How to Prepare for Calculus 2

You’re about to embark on the thrilling adventure known as Calculus 2.

Jenn, Founder Calcworkshop^®, 15+ Years Experience (Licensed & Certified Teacher)

Calculus 2 is also known as Integral Calculus.

From your previous studies, you have understood how calculus describes the rate of change and how we use limits and derivatives to help define and represent that change.

But now we are going to learn a third component: antidifferentiation!

Antidifferentiation is the inverse operation of differentiation, and it is more commonly referred to as integration.

Students going into Calc 2 will jump in, feet first, into how we can use various methods to calculate area, volume, motion, and distance.

Therefore, it is extremely important to be prepared and have a good idea of what to expect along the way.

First, every student is expected to remember their limit and derivative rules.

Why?

Because you will find that just as limits helped us to represent and define derivatives, they will also give us the building blocks and framework for much of what we will do with integration.

Secondly, a solid understanding of functions and domain and range will significantly increase your level of success. You will be finding area between curves and volumes of solids of revolution. Consequently, you will need to remember how to graph various functions and identify key components such as zeroes, vertices, and domain.

Thirdly, a good command of solving polynomial, radical, and trigonometric equations will be an invaluable skill. All throughout your study of Calc 2, you will be learning various integration techniques. For example, when discovering the method of Partial Fractions, you will need to be able to solve equations involving algebraic fractions. And when you are finding the area of Polar Curves, being able to solve trig equations, along with your mastery of the Unit Circle, will be essential.

And one of the most important concepts in this course is Sequences and Series. Therefore, it is a good idea for students to review the basics of summation notation from Algebra 2 and Precalculus.

Now, there are countless other topics that students will see in their study of Calculus 2, but after teaching this course for over 15 years, I have found that if students can remember some basic concepts they will find greater success in their studies.

To assist you, I have prepared this Calculus 2 readiness test, so you can check your understanding of these foundational concepts and get a feel for what is expected as you get ready for Calc 2.

Pre-Test & Answer Key

• Calculus 2 Prep Test: Practice your skills as you get ready for Calculus 2. This readiness test includes 20 practice problems.
• Calculus 2 Prep Key: Check your answers and determine your areas of strength and weakness.

Video Solutions

1 hr 22 min

• Introduction to Video: Are you Ready for Calculus 2?
• 00:00:00 – For #1-3: Evaluate the Limit
• 00:13:04 – For #4-5: Write the equation of the tangent line and find the derivative of the given function
• 00:23:26 – For #6: Find the second derivative using implicit differentiation
• 00:32:15 – For #7-9: Solve the equation
• 00:42:33 – For #10-11: Solve the equation
• 00:54:07 – For #12-14: Sketch the graph and determine domain and range
• 00:59:48 – For #15-16: Sketch the graph and determine domain and range
• 01:07:11 – For #17: Find the points of intersection
• 01:10:51 – For #18: Write the first five terms of the sequence
• 01:15:38 – For #19-21: Find the sum of the series