Calculus Readiness Test

How do you prepare for Calculus the right way?

Maybe you are about to take calculus for the first time and you want to determine your strengths and weaknesses before starting your course.

Or maybe you’re preparing to take a calculus placement test, like Cedarville University has, in order to see if you have the sufficient mathematics background to succeed.

You’re in the right place!

Okay, so let’s be honest. Calculus is a rigorous class whether you take it in high school or college.

Calculus develops your understanding of methods and applications and most instructors will expect you to Express Concepts and Results:

• Geometrically
• Numerically
• Analytically
• Verbally

This means you not only have to know the calculus behind each question but then how to represent your findings in a clear and logical way.

So the big question is…

…are you ready for calculus?

Now, most textbooks and course outlines do their best to prepare you for what is to be expected, but sadly they leave most students anxious or simply scratching their heads in dismay.

The reason is because most instructors and textbooks will expect you to be efficient and accurate in your ability to perform computations tasks, such as simplifying and solving algebraic expressions or equations. As well as being familiar with notation for representing domain and range, as well as the relationships found the various functions listed below:

• Linear
• Polynomial
• Exponential
• Logarithmic
• Trigonometric
• Rational

Likewise, functions may be combined, transformed, and inverted to produce still more functional forms, and they can appear in various ways: formulas, graphs, datasets, tables, etc.

Doesn’t this sound overwhelming?

Please don’t let the fear of the unknown or any of the “big words” like computational, multi-representational or transcendental scare you. In fact, those words scare me too!

Getting ready for calculus is easy as long as you have the right tools and you know where to begin.

After teaching calculus for over 15 years, I can honestly say there are certain skills that are essential for students to know prior to their first day and that is what this ready-made assessment is all about.

It’s exactly what you need to test your skills and determine your preparedness for calculus. This mini placement test is broken into topics to help you recognize what I consider to be the five major skills necessary for any students taking calculus:

1. Algebra Manipulation
2. Solving Algebraic Equations
3. Graphing and Evaluating Functions
4. Simplifying and Solving Exponential and Logarithmic Equations
5. Evaluating and Solving Trigonometric Functions

So let’s break down these five big ticket items into greater detail and chat about why they’re important!

Algebraic Manipulation – Essential Skill for Higher Level Mathematics

Algebraic manipulation is all about being able to distribute and combine like terms, factoring, getting common denominators and using the conjugate.

You may be thinking…

…why do I need this for calculus? Isn’t this all algebra 1 stuff?

Yes!

But did you know that the biggest struggle for calculus students is the algebra…not the calculus!

Being able to take your derivative or integral is straightforward, but knowing how to simplify it is the magic sauce to getting the answer correct. And that’s why it’s important skill so you need to brush up on your techniques and tools.

Solving Algebraic Equations

Of course you can solve an equations!

You wouldn’t be in calculus if you couldn’t, right?

But in calculus, solving algebraic equations is more than just solving a linear equation for the unknown variable.

You need to remember when and how to factor, use the quadratic formula or possibly completing the square, and how to solve radical and rational equations.

And you will encounter questions in calculus that first need to be transformed prior to solving and you will need to remember your techniques for isolating the variable.

So it’s always a good idea to brush up on your solving skills!

Graphing and Evaluating Functions

Why do you need to know how to graph and evaluate functions?

Because you will be expected to analyze functions to determine maximum and minimum values as well as finding the domain and range.

While you can definitely do this algebraically, if you can remember what the graph looks like, you will have a leg up on your classmates.

Why? Because these skills springboard you to the answer your seek without getting bogged down with tedious algebraic steps.

Just knowing how to find vertical and horizontal asymptotes will make you a superstar.

Solving Expos and Logs

The properties for exponential and logarithmic functions are so intimately connected to the properties for derivatives and integrals, that you will smile every time you use them.

In fact, they will surely help you in memorizing your derivative rules for sure!

Furthermore, just knowing how to simplify these transcendental functions will save you time when having to take higher order derivatives or when simplifying integrands.

Yep, you read that correctly, the fancy word transcendental simply means exponential, logarithmic and inverse trig functions…

…And now I bet you’re feeling smarter already!

Evaluating and Solving Trig Functions

And probably the most important skill to review is trigonometry.

In particular, you will need to remember your Unit Circle and radian measures as well as the basic trig identities.

Why?

All throughout calculus, you will be substituting radian measures into various equations or expressions in order to evaluate limits, derivatives, and integrals; therefore, solid trig skills are a must!

In fact, just knowing knowing your Unit Circle and remembering your Pythagorean Identities can move you to the head of the class.

Calculus Assessment Test

While this test does not cover every possible problem or topic that you will encounter in calculus, it gives you a very good idea of what you are expected to know and also helps you to identify any gaps in your understanding, if there is any.

And like any new endeavor that you may pursue when preparing for calculus you just need the proper foundation.

Taking this calculus readiness test will undoubtedly help you get ready and give you the confidence you need to be successful.

Gosh, doesn’t it feel good to know how to prepare for calculus?

Pre-Test & Answer Key

• Calculus Assessment Test: Practice your skills as you get ready for Calculus 1. This readiness test includes 22 practice problems.
• Calculus Assessment Key: Check your answers and determine your areas of strength.

Video Solutions

1 hr 46 min

• Introduction to Video: Are you Ready for Calculus?
• 00:02:02 – For #1-4: Perform The Algebraic Manipulation To Simplify The Expression
• 00:20:04 – For #5-8: Solve Each Algebraic Equation
• 00:40:30 – For #9-12: Evaluate Or Graph The Given Function
• 00:56:13 – For #13-16: Use Exponential And Logarithmic Properties To Simplify, Solve Or Graph
• 01:11:36 – For #17-19: Evaluate The Trigonometric Function
• 01:22:10 – For #20-21: Solve The Trigonometric Equation
• 01:34:24 – For #22: Given A Function Find The Zeros, Sketch The Graph, Label Increasing And Decreasing Intervals And Solve For Tangent Lines