Hungerford & Shaw, Contemporary Precalculus (5th ed.)

OpenStax Precalculus (2nd ed.)
MAA Precalculus: An Investigation of Functions (open source)



The following table lists the minimum set of topics to be included in this course, based on the textbook by Hungerford & Shaw above.  The number of lectures listed for each chapter is only a suggestion and will vary across instructors and semesters.

There are typically 42-43 lecture days in a semester, so lecture periods are available for exams.

Sections Topics Lectures
1.1 – 1.4 Basics (Review) 3
3.1 – 3.7 Functions and Graphs 6
4.1 – 4.7 Polynomial and Rational Functions 8
5.1 – 5.5 Exponential and Logarithmic Functions 6
6.1 – 6.6 Trigonometric Functions 5
7.1 – 7.5 Trigonometric Identities and Equations 3
8.1 – 8.2 Triangle Trigonometry 4
9.1 – 9.2 Applications of Trigonometry 2
10.1 – 10.3 Analytic Geometry 3
Total 40

OPTIONAL TOPICS (time permitting)

  • All lettered sections (e.g. Section 1.2A) are considered optional, but all are good topics and we should consider covering the majority of them.
  • Sections 8.3/8.4 on the Laws of Sines and Cosines, which are traditional but not used in Calculus.
  • Section 10.6 on polar coordinates is natural when discussing the Unit Circle.
  • Other outside topics, readings, videos, or materials the Instructor deems relevant.



  1. Students can interpret and use mathematical notation and vocabulary related to the concepts of a function and the graph of a function.
  2. Students can identify shifts, stretches, compressions, and reflections of a function via its graph and its defining formula.
  3. Students can compose functions, invert functions, and interpret relationships between inverse functions via composition.
  4. Students can compute, compare, and interpret average and instantaneous rates of change of a function.
  5. Students can write equations describing ellipses, hyperbolas, and parabolas, and graph them, identifying their important features.
  6. Students can write and graph quadratic functions, and find and interpret their vertices in a given context.
  7. Students can write and graph polynomial functions, and solve polynomial equations and inequalities.
  8. Students can identify features of rational functions from formulas and graphs, and solve rational equations and inequalities.
  9. Students can write and graph functions representing both exponential growth and exponential decay.
  10. Students can define a logarithm, graph logarithmic functions, and use the properties of logarithms to solve exponential equations.
  11. Students can evaluate trigonometric functions at acute angles in right triangles and solve applied problems involving right triangles.
  12. Students can use the unit circle to find the values of trigonometric functions at special angles measured in degrees or radians.
  13. Students can graph the six basic trigonometric functions and their transformations by hand.
  14. Students can use trigonometric identities to simplify expressions, evaluate trigonometric functions, and solve trigonometric equations.
  15. Students can efficiently find products, quotients, powers, and roots of complex numbers using their polar forms.