# Topics Covered By Infinite Algebra 2

Infinite Algebra 2 covers all typical Algebra 2 material, beginning with a few major Algebra 1 concepts and going through trigonometry. There are over 125 topics in all, from multi-step equations to trigonometric identities. Suitable for any class with advanced algebra content. Designed for all levels of learners, from remedial to advanced.

Beginning
Algebra

Order of operations

Simplifying algebraic expressions

Equations and
Inequalities

Multi-step equations

Work word problems

Distance, rate, time word problems

Mixture word problems

Absolute value equations

Multi-step inequalities

Compound inequalities

Absolute value inequalities

Linear
Relations and Functions

Graphing linear equations

Writing linear equations

Graphing absolute value equations

Graphing linear inequalities

Systems of
Equations and Inequalities

Graphing systems of linear inequalities

Solving systems by graphing (2 variables)

Solving systems by elimination (2 variables)

Solving systems by substitution (2 variables)

Systems of equations word problems (2 variables)

Points in three dimensions

Planes

Solving systems with three variables

Matrices

Operations

Determinants

Inverses

Cramer's Rule

Equations

Geometric transformations

Complex
Numbers

Operations

Graphing

Absolute value

Rationalizing denominators

Quadratic
Functions and Inequalities

Graphing quadratic functions

Graphing quadratic inequalities

Factoring quadratic expressions

Factoring special case quadratic expressions

Solving equations by taking square roots

Solving equations by factoring

Completing the square

Solving equations by completing the square

Solving equations with the Quadratic Formula

The discriminant

Polynomial
Functions

Naming

Adding and subtracting

Multiplying

Multiplying special cases

The Binomial Theorem

Dividing

Factoring by grouping

Factoring a sum/difference of cubes

Factoring quadratic form

Factoring, all techniques

The Remainder Theorem

Writing functions

Conjugate roots & factoring

Conjugate roots & writing functions

Descartes' Rule of Signs

Rational Zero/Root Theorem

Fundamental Theorem of Algebra

Solving polynomial equations

End behavior and general graph shape

Graphing

General
Functions

Evaluating

Operations

Inverses

Radical
Functions and Rational Exponents

Simplifying radicals

Adding and subtracting radical expressions

Multiplying radical expressions

Dividing radical expressions

Connecting radical expressions and rational exponents

Evaluating rational exponent expressions

The properties of exponents

Radical equations

Rational exponent equations

Graphing radical equations

Domain and range of radical functions

Conic Sections

Parabolas, graphing & properties

Parabolas, writing equations

Circles, graphing & properties

Circles, writing equations

Ellipses, graphing & properties

Ellipses, writing equations

Hyperbolas, graphing & properties

Hyperbolas, writing equations

Classifying

Systems of quadratic equations

Rational
Expressions

Graphing

Simplifying

Multiplying and dividing

Adding and subtracting

Complex fractions

Equations

Exponential
and Logarithmic Expressions

Graphing exponential functions

Exponential equations not requiring logarithms

Exponents and logarithms

Evaluating logarithms

Logarithms and exponents as inverses

Properties of logarithms

Writing logs in terms of others

Exponential equations requiring logarithms

Inverses of

Logarithmic equations, simple

Logarithmic equations, hard

Graphing logarithmic functions

Discrete exponential growth and decay

Sequences and
Series

General sequences

Arithmetic sequences

Geometric sequences

Arithmetic and geometric mean

General series

Arithmetic series

Geometric series

Trigonometry

Angles and angle measure

Radians and degrees

Degrees and degrees-minutes-seconds

Coterminal angles

Arc length and sector area

Right triangle trig: Finding ratios

Right triangle trig: Finding angle measures

Right triangle trig: Finding angles and sides

Trig functions of any angle

The Law of Sines

The Law of Cosines

Area and Laws of Sines and Cosines

Graphing trig functions

Angle sum/difference identities

Double-angle/half-angle identities

Equations

Probability
and Statistics

Sample spaces and the Fundamental Counting Principle

Probability of independent and dependent events, word problems

Probability of independent and dependent events

Probability of mutually exclusive events, word problems

Probability of mutually exclusive events

Permutations

Combinations

Permutations vs combinations

Probability with permutations and combinations