Precalculus Math Worksheets with Answers
442 exercises on the 22 chapters of Precalculus, from Functions, Domain and Range to Introduction to Limits, and in Part 2 a worked answer for every one of them.
- 222 US Letter pages
- 22 chapters
- 442 exercises with answers
- PDF to print
- Cards accepted without a PayPal account
- Instant download, up to 3 devices
About this book
The workbook practices all twenty-two chapters, including polynomial division and the factor theorem, inverse trigonometric functions, De Moivre's theorem, sequences and series, and conic sections.
Part 1 holds the worksheets, about 20 exercises per chapter, each with a short title that says what it practices, like Cosine double angle from sine in Trigonometric Identities. Part 2, which starts on page 103, gives the answers in the same order, so checking takes a minute.
For a Precalculus student heading for calculus, a parent, or a tutor. Pair it with the Precalculus Math Lessons to go back to the lesson when a problem gets stuck.
Detailed contents
The 22 chapters of the Precalculus workbook, the number of exercises in each, and the titles of the first ones.
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1
Functions, Domain and Range
- Evaluate a quadratic
- Evaluate a cubic
- Is it a function?
- Domain of a line
- Domain with a denominator
- Domain with a root
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2
Combining and Composing Functions
- Sum of functions at a point
- Difference of functions
- Product of functions
- Domain of a quotient
- Evaluate f of g
- Evaluate g of f
-
3
Inverse Functions
- One-to-one table
- Inverse of a line
- Inverse of a quotient by a constant
- Inverse of a cubic
- Inverse of a rational function
- Inverse of a root
-
4
Transformations of Graphs
- Read a horizontal shift
- Read a vertical shift
- Reflection
- Vertical stretch
- Move a point
- Reflect and shift a point
-
5
Polynomial Functions and Their Graphs
- Degree and leading coefficient
- Expand a product
- End behavior, odd degree
- End behavior, even degree
- Zeros from factors
- Multiplicity
-
6
Polynomial Division and the Factor Theorem
- Divide a quadratic
- Long division, leading coefficient 2
- Remainder from long division
- Synthetic division
- Synthetic division with c = -1
- Remainder Theorem
-
7
Complex Numbers and Complex Zeros
- Square roots of negatives
- Powers of i
- Add complex numbers
- Subtract complex numbers
- Multiply
- Square a complex number
-
8
Rational Functions and Asymptotes
- Domain
- Hole and asymptote
- Equal degrees
- Lower numerator degree
- No horizontal asymptote
- Intercepts
-
9
Exponential Functions and the Number e
- Growth or decay?
- Evaluate
- Equation from two points
- Equation from points two apart
- Town population
- Half-life
-
10
Logarithms and Their Properties
- Exponential to log form
- Log to exponential form
- Evaluate a log
- Log of a fraction
- Common and natural logs
- A fractional answer
-
11
Exponential and Logarithmic Equations
- Same base
- Same base with a shift
- Rewrite the base
- Take a log
- Isolate first
- Base e
-
12
Radians and the Unit Circle
- Degrees to radians
- Radians to degrees
- Calculator conversion
- Coterminal angles
- Reference angle
- Quadrants
-
13
Graphs of Trigonometric Functions
- Amplitude and period
- Reflected cosine
- Period with pi in b
- Phase shifts
- Midline and range
- Write an equation
-
14
Inverse Trigonometric Functions and Equations
- Exact values of inverse trig
- Negative inputs
- Domain and range
- Calculator values
- Inverse properties
- Outside the principal range
-
15
Trigonometric Identities
- Simplify a product
- Pythagorean simplification
- Sum of squares
- Double angle values
- Exact sine of 15 degrees
- Exact cosine of 15 degrees
-
16
Law of Sines and Law of Cosines
- Right triangle: find a leg
- Right triangle: tangent
- Solve a right triangle
- Law of Sines (AAS)
- Law of Sines (ASA-like)
- SSA with one triangle
-
17
Vectors in the Plane
- Component form from two points
- Magnitude
- Direction angle
- Components from magnitude and angle
- Add vectors
- Subtract vectors
-
18
Polar Form and De Moivre's Theorem
- Modulus and argument
- Quadrant II
- On an axis
- Polar to rectangular
- Polar to rectangular in radians
- Quadrant IV
-
19
Sequences and Series
- List terms
- Explicit arithmetic formula
- Formula from two terms
- Geometric formula
- Fractional ratio
- Recursive sequence
-
20
The Binomial Theorem
- Factorials
- Binomial coefficients
- Pascal's triangle
- Expand (x + y)^4
- Expand (x + 2)^5
- Expand (3x + 1)^4
-
21
Conic Sections
- Equation of a circle
- Center and radius
- Circle through a point
- Parts of a parabola
- Parabola opening left
- Equation from focus and directrix
-
22
Introduction to Limits
- Average rate of change
- Average rate of a cubic
- Average velocity
- Shrinking interval
- Limit from a table
- Direct substitution
Sample pages
Three pages from the Precalculus Math Worksheets with Answers, exactly as you will print them. Click to enlarge.
How to use this workbook
Try before you check
Work on Power in rectangular form on scratch paper before opening Part 2: that is where progress happens.
Use the numbering
Answers carry the same chapter and exercise numbers as the 22 Precalculus worksheets, so the right one is easy to find.
Target one chapter
Before a quiz on Introduction to Limits, do its 20 exercises, then redo the ones you missed.
Go further
Frequently asked questions
How many exercises are in the Precalculus workbook?
442 exercises on 222 pages, spread over 22 chapters. Each one has its answer in Part 2.
Where are the answers of the Precalculus worksheets?
In Part 2, at the end of the Precalculus workbook, starting on page 103. They are kept apart from the worksheets so a student can work without seeing them.
Do I need the Precalculus Math Lessons along with the workbook?
No, the Precalculus Math Worksheets with Answers 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 Worksheets with Answers?
Right after paying with PayPal or a card, you reach your download page, where the Precalculus Math Worksheets with Answers is waiting. An email with the link is sent too.
Can I print the Precalculus workbook and open it on several devices?
Yes: the 222-page PDF of the Precalculus Math Worksheets with Answers 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.