Algebra 2 Honors FSA EOC Flashcards

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?

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

What is the power rule in logarithms?

log_b(m^n) = n log_b(m) Signup and view all the answers

What is the Quotient Rule in logarithms?

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

What is the Product Rule in logarithms?

loga + logb = log(ab) Signup and view all the answers

What is the Interest Growth formula?

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

What is the formula for Interest Decay?

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

What is the formula for compounding continuously?

Pe^{rt} Signup and view all the answers

What is an asymptote?

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

What does exponential growth indicate?

As x increases, y increases Signup and view all the answers

What does exponential decay indicate?

As x increases, y decreases Signup and view all the answers

What is the Change of Base formula for calculators?

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

What is the formula for logarithm equations?

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

What is the form of exponential functions?

y = ab^x Signup and view all the answers

How do you calculate the geometric mean for two numbers?

√(4 * 9) = 6 Signup and view all the answers

What is the definition of the arithmetic mean?

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

What defines an arithmetic sequence?

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

What is the formula for the median?

The middle number in a series of values Signup and view all the answers

What does mode mean in a set of values?

Number that appears the most in a series of values Signup and view all the answers

What is the formula for range?

Biggest # - Smallest # Signup and view all the answers

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

To define ratios of the sides in a specific triangle Signup and view all the answers

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

To define ratios of the sides in a specific triangle Signup and view all the answers

Match the following trig functions to their definitions:

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

What is the formula for permutation?

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

What is the combination formula?

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

What is the formula for the Sum of Cubes?

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

What is the formula for the Difference of Cubes?

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

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

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

How do you convert degrees to radians?

Multiply by π/180 Signup and view all the answers

How do you convert radians to degrees?

Multiply by 180/π Signup and view all the answers

What is the formula for Arc Length?

S = r(theta) Signup and view all the answers

What is the definition of a constant function?

Function f(x) = a Signup and view all the answers

What is the definition of a linear function?

Function f(x) = mx + b Signup and view all the answers

What is the function for Absolute Value?

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

What is the function for a Quadratic?

Function f(x) = x^2 Signup and view all the answers

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

1/4c Signup and view all the answers

What is the definition of the axis of symmetry?

The halfway point between two roots Signup and view all the answers

What is an imaginary number?

i = √-1 Signup and view all the answers

What is Pascal's Triangle used for?

To find the value of 'nCr' Signup and view all the answers

What is Interquartile Range (IRQ)?

Q3 - Q1 Signup and view all the answers

What is Synthetic Division?

A method for dividing a polynomial by a binomial using coefficients 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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Description

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.