Precalculus Math Lessons
The Precalculus course in 22 lessons, from Functions, Domain and Range to Introduction to Limits, each one with its Key facts and a closing set of questions and answers.
- 86 US Letter pages
- 22 chapters
- 105 lesson sections
- PDF to print
- Cards accepted without a PayPal account
- Instant download, up to 3 devices
About this book
Precalculus gathers the tools of calculus in one course. The lessons study functions, inverses and transformations, polynomial and rational functions, exponentials and logarithms, then trigonometry from radians to identities.
Every chapter opens with the skills it builds; in Inverse Trigonometric Functions and Equations, for instance: understand the inverse trigonometric functions, evaluate compositions, solve a trigonometric equation. A Key facts box sums up what to remember. Most of the 105 lesson sections of the book are written as questions a student would ask, such as How do you solve a trigonometric equation?
For a Precalculus student heading for calculus, a parent, or a tutor. Pair it with the Precalculus Math Worksheets with Answers to practice each chapter right after reading it.
Detailed contents
The 22 chapters of the Precalculus lesson book, the sections of each lesson and the page where each chapter starts.
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1
Functions, Domain and Range
- What is a function?
- How do you find the domain of a function?
- How do you read domain and range from a graph?
- How do you test whether a graph is a function?
- What is a piecewise function?
- Precalculus functions lesson: questions and answers
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2
Combining and Composing Functions
- How do you combine two functions?
- How do you evaluate a composite function?
- Does the order of composition matter?
- What is the domain of a composite function?
- Function operations lesson: questions and answers
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3
Inverse Functions
- What is an inverse function?
- How do you find an inverse algebraically?
- How are the graphs of f and its inverse related?
- What if the function is not one-to-one?
- Inverse functions lesson: questions and answers
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4
Transformations of Graphs
- What are the basic transformations of a graph?
- How do you move a point through several transformations?
- How do reflections and stretches change a graph?
- What are even and odd functions?
- Precalculus transformations lesson: questions and answers
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5
Polynomial Functions and Their Graphs
- What is a polynomial function?
- How do you find end behavior?
- How do zeros and multiplicity shape the graph?
- How do you sketch a polynomial from factored form?
- Polynomial graphs lesson: questions and answers
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6
Polynomial Division and the Factor Theorem
- How do you divide polynomials?
- What is synthetic division?
- What do the Remainder and Factor Theorems say?
- How do you find all the zeros of a polynomial?
- Precalculus polynomial division lesson: questions and answers
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7
Complex Numbers and Complex Zeros
- What is the imaginary unit?
- How do you add, multiply and divide complex numbers?
- How do you picture a complex number?
- How do complex numbers solve quadratics?
- Precalculus complex numbers lesson: questions and answers
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8
Rational Functions and Asymptotes
- What is a rational function?
- How do you find asymptotes and holes?
- How do you find a slant asymptote?
- How do you solve rational equations?
- Rational functions lesson: questions and answers
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9
Exponential Functions and the Number e
- What is an exponential function?
- How do transformations change the graph?
- How does compound interest work?
- What is the number e?
- Exponential lesson: questions and answers
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10
Logarithms and Their Properties
- What is a logarithm?
- How is a logarithm graph related to an exponential graph?
- What are the properties of logarithms?
- Where are logarithms used?
- Precalculus logarithms lesson: questions and answers
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11
Exponential and Logarithmic Equations
- How do you solve an exponential equation?
- How do you solve a logarithmic equation?
- Why can you solve an equation by graphing?
- How are these equations used in applications?
- Exp log equations lesson: questions and answers
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12
Radians and the Unit Circle
- What is a radian?
- What is the unit circle?
- How do you find trig values for any angle?
- Angles unit circle lesson: questions and answers
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13
Graphs of Trigonometric Functions
- What do the graphs of sine and cosine look like?
- How do you read the equation
- What does the tangent graph look like?
- How do you build a trigonometric model?
- Precalculus trig graphs lesson: questions and answers
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14
Inverse Trigonometric Functions and Equations
- What are the inverse trigonometric functions?
- How do you evaluate compositions?
- How do you solve a trigonometric equation?
- Inverse trig lesson: questions and answers
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15
Trigonometric Identities
- What is a trigonometric identity?
- What are the sum, difference and double-angle formulas?
- How do you verify an identity?
- Trig identities lesson: questions and answers
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16
Law of Sines and Law of Cosines
- How do you solve a right triangle?
- When do you use each law?
- What is the ambiguous case?
- How do you find the area of a triangle?
- Laws sines cosines lesson: questions and answers
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17
Vectors in the Plane
- What is a vector?
- How do you add and scale vectors?
- What is the dot product?
- How are vectors used in applications?
- Vectors lesson: questions and answers
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18
Polar Form and De Moivre's Theorem
- What is the polar form of a complex number?
- How do you multiply and divide in polar form?
- What is De Moivre's theorem?
- How do you find the nth roots of a complex number?
- Polar complex lesson: questions and answers
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19
Sequences and Series
- What is a sequence?
- What is a series and how do you sum it?
- When does an infinite series have a sum?
- Precalculus sequences series lesson: questions and answers
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20
The Binomial Theorem
- What are factorials and binomial coefficients?
- What is Pascal's triangle?
- How do you expand a power of a binomial?
- Binomial theorem lesson: questions and answers
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21
Conic Sections
- What are conic sections?
- What is a parabola?
- What are an ellipse and a hyperbola?
- Conics lesson: questions and answers
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22
Introduction to Limits
- What is the average rate of change?
- What is a limit?
- How do you evaluate limits algebraically?
- What are one-sided limits and continuity?
- Limits lesson: questions and answers
Sample pages
Three pages from the Precalculus Math Lessons, exactly as you will print them. Click to enlarge.
How to use this lesson book
Read one chapter at a time
The 22 chapters follow the order of the Precalculus course; at about 4 pages each, a chapter is one short sitting.
Copy the key facts
Write the Key facts of Vectors in the Plane on an index card: a ready-made summary for the night before a quiz.
Try the closing questions
Cover the answers at the end of Conic Sections and answer first: the best way to check understanding.
Frequently asked questions
What is in the Precalculus lesson book?
86 US Letter pages and 22 chapters, one lesson per chapter, with 105 lesson sections in all. The full contents are listed above on this page.
Does the Precalculus lesson book include exercises?
Each chapter ends with a short set of questions and answers. For full practice, the Precalculus Math Worksheets with Answers follows the same 22 chapters.
Do I need the Precalculus Math Worksheets with Answers along with the lesson book?
No, the Precalculus Math Lessons stands on its own. But both books follow the same 22 chapters of Precalculus; together they make a complete course, lesson then practice.
How do I receive the Precalculus Math Lessons?
Right after paying with PayPal or a card, you reach your download page, where the Precalculus Math Lessons is waiting. An email with the link is sent too.
Can I print the Precalculus lesson book and open it on several devices?
Yes: the 86-page PDF of the Precalculus Math Lessons prints as often as you need and opens on three devices (computer, tablet, phone). It carries your name at the bottom of the pages.
More answers on the shop page, or through our contact form.