Algebra II Exam Review

Flashcards for vocabulary review on key concepts in Algebra II, including factoring, quadratics, functions, complex numbers, logarithms, trigonometry, series, sequences, statistics and probability.

Factoring

Finding common factors in an expression to simplify it.

Greatest Common Factor (GCF)

The first step in factoring; find the largest factor common to all terms.

Difference of Two Perfect Squares (DOTS)

A factoring pattern involving the difference of two squared terms: x² - y² = (x + y)(x - y)

Trinomial (TRI)

A factoring method used for trinomials in the form ax² + bx + c.

"AC" Method

Also known as the 'Earmuff Method,' this method is used to factor trinomials.

Quadratic Formula (QF)

A formula used to find the roots of a quadratic equation: x = (-b ± √(b² - 4ac)) / (2a)

Divisor

The part of a division problem that goes into the Dividend

Quotient

The part of a division problem that results from dividing the Dividend by the Divisor

Long Division of Polynomials

A method to divide polynomials.

Synthetic Division of Polynomials

A simplified method for dividing a polynomial by a linear factor (x - a).

Factor by Grouping

A factoring technique where terms are grouped to find common factors.

Factoring Perfect Cubes by SOAP

A factoring pattern for perfect cubes using the mnemonic SOAP (Same, Opposite, Always Positive).

The Remainder Theorem

When the polynomial f(x) is divided by a binomial in the form of (x - a), the remainder equals f(a).

The Factor Theorem

If f(a) = 0 for polynomial f(x), then a binomial in the form of (x -a) must be a factor of the polynomial.

Quadratic Equation

A polynomial equation with a degree of two (2).

Standard Form of a Quadratic Equation

The standard form is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Sum of the Roots of a Quadratic

r₁ + r₂ = -b/a

Product of the Roots of a Quadratic

r₁ * r₂ = c/a

The Discriminant

b² - 4ac

Root/Zero/X-Intercept

A point on a quadratic where f(x) = 0; where the quadratic intersects the x-axis.

Turning Point (Vertex)

The point on a quadratic where the direction of the function changes.

Axis of Symmetry

A line of symmetry in the form of x = c, where c is a constant. c is same as x value of the turning point.

Focus

A point which lies 'inside' the parabola on the axis of symmetry.

Directrix

A line that is perpendicular to the axis of symmetry & lies 'outside' the parabola.

Function

A relation where each value of x is connected to a unique value of y.

Domain

The largest set of elements available for the independent variable (x).

Restrictions on Domain

Denominator cannot be zero; radicand cannot be negative.

Range

The set of elements for the dependent variable (y).

Composition Functions

Substituting one function into another.

One-to-One Function

No repeating x or y values.

Inverse Functions

The reflection of a function over the line y = x; only one-to-one functions have an inverse.

Onto Function

All x and y values are used.

End Behavior

The direction the function is heading at the ends of the graph.

Multiplicity

How many times a particular number is a zero for a given polynomial.

Multiplicity of 1

Cut Thru

Multiplicity of 2

Bounce

Multiplicity of 3

Snake Thru

Imaginary Unit (i)

The number whose square is negative one.

Fractional Exponent Rule

x^(p/r) = r√(x^p)

Exponential Form

B^e = N, e is the exponent.

Logarithmic Form

log_B(N) = e

Adding/Subtracting Rational Expressions

Requires a common denominator.

Multiplying Rational Expressions

Factor first, reduce, then multiply through.

Dividing Rational Expressions

Flip the second fraction, factor, reduce, then multiply through.

Complex Fractions

Multiply each fraction by the LCD, cancel what's common, and simplify.

Product Property of Logarithms

logb(m * n) = logb(m) + log_b(n)

Quotient Property of Logarithms

logb(m / n) = logb(m) - log_b(n)

Power Property of Logarithms

logb(m^r) = r * logb(m)

sin θ

opposite/hypotenuse

cos θ

adjacent/hypotenuse

tan θ

opposite/adjacent

csc θ

hypotenuse/opposite

sec θ

hypotenuse/adjacent

cot θ

adjacent/opposite

Arc Length of a Circle

s = rθ

Pythagorean Identity

sin²θ + cos²θ = 1

Inverse of y = sin x

y = arcsin(x)

Inverse of y = cos x

y = arccos(x)

Inverse of y = tan x

y = arctan(x)

Amplitude (A)

A = (Max - Min) / 2

Horizontal Shift (C)

Horizontal movement of a function; the sign is opposite the direction.

Vertical Shift (D)

Vertical movement of a function; the sign is the same direction.

Period of Trigonometric Functions

2π / B

Sigma Notation

Used to write a series in a shorthand form.

Sequence

A list of terms or elements in order.

Series

The sum of all the terms of a sequence.

Explicit Formula

Can be used by substituting the number of the term desired into the formula for 'n'.

Recursive Formula

The first term in a sequence is given, and subsequent terms are defined by the term before it.

Common Difference (d)

a2 - a1

Common Ratio (r)

a2 / a1

Arithmetic Sequences

an = a1 + (n-1)d

Geometric Sequences

an = a1 * r^(n-1)

Survey

Gathering facts or opinions, usually asked in a question form.

Observational Study

The observer does not interact with subjects but examines results.

Controlled Experiment

Two groups are studied, with an experiment performed on one but not the other.

Set Notation in Probability

Mutually exclusive or not mutually exclusive.

Confidence Interval

A range of values used to estimate the true value of a population parameter.

Z-Score

(number - mean) / standard deviation

Mutually Exclusive Events in Probability

If A and B are mutually exclusive events, P(A or B) = P(A) + P(B)

Dependent Event

Occurence of the first event changes the probability.

Complement of Events in Probability

P(A') = 1 - P(A)

Conditional Probability

P(B|A)