Precalculus (12th Grade) Math Worksheets, Lessons and Tests (Free PDF)
These precalculus worksheets follow the Common Core State Standards chapter by chapter: each chapter has a lesson, a worksheet of at least 20 worksheet problems with solutions, a timed test with its answer key and an online quiz, all with a free PDF.
Key takeaway: Precalculus prepares calculus: functions and their transformations and inverses, polynomial and rational functions, exponential and logarithmic equations, the unit circle, trigonometric graphs and identities, vectors, polar form of complex numbers, sequences and series, conic sections and an introduction to limits.
Precalculus worksheets: all chapters
1. Functions, Domain and Range
Understand a function · Find the domain of a function · Read domain and range from a graph · Test whether a graph is a function
2. Combining and Composing Functions
Combine two functions · Evaluate a composite function · Understand the domain of a composite function
3. Inverse Functions
Understand an inverse function · Find an inverse algebraically
4. Transformations of Graphs
Understand the basic transformations of a graph · Move a point through several transformations · Understand even and odd functions
5. Polynomial Functions and Their Graphs
Understand a polynomial function · Find end behavior · Sketch a polynomial from factored form
6. Polynomial Division and the Factor Theorem
Divide polynomials · Understand synthetic division · Find all the zeros of a polynomial
7. Complex Numbers and Complex Zeros
Understand the imaginary unit · Add, multiply and divide complex numbers · Picture a complex number
8. Rational Functions and Asymptotes
Understand a rational function · Find asymptotes and holes · Find a slant asymptote · Solve rational equations
9. Exponential Functions and the Number e
Understand an exponential function · Understand the number e
10. Logarithms and Their Properties
Understand a logarithm · Understand the properties of logarithms
11. Exponential and Logarithmic Equations
Solve an exponential equation · Solve a logarithmic equation
12. Radians and the Unit Circle
Understand a radian · Understand the unit circle · Find trig values for any angle
13. Graphs of Trigonometric Functions
Read the equation \(y=a\sin(b(x-h))+k\) · Build a trigonometric model
14. Inverse Trigonometric Functions and Equations
Understand the inverse trigonometric functions · Evaluate compositions · Solve a trigonometric equation
15. Trigonometric Identities
Understand a trigonometric identity · Understand the sum, difference and double-angle formulas · Verify an identity
16. Law of Sines and Law of Cosines
Solve a right triangle · Understand the ambiguous case · Find the area of a triangle
17. Vectors in the Plane
Understand a vector · Add and scale vectors · Understand the dot product
18. Polar Form and De Moivre's Theorem
Understand the polar form of a complex number · Multiply and divide in polar form · Understand De Moivre's theorem · Find the nth roots of a complex number
20. The Binomial Theorem
Understand factorials and binomial coefficients · Understand Pascal's triangle · Expand a power of a binomial
21. Conic Sections
Understand conic sections · Understand a parabola · Understand an ellipse and a hyperbola
What students learn in Precalculus
Precalculus prepares students for Calculus by making function skills fast and precise. Students review every major family of functions and analyze their graphs, limits of behavior and inverses.
In addition, the course covers trigonometry in depth: the unit circle, trigonometric graphs, identities and equations. It also includes vectors, polar coordinates, conic sections and an introduction to limits.
- Functions: polynomial, rational, exponential and logarithmic models, and their transformations.
- Trigonometry: the unit circle, graphs, identities, inverse functions, and the laws of sines and cosines.
- Vectors and polar coordinates: vectors, matrices, polar graphs, and complex numbers in polar form.
- Conics and limits: conic sections, sequences and series, and an introduction to limits.
A year plan with these precalculus worksheets
Start with a full review of functions, then spend a long block on trigonometry, because Calculus uses it constantly. Next, cover vectors and polar coordinates. Finally, conic sections, sequences and limits close the year and lead directly into Calculus.
How to use these precalculus worksheets
Pick a chapter, read its one-page lesson, then solve the worksheet on paper and check every answer with the solutions page. Take the ten-question quiz to see what is still unclear, and finish with the timed test. Every page can be printed from its PDF button, and the quick practice at the bottom of each page gives ten new questions at every visit.
Precalculus math: common questions
What grade is Precalculus?
Precalculus is usually taken in 12th grade, or in 11th grade by students who plan to take calculus.
What topics are in Precalculus?
Functions, logarithms, trigonometry and identities, vectors, complex numbers in polar form, sequences and series, conic sections and limits.
Is Precalculus harder than Algebra 2?
It goes further in the same topics, especially trigonometry, and adds vectors, conics and limits.
Can I download Precalculus worksheets?
Yes. Every lesson, worksheet and test has a free PDF to print.
Do I need Precalculus before AP Calculus?
Most students do. Precalculus builds the trigonometry, function analysis and algebra speed that AP Calculus assumes. Students who skip it often lose time reviewing these skills during the Calculus course.
What is the unit circle used for?
The unit circle gives the sine and cosine of any angle as the coordinates of a point on a circle of radius 1. For example, at 60°, the point is (1/2, √3/2), so cos 60° = 1/2.