Algebra 2 Regents Exam Review
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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?

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

What are explicit formulas?

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

What does 'd' represent in sequences?

<p>Common difference</p> Signup and view all the answers

What does 'r' represent in sequences?

<p>Common ratio</p> Signup and view all the answers

What is the Recursive formula for an Arithmetic Sequence?

<p>Recursive formula for an Arithmetic Sequence</p> Signup and view all the answers

What is the Explicit formula for an Arithmetic Sequence?

<p>Explicit formula for an Arithmetic Sequence</p> Signup and view all the answers

What is the Recursive formula for a Geometric Sequence?

<p>Recursive formula for a Geometric Sequence</p> Signup and view all the answers

What is the Explicit formula for a Geometric Sequence?

<p>Explicit formula for a Geometric Sequence</p> Signup and view all the answers

What is a Geometric sequence?

<p>Based on constant multiplying to get the next term.</p> Signup and view all the answers

What is an Arithmetic sequence?

<p>Based on constant addition to get the next term.</p> Signup and view all the answers

What is summation (Sigma) notation?

<p>Summation notation.</p> Signup and view all the answers

What is a series in mathematics?

<p>The sum of the terms of a sequence.</p> Signup and view all the answers

What is the Arithmetic Series Formula?

<p>Arithmetic Series Formula.</p> Signup and view all the answers

What is the Geometric Series Formula?

<p>Geometric Series Formula.</p> Signup and view all the answers

What is a horizontal asymptote?

<p>A horizontal line the graph approaches.</p> Signup and view all the answers

What is domain in a function?

<p>Set of all inputs.</p> Signup and view all the answers

What is range in a function?

<p>Set of all outputs.</p> Signup and view all the answers

What is the basic form of an exponential function?

<p>Where a is the y-intercept and b is the base.</p> Signup and view all the answers

What characterizes a decreasing exponential function?

<p>Where 0 &lt; b &lt; 1.</p> Signup and view all the answers

What characterizes an increasing exponential function?

<p>Where b &gt; 1.</p> Signup and view all the answers

What is exponential regression?

<p>Fitting data to an exponential function.</p> Signup and view all the answers

What does (x²)(x³) equal?

<p>x⁵</p> Signup and view all the answers

What is x⁸ ÷ x⁵ equal to?

<p>x³</p> Signup and view all the answers

What is 4⁻²?

<p>1/16</p> Signup and view all the answers

What does 5⁰ equal?

<p>1</p> Signup and view all the answers

What does (x³)⁵ equal?

<p>x¹⁵</p> Signup and view all the answers

What is (2xy²)³ equal to?

<p>8x³y⁶</p> Signup and view all the answers

What does (3/x⁴)³ equal?

<p>27/x¹²</p> Signup and view all the answers

What does 25 ^ ½ equal?

<p>5</p> Signup and view all the answers

What does 4^3/2 equal?

<p>8</p> Signup and view all the answers

What is a vertical asymptote?

<p>A vertical line the graph approaches.</p> Signup and view all the answers

What is the Exponential Growth and Decay Model?

<p>Exponential Growth and Decay Model.</p> Signup and view all the answers

What is solving an exponential equation using logs?

<p>Solving an Exponential Equation Using Logs.</p> Signup and view all the answers

What is the Product Log Law?

<p>Product Log Law.</p> Signup and view all the answers

What is the Quotient Log Law?

<p>Quotient Log Law.</p> Signup and view all the answers

What is the Power Log Law?

<p>Power Log Law.</p> Signup and view all the answers

What is the Exponential Function Graph?

<p>Exponential Function Graph.</p> Signup and view all the answers

What is the Logarithmic Function Graph?

<p>Logarithmic Function Graph.</p> Signup and view all the answers

What are inverse functions?

<p>Switch the x and y.</p> Signup and view all the answers

What is a common log?

<p>Base 10.</p> Signup and view all the answers

What is a natural log?

<p>Base e.</p> Signup and view all the answers

What is the Compound Interest Formula?

<p>Compound Interest Formula.</p> Signup and view all the answers

What is the Continuous Compound Interest Formula?

<p>Continuous Compound Interest Formula.</p> Signup and view all the answers

What is the Half-Life Formula?

<p>Half-Life Formula.</p> Signup and view all the answers

What is the Method of Common Bases?

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

What are Trig facts (Unit Circle)?

<p>Trig facts related to the unit circle.</p> Signup and view all the answers

What is the equation of the unit circle?

<p>x² + y² = 1.</p> Signup and view all the answers

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

<p>The y-coordinate.</p> Signup and view all the answers

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

<p>The x-coordinate.</p> Signup and view all the answers

What is a reference angle?

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

What are coterminal angles?

<p>Angles in standard position that share the same terminal side.</p> 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.

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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.

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