Algebra 2 Regents Exam Review

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is a sequence?

An ordered list of numbers.

What does f(1) or a₁ represent?

1st term

What is a previous term in a sequence?

Previous term

What are recursive formulas?

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

What are explicit formulas?

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

What does 'd' represent in sequences?

Common difference Signup and view all the answers

What does 'r' represent in sequences?

Common ratio Signup and view all the answers

What is the Recursive formula for an Arithmetic Sequence?

Recursive formula for an Arithmetic Sequence Signup and view all the answers

What is the Explicit formula for an Arithmetic Sequence?

Explicit formula for an Arithmetic Sequence Signup and view all the answers

What is the Recursive formula for a Geometric Sequence?

Recursive formula for a Geometric Sequence Signup and view all the answers

What is the Explicit formula for a Geometric Sequence?

Explicit formula for a Geometric Sequence Signup and view all the answers

What is a Geometric sequence?

Based on constant multiplying to get the next term. Signup and view all the answers

What is an Arithmetic sequence?

Based on constant addition to get the next term. Signup and view all the answers

What is summation (Sigma) notation?

Summation notation. Signup and view all the answers

What is a series in mathematics?

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

What is the Arithmetic Series Formula?

Arithmetic Series Formula. Signup and view all the answers

What is the Geometric Series Formula?

Geometric Series Formula. Signup and view all the answers

What is a horizontal asymptote?

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

What is domain in a function?

Set of all inputs. Signup and view all the answers

What is range in a function?

Set of all outputs. 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. Signup and view all the answers

What characterizes a decreasing exponential function?

Where 0 Signup and view all the answers

What characterizes an increasing exponential function?

Where b > 1. Signup and view all the answers

What is exponential regression?

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

What does (x²)(x³) equal?

x⁵ Signup and view all the answers

What is x⁸ ÷ x⁵ equal to?

x³ Signup and view all the answers

What is 4⁻²?

1/16 Signup and view all the answers

What does 5⁰ equal?

1 Signup and view all the answers

What does (x³)⁵ equal?

x¹⁵ Signup and view all the answers

What is (2xy²)³ equal to?

8x³y⁶ Signup and view all the answers

What does (3/x⁴)³ equal?

27/x¹² Signup and view all the answers

What does 25 ^ ½ equal?

5 Signup and view all the answers

What does 4^3/2 equal?

8 Signup and view all the answers

What is a vertical asymptote?

A vertical line the graph approaches. Signup and view all the answers

What is the Exponential Growth and Decay Model?

Exponential Growth and Decay Model. Signup and view all the answers

What is solving an exponential equation using logs?

Solving an Exponential Equation Using Logs. Signup and view all the answers

What is the Product Log Law?

Product Log Law. Signup and view all the answers

What is the Quotient Log Law?

Quotient Log Law. Signup and view all the answers

What is the Power Log Law?

Power Log Law. Signup and view all the answers

What is the Exponential Function Graph?

Exponential Function Graph. Signup and view all the answers

What is the Logarithmic Function Graph?

Logarithmic Function Graph. Signup and view all the answers

What are inverse functions?

Switch the x and y. Signup and view all the answers

What is a common log?

Base 10. Signup and view all the answers

What is a natural log?

Base e. Signup and view all the answers

What is the Compound Interest Formula?

Compound Interest Formula. Signup and view all the answers

What is the Continuous Compound Interest Formula?

Continuous Compound Interest Formula. Signup and view all the answers

What is the Half-Life Formula?

Half-Life Formula. Signup and view all the answers

What is the Method of Common Bases?

Find a common base then rewrite each expression using that base. Signup and view all the answers

What are Trig facts (Unit Circle)?

Trig facts related to the unit circle. Signup and view all the answers

What is the equation of the unit circle?

x² + y² = 1. Signup and view all the answers

What does sin(θ) in the unit circle equal?

The y-coordinate. Signup and view all the answers

What does cos(θ) in the unit circle equal?

The x-coordinate. Signup and view all the answers

What is a reference angle?

The positive acute angle formed by the terminal ray and the x-axis. Signup and view all the answers

What are coterminal angles?

Angles in standard position that share the same terminal side. Signup and view all the answers

Study Notes

Sequences

A sequence is an ordered list of numbers, defined as a function with the domain of positive integers.
The first term of a sequence is denoted as f(1) or a₁.
A recursive formula generates terms based on previous terms, while an explicit formula uses the term's index (position) to find its value.

Arithmetic and Geometric Sequences

In an arithmetic sequence, the common difference (d) is the constant amount added to get the next term.
In a geometric sequence, the common ratio (r) is the constant factor used to multiply terms to find the next.
Recursive formulas for arithmetic sequences involve the previous term plus the common difference, while explicit formulas compute terms using the index.
Geometric sequences follow similar patterns with their recursive and explicit formulations.

Series and Summation

A series is the sum of the terms of a sequence.
Summation (Sigma) notation is a concise way to represent the sum of a sequence's terms.
Arithmetic and geometric series have distinctive formulas for sum calculation.

Asymptotes

Horizontal asymptotes are horizontal lines that a graph approaches as the x-values either increase or decrease indefinitely.
Vertical asymptotes are vertical lines indicating undefined values for a function, often where it tends towards infinity.

Functions and Graphs

The basic form of an exponential function has the form y = a*b^x, where 'a' is the y-intercept and 'b' is the base (multiplier).
Decreasing exponential functions have a base (b) between 0 and 1, while increasing exponential functions have a base greater than 1.
Graphs of exponential and logarithmic functions have specific characteristics and transformations relating to their bases.

Logarithms

The common logarithm has a base of 10 (y = log(x)), while the natural logarithm is based on 'e' (y = ln(x)).
Logarithmic properties include Product, Quotient, and Power log laws that simplify complex logarithmic expressions.

Exponential Models

Exponential growth and decay are modeled using specific formulas that incorporate the base, time, and initial value.
The compound interest formula calculates interest on an initial amount over time, while continuous compound interest uses a variation for continuous growth.
The half-life formula relates to exponential decay in the context of radioactive substances, indicating the time required for half of a quantity to decay.

Trigonometry and the Unit Circle

The unit circle equation is x² + y² = 1, centered at (0, 0) with a radius of 1.
The sine of an angle (sin(θ)) corresponds to the y-coordinate, while the cosine (cos(θ)) corresponds to the x-coordinate.
Reference angles are the acute angles between the terminal side of an angle and the x-axis, which help in calculating trigonometric values.

General Concepts

Inverse functions are formed by switching x and y, and their graphs are symmetric around the line y = x.
Understanding how to find common bases is crucial for solving exponential equations, followed by equating the exponents for simplification.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

This quiz features flashcards designed to help you review key concepts for the Algebra 2 Regents Exam. It includes definitions and examples of sequences, terms, recursive formulas, and more. Perfect for students looking to sharpen their understanding before the exam.