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Pre-Calculus

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Pre-Calculus 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

  • Where will a cannonball land after firing? How does a harmonograph create art? How can logarithm scales help us represent the universe? Through motivating questions and interactive graphing, you’ll learn pre-calculus without relying on memorization.

    By the end of this course, you’ll have mastered the foundational skills for working with exponential equations, logarithms, conic sections, and parametric equations.

Syllabus

    • Introduction to Pre-Calculus: Get a start with exponential growth and logarithms.
      • Exponential Growth to the Moon: Start thinking about exponential functions with this estimation and stacking challenge.
      • Logarithms: What is a logarithm, and how do you solve one?
      • Logarithmic Scales in Space: Unify exponential and logarithm ideas as you chart a map through space.
    • Exponentials: It gets large (or small) faster than you might think!
      • Exponential Growth: Keep on doubling!
      • Changing the Base: What happens when you change the base of an exponential?
      • Exponential Arithmetic: Get some practice algebraically and graphically transforming exponents.
      • Financial Investing: Learn some of the money-related applications of exponents.
    • Logarithms: Invert exponentials to get these.
      • Defining Logarithms: Get started with the basic ideas behind logarithms.
      • Log Scales: Practice the application of log scales.
      • Graphing Logs: What does a log look like when you graph it?
      • Understanding Log Arithmetic: Add, subtract and multiply with logarithms.
      • Log Arithmetic Practice: Strengthen your logarithm arithmetic skills with some problem solving.
      • Change of Base: Learn and apply a special formula that changes the base of the logarithm.
      • Log Equations: Solve for x when a logarithm is involved.
      • Applying Log Scales: Look at some special applications of the logarithm.
    • Conic Sections: Slice a cone and open a whole new class of curves.
      • Introduction to Conic Sections: Strengthen your intuition for conic sections and the parabola as a special case of conic slices.
      • Circles: Practice moving circles around the coordinate plane.
      • Ellipses: Stretch circles into ellipses and understand the relationship between an ellipse's foci and its function.
      • Parabolas: Learn another way to define a parabolic curve using a focus point and directrix line.
      • Mirrors and Lenses: What happens when mirrors are shaped like parabolas?
      • Hyperbolas: Cut a cone vertically to get this strange set of conic sections.
    • Parametric Equations: Separate the horizontal and the vertical.
      • Horizontal and Vertical: Describe motion with equations.
      • Lines: Use two equations to track a point on a line.
      • Projectiles: Unleash more parametric power to hurl objects through the air.
      • Pendulums: Join conic sections with parametric equations and preview trigonometry along the way.

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