# Algebra

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## Operations with Numbers

Develop or review basic mathematical skills. Understand order of operations, signs and value, manipulating and working with fractions, and evaluating exponent values. Learn how to use number lines and represent expressions and inequalities while building your algebra skills.

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## Algebraic Expression

Learn to identify, write, and manipulate mathematical expressions using both variables and constants. Apply rules and conventions that will help organize and combine terms, where applicable. Then wrap it all up with FOIL and the multiplication of monomials, binomials, and trinomials.

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## Properties of Numbers

Terms contain comparable characterstics useful for sorting or creating logical statements. Put your basic math to the test in these challenging puzzle questions that you will learn can be more easily solved by algebra.

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## Factoring

Learn to mathematically separate a term into useful component parts based on constants, variables, and factors. Apply the exponent laws, special product rules, and factorization of constants with challenging real-world examples.

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## Fractions

Revisit numerators and denominators with greater complexity as expressions replace constants. Learn to manipulate and simplify a complex fraction into its most reduced form while maintaining its appropriate value.

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## Exponents

Exponents are notations that indicate how many times to multiply the base number by itself. Discover exponent laws that can be used to simplify longer expressions. Buckle down on these rules that will be invaluable moving forward into higher level mathematics.

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### Laws and Notation

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Simplify radical expressions, demonstrating a root based on a base number. Learn the inverse of exponent laws and apply factoring to simplify expressions given the radical function.

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## Equations

Equations are mathematical "sentences" that set equal two expressions. The concept of equality is fundamental to all branches of mathematics. Learn to manipulate and transform equations to identify an unknown. Apply equations to real-world examples to generate an equation from a situation and then use the equation to solve for the unknown value. Learn about how equations are used as functions to be mapped onto a coordinate plane.

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## Ratio, Proportion, and Variation

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## Functions and Graphs

Functions and graphs are alternative ways of looking at the relationships produced by equations. Functions focus on mapping inputs to outputs while graphs are a visual way of seeing the larger "picture" of a relationship. Practice substituting to find solutions, writing equations, and create equations based on modeling data. Explore different types of equations and how their graphs differ based on coefficients.

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## Linear Equations

Delve deeper into equations by creating graphs from the linear form. See how equations interact though systems of equations to find the common solution, or the intersection. Continue applying equations to real-life situations involving rates and costs.

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## Equations of Lines

Analyze the form and structure of the basic equation of a line. Understand y-intercept form, describing the slope and y-intercept of a line. Learn to recognize these values from a graph and apply them to writing a full equation. Then apply these equations to help you figure out costs and changes over time, to list a couple of examples. Learn to differentiate between parallel, perpendicular, and intersecting lines based on their graphs and equations.

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### Forms of Equations

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Practice on a new function: the quadratic function. With a degree of 2, the function of the graph changes significantly compared to linear equations. Apply the quadratic formula' to the equation of the parabola to determine the solutions to the graph when $y=0$, also known as the roots of the quadratic. These roots become incredibly important in future math courses.

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## Inequalities

Apply what you know about equations with a new form of relationship: inequalities. Instead of having only several possible solutions to the equation, inequalities may present an infinite number of solutions. Writing out these solutions and graphing them will be the first step towards finding solutions of systems of inequalities, where the solutions must apply for both inequalities.

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## Polynomial Functions

Ramping up the difficulty can be achieved by raising the exponent of an equation. Try your hand at polynomial functions with equations that will challenge your equation solving skills to find solutions. Put all the exponent laws, radical rules, and equation manipulations to the test with these challenging problems!

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## Rational Functions

Rational functions are quotients of polynomials in both the numerator and denominator. Sometimes, polynomial equations may contain asymptotes, or a value that cannot serve as a solution for that function. Begin to learn how to identify these gaps in functions in situations involving rational functions.

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## Sequences and Series

Sequences and series are sets of data that change in a consistent manner, often though a constant or a ratio. Learn the attributes of both and apply that to write a function for the set, predict later values, or determine sums of certain values.

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## Logarithms

Explore logarithms, special functions based on multiples of any base number though typically 10. Learn the logarithm laws and apply them in manipulating equations and expressions with logarithms.

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## Applications of Logarithms and Exponents

Apply logarithms and exponents and use them to model growth in both simple and compound interest questions. Explore how the functions can be used to model financial and scientific data to predict future outcomes in account values, bacterial growth, and radioactive decay.

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## Permutations and Combinations

Why are some numbers so excited (e.g. 4!)? Explore factorials, a notation used within permutations to calculate outcomes. On the path towards determining probability, delve deeper by looking at all the possibilities. Learn how to calculate the number of possible outcomes and combinations before utilizing them in probability for a specific outcome.

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## Probability and Binomial Theorem

Wonder how poker players make choices based on their cards? Think no further than probability and knowing that certain outcomes exist in a closed system. Apply permutations and combinations towards a particular outcome and determine if the odds are truly ever in your favor. Use binomial theorem to quickly determine the equation for an expanded binomial expression.

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## Determinants

Enter the matrices and learn how to calculate the determinants for simple matrices. Then apply determinants to systems of equations to solve for solutions using Cramer's Rule.

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### Homogenous Linear Equations

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They're baa-a-ack. Dig deep with fractions by simplifying fractions with rational expressions in their numerators and denominators. By connecting factoring of polynomials and simplifying, you are on the path to build this advanced set of algebra skills for higher order math.

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