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Algebra II

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Algebra II provided by Brilliant is a comprehensive online course, which lasts for 4 hours worth of material. Upon completion of the course, you can receive an e-certificate from Brilliant. The course is taught in Englishand is Paid Course. Visit the course page at Brilliant for detailed price information.

via Brilliant
4 hours worth of material
Self Paced
Overview

  • Use interactive graphing apps to explore and transform functions of all varieties: polynomials, exponents, logarithms, absolute value, and more. Learn a method of factoring not commonly taught in school, practice modeling scenarios, and do problem solving that reveals the beauty of mathematics.

Syllabus

    • Introduction: Use experiments and play with graphs to learn algebra!
      • Modeling and Functions: Interact with functions by sliding their variables higher and lower to see what happens!
      • Transforming Functions: Practice predicting the behavior of function transformations.
      • Factoring and Beyond: Explore factoring polynomials from a new perspective, and learn a new factoring technique.
    • Function Fundamentals: Function notation, domain, range, and a plethora of graph types.
      • Function Notation: Review the definition of "function" and the notation used to represent functions.
      • Playing With Functions: Explore a variety of function types by experimenting and playing with their graphs.
      • Domain and Range: Learn how the domains and ranges of functions depend on each other — and on the function types.
      • So Many Functions: Strengthen your skills working with quadratic, cubic, exponential, and trigonometric functions.
    • Transformations: Move any function around or change its shape with a fixed set of rules.
      • Shifts and Stretches: How can a function wind up stretched and transposed up, down, left, or right on the plane?
      • Symmetry: Throw some negatives into the mix and see what happens!
      • Inverse Functions: What happens when the input becomes the output and the output becomes the input?
      • Composition: First apply one function and then another, how does the initial input relate to the final output?
      • Compositions as Transformations: Explore the close connection between composing functions and applying internal function transformations.
    • Powers and Radicals: Explore exponents and roots of all kinds.
      • Powers: Explore a fast-growing power function used to model growth in finance and biology.
      • Zero and Negative Exponents: What happens when the exponent is less than 1?
      • Fractional Exponents: What happens when the exponent isn't an integer?
      • Radical Conjugates: This simplification technique lets you move and remove radicals.
      • Infinite Nests: Solve some unusual problems where the functions are defined as infinite compositions of square roots.
    • Polynomials: Here you'll find every degree from zero to infinity.
      • Playing With Polynomials: Get a feel for how polynomials work by interacting with their graphs.
      • Polynomial Graph Basics: Solidify your understanding of how the graphs of polynomials are related to their functions.
      • Polynomial Symmetries: Sometimes a bit of reflection can make things a lot easier.
      • Projectile Motion: Apply quadratics to study and draw conclusions about these flying and falling objects!
      • Polynomial Arithmetic: Practice adding, subtracting, and multiplying polynomials.
    • Factoring Polynomials: Split polynomials down to their smallest parts!
      • Playing With Factored Form: Explore the art of factoring polynomials from new, graphical perspectives.
      • Factoring Quadratic Polynomials: Master the techniques for quadratic factoring!
      • More Factoring: Expand your factoring skills to cover cases where the leading coefficient is greater than 1.
      • The Quadratic Formula: Apply one of the most famous formulas in early mathematics to factor some polynomials.
      • Polynomial Long Division: Learn how to divide by polynomials using a technique similar to what's used in arithmetic with numbers.
      • Polynomial Problem Solving: Combine all of the techniques you've learned to tackle a variety of challenging polynomial problems.
      • The Binomial Theorem: Learn how to apply Pascal's triangle to quickly expand binomials.
    • Rational Functions: Put together two polynomials with division, and a new world opens up.
      • Direct and Inverse Variation: When one variable goes up, does the other go up with it?
      • Direct and Inverse Variation With Powers: Explore what variation looks like when larger powers are involved.
      • Asymptotic Behavior Part 1: Get closer and closer and closer... to infinity.
      • Asymptotic Behavior Part 2: Learn how to tackle these tricky horizontal and slant asymptote cases!
      • Problem Solving: Combine all of the techniques you've learned so far to solve these rational function problems.
    • Piecewise Functions: Make new functions by mashing together old ones.
      • Absolute Value Introduction: What are absolute value functions and how does arithmetic interact with them?
      • Modeling Absolute Value Scenarios: Consider some real-life scenarios where the concept of absolute value applies.
      • Absolute Value Problem Solving: Practice and strengthen your skills by solving some challenging absolute value problems.
      • Piecewise Functions: Create Frankenstein functions out of the pieces of spliced-up common functions!
      • Floor and Ceiling: Explore functions defined by the operation of rounding down or up to the nearest integer.

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