a sequence.

What are recursive formulas?

Formulas where terms of a sequence are found by performing operations on previous terms. Signup and view all the answers

What are explicit formulas?

Formulas where terms of a sequence are found using the term's index (position). Signup and view all the answers

What is the common difference (d) in sequences?

The difference between any two consecutive terms in an arithmetic sequence. Signup and view all the answers

What is the common ratio (r) in sequences?

The ratio between any two consecutive terms in a geometric sequence. Signup and view all the answers

What is the recursive formula for an arithmetic sequence?

The formula that defines the terms of an arithmetic sequence in terms of previous terms. Signup and view all the answers

What is the explicit formula for an arithmetic sequence?

The formula that allows direct calculation of the n-th term based on its index. Signup and view all the answers

What is the recursive formula for a geometric sequence?

The formula that defines the terms of a geometric sequence in terms of previous terms. Signup and view all the answers

What is the explicit formula for a geometric sequence?

The formula that allows direct calculation of the n-th term based on its index. Signup and view all the answers

What is a geometric sequence?

A sequence based on constant multiplying to get the next term. Signup and view all the answers

What is an arithmetic sequence?

A sequence based on constant addition to get the next term. Signup and view all the answers

What does summation (Sigma) notation represent?

It represents the sum of the terms of a sequence. Signup and view all the answers

What is a series?

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

What is the horizontal asymptote?

A horizontal line that the graph approaches. Signup and view all the answers

What is the domain in mathematics?

The set of all inputs (x's) for a function. Signup and view all the answers

What is the range in mathematics?

The set of all outputs (y's) for a function. Signup and view all the answers

What is the basic form of an exponential function?

Where a is the y-intercept and b is the base (multiplier). Signup and view all the answers

What characterizes a decreasing exponential function?

When $0 Signup and view all the answers

What characterizes an increasing exponential function?

When $b > 1$. Signup and view all the answers

What is exponential regression?

Fitting data to an exponential function. Signup and view all the answers

How do you perform an exponential regression on the TI-Nspire?

On the scatter plot page: menu, 4, 6, 8. Signup and view all the answers

What is the exponent law for $(x²)(x³)$?

It simplifies to $x⁵$. Signup and view all the answers

What is the exponent law for $x⁸ ÷ x⁵$?

It simplifies to $x³$. Signup and view all the answers

What is the exponent law for $4^{-2}$?

$1/16$. Signup and view all the answers

What does $5^0$ equal?

<ol> <li></li> </ol> Signup and view all the answers

What is the exponent law for $(x³)⁵$?

$x^{15}$. Signup and view all the answers

What is the exponent law for $(2xy²)³$?

$8x³y^6$. Signup and view all the answers

What is the exponent law for $(3/x⁴)³$?

$27/x^{12}$. Signup and view all the answers

What is $25^{1/2}$?

<ol start="5"> <li></li> </ol> Signup and view all the answers

What is $4^{3/2}$?

<ol start="8"> <li></li> </ol> Signup and view all the answers

What is a vertical asymptote?

A vertical line that the graph approaches, formed when a function is undefined. Signup and view all the answers

What is the Exponential Growth and Decay Model?

A mathematical model that describes how quantities grow or decrease exponentially over time. Signup and view all the answers

How do you solve an exponential equation using logs?

By applying logarithms to both sides of the equation. Signup and view all the answers

What is the Product Log Law?

A law that states $log(a imes b) = log(a) + log(b)$. Signup and view all the answers

What is the Quotient Log Law?

A law that states $log(a ÷ b) = log(a) - log(b)$. Signup and view all the answers

What is the Power Log Law?

A law that states $log(a^b) = b imes log(a)$. Signup and view all the answers

What characterizes an exponential function graph?

It shows rapid growth or decay depending on the base. Signup and view all the answers

What characterizes a logarithmic function graph?

It shows the inverse relationship of exponential functions, gradually increasing. Signup and view all the answers

What are inverse functions?

Functions that switch x and y coordinates, symmetric with the line y = x. Signup and view all the answers

What is a common log?

A logarithm with base 10, represented as $y = log(x)$. Signup and view all the answers

What is a natural log?

