Calculus: 1001 Practice Problems For Dummies (+ Free Online Practice). Patrick Jones
Fortunately, you have now 1,001 practice opportunities right in front of you. These questions cover a variety of calculus-related concepts and range in difficulty from easy to hard. Master these problems, and you’ll be well on your way to a very solid calculus foundation.
Here are the types of problems that you can expect to see:
Algebra review (Chapter 1)
Trigonometry review (Chapter 2)
Limits and continuity (Chapter 3)
Derivative fundamentals (Chapters 4 through 7)
Applications of derivatives (Chapter 8)
Antiderivative basics (Chapters 9 and 10)
Applications of antiderivatives (Chapter 11)
Antiderivatives of other common functions and L’Hôpital’s rule (Chapter 12)
More integration techniques (Chapters 13 and 14)
Improper integrals, the trapezoid rule, and Simpson’s rule (Chapter 15)
Chapter 1
Algebra Review
Performing well in calculus is impossible without a solid algebra foundation. Many calculus problems that you encounter involve a calculus concept but then require many, many steps of algebraic simplification. Having a strong algebra background will allow you to focus on the calculus concepts and not get lost in the mechanical manipulation that's required to solve the problem.
The Problems You’ll Work On
In this chapter, you see a variety of algebra problems:
Simplifying exponents and radicals
Finding the inverse of a function
Understanding and transforming graphs of common functions
Finding the domain and range of a function using a graph
Combining and simplifying polynomial expressions
What to Watch Out For
Don't let common mistakes trip you up. Some of the following suggestions may be helpful:
Be careful when using properties of exponents. For example, when multiplying like bases, you add the exponents, and when dividing like bases, you subtract the exponents.
Factor thoroughly in order to simplify expressions.
Check your solutions for equations and inequalities if you're unsure of your answer. Some solutions may be extraneous!
It's easy to forget some algebra techniques, so don't worry if you don't remember everything! Review, review, review.
Simplifying Fractions
1–13 Simplify the given fractions by adding, subtracting, multiplying, and/or dividing.
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Simplifying Radicals
14–18 Simplify the given radicals. Assume all variables are positive.
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Writing Exponents Using Radical Notation
19–20 Convert between exponential and radical notation.
19. Convert
20. Convert
The Horizontal Line Test
21–23 Use the horizontal line test to identify one-to-one functions.
21. Use the horizontal line test to determine which of the following functions is a one-to-one function and therefore has an inverse.
(A)