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AP Precalculus

The functions calculus is built on, from polynomials and logarithms to polar and parametric curves.

12 units · 70 lessons · 688 practice items · 111 videos

AP Precalculus builds the function toolkit that later calculus depends on. You work through polynomial and rational functions, then exponential and logarithmic models, then trigonometry, before moving into polar, parametric, and vector-valued functions along with an introduction to matrices. Each unit develops one family of functions at a time, with lessons that connect the algebra to what the matching graphs and tables are doing.

The practice is built around the graphs themselves: you place points, sketch curves, transform a parent function, or adjust a model's parameters until it fits the data, and short video walkthroughs run alongside the text. Hints are available on many problems, revealed one step at a time, so a hard problem narrows before it gives itself away. Units close with a unit test, and semester exams sit on the course map as units of their own.

This course follows the College Board's published AP Precalculus framework.

Syllabus

Every published lesson in this course, by unit.

1APolynomial functions7 lessons
  1. 11.1 Change in tandem
  2. 21.2 Rates of change
  3. 31.3 Rates of change in linear and quadratic functions
  4. 41.4 Polynomial functions and rates of change
  5. 51.5 Polynomial functions and complex zeros
  6. 61.6 Polynomial functions and end behavior
  7. 7Unit 1A test
1BRational functions9 lessons
  1. 11.7 Rational functions and end behavior
  2. 21.8 Rational functions and zeros
  3. 31.9 Rational functions and vertical asymptotes
  4. 41.10 Rational functions and holes
  5. 51.11 Equivalent representations of polynomial and rational expressions
  6. 61.12 Transformations of functions
  7. 71.13 Function model selection and assumption articulation
  8. 81.14 Function model construction and application
  9. 9Unit 1B test
ExamSemester 1 midterm1 lesson
  1. 1Semester 1 midterm exam
2AExponential functions9 lessons
  1. 12.1 Change in arithmetic and geometric sequences
  2. 22.2 Change in linear and exponential functions
  3. 32.3 Exponential functions
  4. 42.4 Exponential function manipulation
  5. 52.5 Exponential function context and data modeling
  6. 62.6 Competing function model validation
  7. 72.7 Composition of functions
  8. 82.8 Inverse functions
  9. 9Unit 2A test
2BLogarithmic functions8 lessons
  1. 12.9 Logarithmic expressions
  2. 22.10 Inverses of exponential functions
  3. 32.11 Logarithmic functions
  4. 42.12 Logarithmic function manipulation
  5. 52.13 Exponential and logarithmic equations and inequalities
  6. 62.14 Logarithmic function context and data modeling
  7. 72.15 Semi-log plots
  8. 8Unit 2B test
ExamSemester 1 final1 lesson
  1. 1Semester 1 final exam
3ATrigonometric functions8 lessons
  1. 13.1 Periodic phenomena
  2. 23.2 Sine, cosine, and tangent
  3. 33.3 Sine and cosine function values
  4. 43.4 Sine and cosine function graphs
  5. 53.5 Sinusoidal functions
  6. 63.6 Sinusoidal function transformations
  7. 73.7 Sinusoidal function context and data modeling
  8. 8Unit 3A test
3BPolar functions9 lessons
  1. 13.8 The tangent function
  2. 23.9 Inverse trigonometric functions
  3. 33.10 Trigonometric equations and inequalities
  4. 43.11 The secant, cosecant, and cotangent functions
  5. 53.12 Equivalent representations of trigonometric functions
  6. 63.13 Trigonometry and polar coordinates
  7. 73.14 Polar function graphs
  8. 83.15 Rates of change in polar functions
  9. 9Unit 3B test
ExamSemester 2 midterm1 lesson
  1. 1Semester 2 midterm exam
4AParametric functions8 lessons
  1. 14.1 Parametric functions
  2. 24.2 Parametric functions modeling planar motion
  3. 34.3 Parametric functions and rates of change
  4. 44.4 Parametrically defined circles and lines
  5. 54.5 Implicitly defined functions
  6. 64.6 Conic sections
  7. 74.7 Parametrization of implicitly defined functions
  8. 8Unit 4A test
4BVector-valued functions and matrices8 lessons
  1. 14.8 Vectors
  2. 24.9 Vector-valued functions
  3. 34.10 Matrices
  4. 44.11 The inverse and determinant of a matrix
  5. 54.12 Linear transformations and matrices
  6. 64.13 Matrices as functions
  7. 74.14 Matrices modeling contexts
  8. 8Unit 4B test
ExamSemester 2 final1 lesson
  1. 1Semester 2 final exam