A logarithm with base e, represented as $y = ln(x)$. Signup and view all the answers

What is the compound interest formula?

A formula used to calculate the amount of interest earned or paid on a principal over time. Signup and view all the answers

What is the continuous compound interest formula?

A formula that calculates interest continuously over time. Signup and view all the answers

What is the half-life formula?

A formula to determine the time it takes for a substance to reduce to half its initial amount. Signup and view all the answers

What is the method of common bases?

A method that involves finding a common base, rewriting expressions, simplifying using power laws, and solving for exponents. Signup and view all the answers

What are trig facts (unit circle)?

Important relationships and values about angles and the unit circle. Signup and view all the answers

What is the equation of the unit circle?

The equation is $x^2 + y^2 = 1$, with center (0, 0) and radius = 1. Signup and view all the answers

What is sin(θ) in the unit circle?

The y-coordinate. Signup and view all the answers

What is cos(θ) in the unit circle?

The x-coordinate. Signup and view all the answers

What is a reference angle?

The acute angle formed by the terminal side of an angle in standard position and the x-axis. Signup and view all the answers

Study Notes

Sequences and Series

A sequence is an ordered list of numbers, defined formally as a function with positive integers as its domain.
The first term in a sequence is denoted as f(1) or a₁.
Recursive formulas derive terms by performing operations on previous terms.
Explicit formulas derive terms using the term's index or position in the sequence.
The common difference (d) is the difference between any two consecutive terms in an arithmetic sequence.
The common ratio (r) is the ratio between any two consecutive terms in a geometric sequence.

Arithmetic and Geometric Sequences

An arithmetic sequence is characterized by constant addition to obtain the next term.
A geometric sequence utilizes a constant multiplication pattern to find the next term.
Recursive formulas for arithmetic and geometric sequences are used but need to be specified.
Explicit formulas for both types of sequences must be defined for full understanding.

Summations and Series

Summation (Sigma) notation represents the sum of a sequence's terms.
A series is defined as the sum of the terms of a sequence.
Arithmetic series and geometric series formulas provide methods to calculate these sums.

Exponential Functions

Basic exponential function form includes a as the y-intercept and b as the base (multiplier).
Decreasing exponential functions occur when 0 < b < 1.
Increasing exponential functions occur when b > 1.
Exponential regression fits data to an exponential function.

Exponent Laws

Exponent Law 1: (x²)(x³) = x⁵ demonstrates the product of powers.
Exponent Law 2: x⁸÷x⁵ = x³ illustrates the quotient of powers.
Negative exponents transform into reciprocal forms: 4⁻² = 1/16.
Exponent Law 4 states 5⁰ = 1.
Exponent Law 5: (x³)⁵ = x¹⁵ shows power of a power rule.
Exponent Law 6: (2xy²)³ expands to 8x³y⁶ through multiplication.
Exponent Law 7 simplifies fractions with exponents: (3/x⁴)³ = 27/x¹².
Square roots represented as exponents: 25 ^ ½ = 5.
Exponent Law 9: 4^ 3/2 simplifies to 8 by rewriting as (√4)³.

Asymptotes

A horizontal asymptote is a horizontal line that a graph approaches at infinity.
A vertical asymptote is a vertical line that a graph approaches where the function is undefined.

Logarithms and Inverse Functions

Inverse functions switch x and y, reflecting symmetrically across the line y = x.
Common logs have base 10 (y = log(x)), while natural logs use base e (y = ln(x)).

Interest and Growth Models

Formulas for compound interest and continuous compound interest provide methods for financial calculations.
The half-life formula is used in decay models.

Additional Concepts

The equation of the unit circle is x² + y² = 1, centered at (0, 0) with a radius of 1.
In the unit circle, sin(θ) corresponds to the y-coordinate, while cos(θ) corresponds to the x-coordinate.

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Description

This quiz consists of flashcards designed to enhance your understanding of key concepts in Algebra 2, particularly focusing on sequences, formulas, and their definitions. Dive into the definitions of terms like 'sequence', 'recursive formulas', and 'explicit formulas' to reinforce your knowledge. Perfect for preparing for the Algebra 2 Regents exam.