Patrick Jones - Calculus - 1001 Practice Problems For Dummies (+ Free Online Practice)

Calculus For Dummies: This book provides instruction parallel to the 1,001 calculus practice problems found here.

Calculus II For Dummies: This book provides content similar to what you may encounter in a second-semester college calculus course.

Pre-Calculus For Dummies: Use this book to brush up on the foundational skills and concepts you need for calculus — solving polynomials, graphing functions, using trig identities, and the like.

Trigonometry For Dummies: Try this book if you need a refresher on trigonometry.

Part 1

IN THIS PART …

The only way to become proficient in math is through a lot of practice. 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 4through 7)

Applications of derivatives ( Chapter 8)

Antiderivative basics ( Chapters 9and 10)

Applications of antiderivatives ( Chapter 11)

Antiderivatives of other common functions and L’Hôpital’s rule ( Chapter 12)

More integration techniques ( Chapters 13and 14)

Improper integrals, the trapezoid rule, and Simpson’s rule ( Chapter 15)

Chapter 1

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.

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

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.

1–13Simplify the given fractions by adding, subtracting, multiplying, and/or dividing.

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14–18Simplify the given radicals. Assume all variables are positive.

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19–20Convert between exponential and radical notation.

19. Convert to radical notation. ( Note: The final answer can have more than one radical sign.)

20. Convert to exponential notation.