Mr. Integral

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Pre-Calculus

Get comfortable with the language of calculus: graphs, algebra, trigonometry and functions.

Start learning 6 units · 80 lessons

The course, unit by unit.

Open a unit for its introduction, map and lesson route.

01Analytic GeometryPoints, distance, slope, and lines - the coordinate toolkit calculus assumes.16 lessons

How can a picture become an equation?

Start with the introduction & map →
Unit cheat sheet All the key ideas in one reference

Coordinates and distance

  1. 01The Coordinate Plane
  2. 02Regions of the Plane
  3. 03Distance Between Two Points
  4. 04The Midpoint Formula

Slope and line equations

  1. 05Defining Slope
  2. 06Finding Slope
  3. 07Writing Line Equations
  4. 08Horizontal and Vertical Lines
  5. 09Equations from Intercepts

Reading and comparing lines

  1. 10Testing a Point Against a Line
  2. 11Intersection of Two Lines
  3. 12Graphing Lines
  4. 13Relative Positions of Two Lines
  5. 14Parallel Lines
  6. 15Perpendicular Lines
  7. 16Coincident Lines
02TrigonometryAngles, the unit circle, and the sine-cosine toolkit calculus leans on.8 lessons

How does an angle become a number?

Start with the introduction & map →
Unit cheat sheet All the key ideas in one reference

Basic Trigonometry

  1. 01Ratios in a Right Triangle
  2. 02Values at 30, 45 and 60 Degrees
  3. 03The Unit Circle
  4. 04The Identities Calculus Assumes

Inverse Trigonometric Functions

  1. 05Inverse Trig: Choosing One Angle
  2. 06Arcsin
  3. 07Arccos
  4. 08Arctan and Arccot
03LogarithmsExponents in reverse - the rules that tame growth and products.15 lessons

How long does repeated growth take?

Start with the introduction & map →
Unit cheat sheet All the key ideas in one reference

Exponential Functions

  1. 01Defining the Exponential Function
  2. 02Graphing Exponential Functions

Definition and Basic Concepts

  1. 03Defining the Logarithm
  2. 04The Inverse of an Exponential Function
  3. 05The Inverse of a Logarithmic Function
  4. 06Conditions on the Base and the Argument

The Rules

  1. 07The Four Basic Rules
  2. 08When the Base Is Not Written
  3. 09The Natural Logarithm
  4. 10The Product Rule
  5. 11The Quotient Rule
  6. 12Swapping the Base and the Exponent
  7. 13When a Logarithm Is the Exponent
  8. 14Changing the Base

Graphing Logarithmic Functions

  1. 15Graphing Logarithmic Functions
04FactoringRewriting expressions as products - the number-one limit-solving move.11 lessons

Which hidden products make algebra simpler?

Start with the introduction & map →
Unit cheat sheet All the key ideas in one reference

Choose a method

  1. 01An Overview of the Methods
  2. 02Taking Out a Common Factor

Quadratics and grouping

  1. 03Factoring ax² + bx + c
  2. 04Factoring by Grouping
  3. 05Perfect Squares

Recognize power patterns

  1. 06The Difference of Two Squares
  2. 07The Sum and Difference of Cubes
  3. 08Perfect Cubes
  4. 09Factoring xⁿ ± yⁿ

Rewrite before factoring

  1. 10Factoring by Substitution
  2. 11Adding and Subtracting a Term
05InequalitiesSign tables and intervals - where a function is positive, and where it is not defined.3 lessons

Where is a whole expression positive?

Start with the introduction & map →
Unit cheat sheet All the key ideas in one reference

Polynomial Inequalities

  1. 01Quadratic and Higher-Degree Inequalities

Rational Inequalities

  1. 02Rational Inequalities

Systems of Inequalities

  1. 03Systems of Inequalities
06Functions ReviewThe language calculus is written in - domain, inverse, composition, and what a graph move does.27 lessons

What does a function tell us—and what can it hide?

Start with the introduction & map →
Unit cheat sheet All the key ideas in one reference

Read and evaluate functions

  1. 01Defining a Function
  2. 02Evaluating a Function
  3. 03Domain, Codomain and Range
  4. 04What Makes a Rule a Function
  5. 05Properties of the Range
  6. 06Reading Domain and Range off a Graph
  7. 07Domain and Range of a Rational Function

Recognize function families

  1. 08Linear Functions
  2. 09Piecewise Functions
  3. 10Writing an Absolute Value Piecewise

Read symmetry and transformations

  1. 11Even Functions
  2. 12Odd Functions
  3. 13Arithmetic on Even and Odd Functions
  4. 14Symmetry of a Graph
  5. 15Translating a Graph
  6. 16Stretching and Compressing a Graph

Combine and invert functions

  1. 17Defining Composition
  2. 18Properties of Composition
  3. 19One-to-One Functions
  4. 20Functions That Are Not Onto
  5. 21Onto Functions
  6. 22Why One-to-One and Onto Matter
  7. 23Finding the Inverse of a Function
  8. 24A Shortcut for the Inverse
  9. 25A Function and Its Inverse on the Graph

Describe the behavior of a graph

  1. 26Increasing and Decreasing Intervals
  2. 27Local and Absolute Maxima and Minima