Algebra 2 Honors FSA EOC Flashcards
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Questions and Answers

What is the formula for Standard Deviation?

o = √((1st #-mean)^2 + .... + (Last #-mean)^2/n)

What is the formula for a Logarithm Solution?

x = log(285) / (3 * log(15))

What is the standard form of a quadratic equation?

Ax^2 + Bx + C = 0

What is the Vertex Form of a quadratic equation?

<p>Y = (x - h)^2 + k</p> Signup and view all the answers

What is the power rule in logarithms?

<p>log_b(m^n) = n log_b(m)</p> Signup and view all the answers

What is the Quotient Rule in logarithms?

<p>loga - logb = log(a/b)</p> Signup and view all the answers

What is the Product Rule in logarithms?

<p>loga + logb = log(ab)</p> Signup and view all the answers

What is the Interest Growth formula?

<p>a = p(1 + r)^t</p> Signup and view all the answers

What is the formula for Interest Decay?

<p>a = p(1 - r)^t</p> Signup and view all the answers

What is the formula for compounding continuously?

<p>Pe^{rt}</p> Signup and view all the answers

What is an asymptote?

<p>A line that a graph approaches as x or y increases in absolute value</p> Signup and view all the answers

What does exponential growth indicate?

<p>As x increases, y increases</p> Signup and view all the answers

What does exponential decay indicate?

<p>As x increases, y decreases</p> Signup and view all the answers

What is the Change of Base formula for calculators?

<p>log base 5 3 = log(3)/log(5)</p> Signup and view all the answers

What is the formula for logarithm equations?

<p>X = b^y, then log base b x = y</p> Signup and view all the answers

What is the form of exponential functions?

<p>y = ab^x</p> Signup and view all the answers

How do you calculate the geometric mean for two numbers?

<p>√(4 * 9) = 6</p> Signup and view all the answers

What is the definition of the arithmetic mean?

<p>The sum of the data divided by the total number of values in the set</p> Signup and view all the answers

What defines an arithmetic sequence?

<p>{-5, -3, -1, 1, ...} with a common difference of +2</p> Signup and view all the answers

What is the formula for the median?

<p>The middle number in a series of values</p> Signup and view all the answers

What does mode mean in a set of values?

<p>Number that appears the most in a series of values</p> Signup and view all the answers

What is the formula for range?

<p>Biggest # - Smallest #</p> Signup and view all the answers

What is the purpose of the Special Right Triangle 60-60-90?

<p>To define ratios of the sides in a specific triangle</p> Signup and view all the answers

What is the purpose of the Special Right Triangle 45-45-90?

<p>To define ratios of the sides in a specific triangle</p> Signup and view all the answers

Match the following trig functions to their definitions:

<p>sin = o/h cos = a/h tan = o/a cscx = 1/sinx secx = 1/cosx cotx = 1/tanx</p> Signup and view all the answers

What is the formula for permutation?

<p>n! / (n - r)!</p> Signup and view all the answers

What is the combination formula?

<p>nCr = n! / (n - r)! r!</p> Signup and view all the answers

What is the formula for the Sum of Cubes?

<p>a^3 + b^3 = (a + b)(a^2 - ab + b^2)</p> Signup and view all the answers

What is the formula for the Difference of Cubes?

<p>a^3 - b^3 = (a - b)(a^2 + ab + b^2)</p> Signup and view all the answers

How do you find the vertex of a parabola from standard form?

<p>(-b / 2a, plug in to get y)</p> Signup and view all the answers

How do you convert degrees to radians?

<p>Multiply by π/180</p> Signup and view all the answers

How do you convert radians to degrees?

<p>Multiply by 180/π</p> Signup and view all the answers

What is the formula for Arc Length?

<p>S = r(theta)</p> Signup and view all the answers

What is the definition of a constant function?

<p>Function f(x) = a</p> Signup and view all the answers

What is the definition of a linear function?

<p>Function f(x) = mx + b</p> Signup and view all the answers

What is the function for Absolute Value?

<p>Function f(x) = m|x| + b</p> Signup and view all the answers

What is the function for a Quadratic?

<p>Function f(x) = x^2</p> Signup and view all the answers

How do you find the 'a' value for a parabola equation?

<p>1/4c</p> Signup and view all the answers

What is the definition of the axis of symmetry?

<p>The halfway point between two roots</p> Signup and view all the answers

What is an imaginary number?

<p>i = √-1</p> Signup and view all the answers

What is Pascal's Triangle used for?

<p>To find the value of 'nCr'</p> Signup and view all the answers

What is Interquartile Range (IRQ)?

<p>Q3 - Q1</p> Signup and view all the answers

What is Synthetic Division?

<p>A method for dividing a polynomial by a binomial using coefficients</p> Signup and view all the answers

Study Notes

Standard Deviation

  • Formula: ( o = \sqrt{\frac{(1st # - mean)^2 + ... + (Last # - mean)^2}{n}} )
  • Example with data set (9, 10, 11, 7, 13) yields SD = 2 after calculations.

Logarithm Solution

  • Solve ( 15^{3x} = 6000 ) using log properties.
  • Final solution for ( x ) approximates to 0.6958.

Standard Form

  • General representation of a quadratic equation: ( Ax^2 + Bx + C = 0 ).

