Interactive Course

Pre-Calculus

Master the fundamentals of exponential, logarithmic, hyperbolic, and parametric equations.

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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.

Topics covered

  • Conic Sections
  • Ellipses
  • Exponential Growth
  • Hyperbolas
  • Log Scales
  • Logarithmic Identities
  • Parabolas
  • Parabolic Mirrors
  • Parametric Equations
  • Transforming Functions

Interactive quizzes

25

Concepts and exercises

180+

Course map

Prerequisites and Next Steps

  1. 1

    Introduction to Pre-Calculus

    Get a start with exponential growth and logarithms.

    1. Exponential Growth to the Moon

      Start thinking about exponential functions with this estimation and stacking challenge.

      1
    2. Logarithms

      What is a logarithm, and how do you solve one?

      2
    3. Logarithmic Scales in Space

      Unify exponential and logarithm ideas as you chart a map through space.

      3
  2. 2

    Exponentials

    It gets large (or small) faster than you might think!

    1. Exponential Growth

      Keep on doubling!

      4
    2. Changing the Base

      What happens when you change the base of an exponential?

      5
    3. Exponential Arithmetic

      Get some practice algebraically and graphically transforming exponents.

      6
    4. Financial Investing

      Learn some of the money-related applications of exponents.

      7
  3. 3

    Logarithms

    Invert exponentials to get these.

    1. Defining Logarithms

      Get started with the basic ideas behind logarithms.

      8
    2. Log Scales

      Practice the application of log scales.

      9
    3. Graphing Logs

      What does a log look like when you graph it?

      10
    4. Understanding Log Arithmetic

      Add, subtract and multiply with logarithms.

      11
    5. Log Arithmetic Practice

      Strengthen your logarithm arithmetic skills with some problem solving.

      12
    6. Change of Base

      Learn and apply a special formula that changes the base of the logarithm.

      13
    7. Log Equations

      Solve for x when a logarithm is involved.

      14
    8. Applying Log Scales

      Look at some special applications of the logarithm.

      15
  4. 4

    Conic Sections

    Slice a cone and open a whole new class of curves.

    1. Introduction to Conic Sections

      Strengthen your intuition for conic sections and the parabola as a special case of conic slices.

      16
    2. Circles

      Practice moving circles around the coordinate plane.

      17
    3. Ellipses

      Stretch circles into ellipses and understand the relationship between an ellipse's foci and its function.

      18
    4. Parabolas

      Learn another way to define a parabolic curve using a focus point and directrix line.

      19
    5. Mirrors and Lenses

      What happens when mirrors are shaped like parabolas?

      20
    6. Hyperbolas

      Cut a cone vertically to get this strange set of conic sections.

      21
  5. 5

    Parametric Equations

    Separate the horizontal and the vertical.

    1. Horizontal and Vertical

      Describe motion with equations.

      22
    2. Lines

      Use two equations to track a point on a line.

      23
    3. Projectiles

      Unleash more parametric power to hurl objects through the air.

      24
    4. Pendulums

      Join conic sections with parametric equations and preview trigonometry along the way.

      25