Advanced Placement
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AP Precalculus

Polynomials · Exponentials · Trigonometry · Polar curves

Topic 1.2

Rates of Change

Average rate of change, the rate at a point, and what the sign means

Watch25 min

Unit 1 Polynomial and Rational Functions

  1. Topic 1.120 minChange in Tandem
  2. Topic 1.225 minRates of Change
  3. Topic 1.325 minRates of Change in Linear and Quadratic Functions
  4. Topic 1.420 minPolynomial Functions and Rates of Change
  5. Topic 1.523 minPolynomial Functions and Complex Zeros
  6. Topic 1.619 minPolynomial Functions and End Behavior
  7. Topic 1.723 minRational Functions and End Behavior
  8. Topic 1.821 minRational Functions and Zeros
  9. Topic 1.922 minRational Functions and Vertical Asymptotes
  10. Topic 1.1018 minRational Functions and Holes
  11. Topic 1.1124 minEquivalent Representations of Polynomial and Rational Expressions
  12. Topic 1.1219 minTransformations of Functions
  13. Topic 1.1319 minFunction Model Selection and Assumption Articulation
  14. Topic 1.1423 minFunction Model Construction and Application

Unit 2 Exponential and Logarithmic Functions

  1. Topic 2.121 minChange in Arithmetic and Geometric Sequences
  2. Topic 2.221 minChange in Linear and Exponential Functions
  3. Topic 2.322 minExponential Functions
  4. Topic 2.421 minExponential Function Manipulation
  5. Topic 2.523 minExponential Function Context and Data Modeling
  6. Topic 2.618 minCompeting Function Model Validation
  7. Topic 2.722 minComposition of Functions
  8. Topic 2.819 minInverse Functions
  9. Topic 2.920 minLogarithmic Expressions
  10. Topic 2.1020 minInverses of Exponential Functions
  11. Topic 2.1121 minLogarithmic Functions
  12. Topic 2.1221 minLogarithmic Function Manipulation
  13. Topic 2.1320 minExponential and Logarithmic Equations and Inequalities
  14. Topic 2.1420 minLogarithmic Function Context and Data Modeling
  15. Topic 2.1519 minSemi-log Plots

Unit 3 Trigonometric and Polar Functions

  1. Topic 3.118 minPeriodic Phenomena
  2. Topic 3.219 minSine, Cosine, and Tangent
  3. Topic 3.319 minSine and Cosine Function Values
  4. Topic 3.416 minSine and Cosine Function Graphs
  5. Topic 3.516 minSinusoidal Functions
  6. Topic 3.620 minSinusoidal Function Transformations
  7. Topic 3.718 minSinusoidal Function Context and Data Modeling
  8. Topic 3.820 minThe Tangent Function
  9. Topic 3.918 minInverse Trigonometric Functions
  10. Topic 3.1019 minTrigonometric Equations and Inequalities
  11. Topic 3.1118 minThe Secant, Cosecant, and Cotangent Functions
  12. Topic 3.1221 minEquivalent Representations of Trigonometric Functions
  13. Topic 3.1320 minTrigonometry and Polar Coordinates
  14. Topic 3.1418 minPolar Function Graphs
  15. Topic 3.1516 minRates of Change in Polar Functions

Unit 4 Functions Involving Parameters, Vectors, and Matrices

  1. Topic 4.119 minParametric Functions
  2. Topic 4.221 minParametric Functions Modeling Planar Motion
  3. Topic 4.319 minParametric Functions and Rates of Change
  4. Topic 4.420 minParametrically Defined Circles and Lines
  5. Topic 4.520 minImplicitly Defined Functions
  6. Topic 4.621 minConic Sections
  7. Topic 4.722 minParametrization of Implicitly Defined Functions
  8. Topic 4.821 minVectors
  9. Topic 4.918 minVector-Valued Functions
  10. Topic 4.1018 minMatrices
  11. Topic 4.1120 minThe Inverse and Determinant of a Matrix
  12. Topic 4.1220 minLinear Transformations and Matrices
  13. Topic 4.1321 minMatrices as Functions
  14. Topic 4.1420 minMatrices Modeling Contexts