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Precalculus

Free Precalculus study guide: 11 units with summaries, key ideas, flashcards and 263 practice questions with step-by-step solutions.

Lines up with: AP Precalculus; CLEP Precalculus.

Start studying PrecalculusFormula and fact sheet

Units

  1. UNIT 01

    Functions review & rates of change

    Precalculus studies functions by how they change. Average rate of change, increasing and decreasing behavior, and concavity are the main tools.
  2. UNIT 02

    Polynomial functions

    Polynomial functions are smooth and continuous. Their degree controls end behavior and the number of zeros and turning points.
  3. UNIT 03

    Rational functions

    Rational functions are ratios of polynomials. Their graphs are shaped by asymptotes and holes.
  4. UNIT 04

    Transformations & function modeling

    New functions come from transforming, combining and inverting known ones. Choosing the right model for data is the applied side of the same skill.
  5. UNIT 05

    Exponential & logarithmic functions

    Exponential functions change by equal factors over equal intervals. Logarithms invert them and turn multiplication into addition.
  6. UNIT 06

    Right-triangle & unit-circle trig

    Trigonometry starts with angles measured in radians and the unit circle, which defines sine and cosine for any angle.
  7. UNIT 07

    Graphs of trig functions

    Sine and cosine graphs are waves. Four numbers control them: amplitude, period, phase shift and vertical shift.
  8. UNIT 08

    Inverse trig & trig equations

    Inverse trig functions undo sine, cosine and tangent on restricted domains. They let you solve trig equations for an angle.
  9. UNIT 09

    Trig identities

    Trig identities are equations true for every angle. They let you rewrite expressions to simplify or solve them.
  10. UNIT 10

    Polar coordinates & graphs

    Polar coordinates locate a point by distance r and angle θ instead of x and y. Some curves are much simpler in polar form.
  11. UNIT 11

    Conics, parametrics, vectors & matrices

    This unit extends functions into parametric equations, vectors and matrices, which set up multivariable calculus and linear algebra. (It isn't on the AP Precalculus exam.)