Vertex Form

  • Quadratic function expressed as ( Y = (x-h)^2 + k ), with vertex at point ( (h, k) ).

Power Rule

  • Logarithmic identity: ( \log_b{m^n} = n \cdot \log_b{m} ).
  • Example simplifies to ( 8 ) when applying the rule to ( \log_3{9^4} ).

Quotient Rule

  • Logarithmic property: ( \log_a - \log_b = \log_a/b ).
  • Example for ( \log_2{(x/2)} ) simplifies to ( \log_2{x} - 1 ).

Product Rule

  • Logarithmic identity: ( \log_a + \log_b = \log_a \cdot b ).
  • Example with ( \log_2{(4 \times 8)} ) results in ( 5 ).

Interest Growth Formula

  • Compound interest formula: ( a = p(1 + r)^t ).

Interest Decay Formula

  • Formula for exponential decay: ( a = p(1 - r)^t ).

Compounding Continuously

  • Formula: ( a = Pe^{rt} ), where ( P ) is principal, ( r ) is rate, ( t ) is time.

Asymptote

  • A line approached by a graph as ( x ) or ( y ) values increase.

Exponential Growth

  • When ( x ) increases, ( y ) also increases.

Exponential Decay

  • As ( x ) increases, ( y ) decreases.

Change of Base Formula

  • For calculators: ( \log_5{3} = \frac{\log{3}}{\log{5}} ).

Logarithm Equations

  • If ( X = b^y ), then ( \log_b{X} = y ); e.g., ( log_{10}{100} = 2 ).

Exponential Functions

  • Form: ( y = ab^x ), with ( b ) as a constant.

Compounding Interest

  • Example: For 7% compounded annually, calculation varies with time ( t ).

Arithmetic Mean

  • Calculated by summing values and dividing by the total number of values.

Geometric Mean

  • Found by multiplying data values and taking the ( n )-th root of the product. Example yields 6 for numbers 4 and 9.

Arithmetic Sequences

  • Sequence example: {-5, -3, -1, 1...} with a common difference of 2.

Arithmetic Series

  • Constant difference series; the sum is calculated using the average of the first and last terms.

Geometric Series

  • Sequence format: ( {a, ar, ar^2, ar^3...} ) where ( r ) represents the common ratio.

Functions

  • Types include:
    • Direct: ( y = kx )
    • Inverse: ( y = \frac{k}{x} )
    • Joint: ( \frac{y}{x^2} = k )

Median

  • The value in the middle of an ordered data set.

Mode

  • The most frequently appearing number in a dataset.

Range

  • Difference between the largest and smallest numbers in a dataset.

Special Right Triangles

  • 60-60-90 and 45-45-90 triangles have specific angle relationships and side ratios.

Trigonometric Functions

  • Definitions include:
    • ( \sin = \frac{o}{h} )
    • ( \cos = \frac{a}{h} )
    • ( \tan = \frac{o}{a} )
    • Reciprocal functions like ( \csc, \sec, \cot ).

Permutation Formula

  • Represents choices when order matters: ( nPr = \frac{n!}{(n-r)!} ).

Combination Formula

  • Represented as ( nCr = \frac{n!}{(n-r)!r!} ), used when order does not matter.

Sum of Cubes Formula

  • Formula: ( a^3 + b^3 = (a + b)(a^2 - ab + b^2) ).

Difference of Cubes Formula

  • Formula: ( a^3 - b^3 = (a - b)(a^2 + ab + b^2) ).

Vertex of a Parabola

  • Found using formula ( (-\frac{b}{2a}, y) ), where ( y ) is determined by substitution.

Degree to Radian Conversion

  • Convert by multiplying degrees by ( \frac{\pi}{180} ).

Radian to Degree Conversion

  • Convert radians by multiplying by ( \frac{180}{\pi} ).

Arc Length

  • Formula for arc length in radians: ( S = r(\theta) ).

Constant Function

  • Defined as ( f(x) = a ), representing a horizontal line.

Linear Function

  • Defined as ( f(x) = mx + b ), representing a diagonal line.

Absolute Value Function

  • Defined as ( f(x) = m|x| + b ), representing a V-shaped graph.

Quadratic Function

  • Defined as ( f(x) = x^2 ), forming a parabola.

Finding "a" Value in Parabola

  • Calculated using formula ( \frac{1}{4c} ).

Axis of Symmetry

  • The midpoint that divides a parabola into mirror-image halves.

Imaginary Number

  • Defined as ( i = \sqrt{-1} ) with properties such as ( i^2 = -1 ).

Pascal's Triangle

  • Useful for determining combinations, where the row correlates to values of ( n ).

Interquartile Range (IQR)

  • Steps to find IQR:
    • Order numbers
    • Find median
    • Identify ( Q1 ) and ( Q3 )
    • Calculate ( IQR = Q3 - Q1 ).

Synthetic Division

  • Method for polynomial division involving organized steps for efficiency.

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Test your knowledge with these flashcards designed for the Algebra 2 Honors FSA End of Course exam. Each card covers critical mathematical concepts like standard deviation and logarithmic solutions, providing both definitions and examples. Perfect for quick review and reinforcement of key algebra topics.

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