# FREE CLEP PRACTICE TEST:

COLLEGE MATHEMATICS

#### Table of Contents

You are probably wanting to enhance your college degree or just skipping a beginner course by taking the College Mathematics CLEP exam. You want to play with those X’s and Y‘s brothers. That’s great. But before we talk about that, here are some few things you need to know.

This easy exam (as you will discover why, soon) covers material not meant for people in fields requiring knowledge of advanced math, but geared towards testing some basic math stuff. Basic topics ranging from Algebra and Functions to much more fun topics like logic and sets, numbers, geometry will be tested.

Then we will get into interesting topics like counting and probability, financial mathematics, data analysis and statistics. Hey! You do not have to work out your brain trying to do a complex calculation. That’s because there is a scientific calculator built into the exam software which is available for use by candidates during the exam. Hope you are beginning to see how easy this is.

So, if you have played this X and Y video game at high school or during some extracurriculars, you’ll likely find this test super easy and fun. If you did not get the chance to play this video game while at high school, don’t be worried. You can still learn how to play it in no time. Well, at least before you sit in for the exams. It is just basic Math so you should not be intimidated. Being basic doesn’t mean you have to neglect it. Sure, you need to get prepared. You need to learn how to use the game controllers and learn some key moves that is going to make you win.

## Fast College Mathematics

Study Guide

The seven-sectioned exam is divided into the following:

#### Algebra and Functions (20%)

In this section, candidates are required to play the X and Y game in solving linear equations and linear inequalities, Interpret, represent and evaluate functions using numerical, graphical, symbolic, and descriptive methods. You also need to be able to understand some basics of graphs of functions like translations, symmetry and reflections about the x-axis, y-axis and the origin. It will be then required to know some applications of these functions. Mathematics, especially functions is fun (you even see ‘fun’ in functions) because you just follow a rule and that’s it. You are there.

#### Counting and Probability (10%)

This section deals with straight forward counting problems involving permutations, combinations and the multiplication rule. Then probability questions will be given which will cover topics like conditional probabilities, union, intersection, independent events, mutually exclusive events and complementary events. Yes, you need to know some application problems too.

#### Data Analysis and Statistics (15%)

Here, you need to know about Data interpretation and representation techniques such as histograms, bar graphs, line graphs, circle graphs, pie charts, scatterplots, and tables. You should also be able to perform some simple calculations on numerical data like finding the mean (average), median, mode, and range, standard deviation and normal distribution of a set of data and some application questions.

#### Financial Mathematics (20%)

This is that section even my grandma will be able to do because it deals with money calculations like profit and loss, discounts, taxes, simple and compound interest, continuous interest, effective interest rate, effective annual yield or annual percentage rate (APR) and some application questions. Even if we are bad at other areas, when we deal with money we are actually working with something already know.

#### Geometry (10%)

We deal with various shapes every day and so this section is going to be fun dealing with. Properties of triangles and quadrilaterals such as perimeter, area, similarity, and the Pythagorean theorem are things you will see together with trivial stuff like Parallel and perpendicular lines. Another easy topic in this section will be circles and its properties including circumference, area, central angles, inscribed angles, and sectors. This section is very basic.

#### Logic and Sets (15%)

Even if you have problems performing some calculations or loathe remembering formulas, then this is your section. Pretty easy! You will deal with Logical operations and statements like conditional statements, conjunctions, disjunctions, negations, hypotheses, logical conclusions, converses, inverses, counterexamples, contrapositives and logical equivalence. You see set applications every day, so applying them on paper should not be a big deal. You will be required to know easy Set stuff like Set relationships, subsets, disjoint sets, equality of sets, and Venn diagrams and also Operations on sets such as union, intersection, and complement.

#### Numbers (10%)

Finally, Numbers. We use this all the time in finance, quantity of groceries purchased at the grocery store and the list keeps going. This section is definitely not your nightmare. Things like Properties of numbers such as integers and rational, irrational, and real numbers and their operations will be tested upon. Furthermore, Elementary number theory including factors and divisibility, primes and composites, odd and even integers, and the fundamental theorem of arithmetic. They will also want to test your measurement skills here in the areas of unit conversion, scientific notation, numerical precision and Absolute value. These will all be seen in applications.

#### In Summary

So, as earlier mentioned, all these areas to be tested on were not frightening as you may have envisaged. For those you think you may have some slight challenges, the CLEP board offers you the Scientific calculator. That is just like giving you a cheat sheet during an exam. Yes, it is. The scientific calculator allows you perform those numerical calculations you don’t want to over work on. It is just no ordinary calculator but a scientific one. That is how easy and less stressful the CLEP College Mathematics exam has been made to be. Don’t get super excited with the easy nature of this exam and forget to do your homework. Don’t just underestimate the exam. Prepare enough and you should be good to go.

## College Mathematics

Practice Quiz

So, let’s quit the math talk and give it a try. Are you ready? Get your pen and paper and see how well you can play this game. Once you have your answers, write them down and check against the answers and explanations below (click or tap on your phone).

###### Warning

Please do keep in mind that we can’t guarantee the accuracy of this quiz, so we do recommend you also run through a full-length practice exam. The CollegeBoard offers a good one that we’ll share in the resources section below.#### Question 1. Which of the following is the converse to the statement “All footballers are rich people”

a. Some footballers are poor

b. All rich people are footballers

c. Rich people must not be footballers

d. Some poor people are footballers

In logic, the converse of a statement is a result of reversing its two parts i.e. If W implies X then the converse will be X implies W. So, applying that to our statement, we just need to reverse the two parts of the statement to give “All rich people are footballers”

#### Question 2. What is the largest real number less than 20?

a. 19

b. There is no largest real number less than 20

c. 19.999…….

d. None of the above

Very tricky a question. At the first glance, you might want to choose 19. Then on a second thought you might think it’s C). But hey! The largest real number less than 20 and C) says it continues on and on. That simply tells you it goes on to infinity and thus there is real no real number less than 20.

#### Question 3. What are the X- and the Y- intercepts of this equation: 4X + 16Y = 32

a. X=8 Y=2

b. X=2 Y=8

c. X=0 Y=0

d. X=4 Y=16

The X- intercept is gotten by setting Y=0 and solving for X which gives you 8.

Similarly, the Y- intercept is gotten by setting X=0 and solving for Y which gives Y=2.

#### Question 4. If A= (2,4,8,15) and B= (3,6,10,12) how many elements are in the union of A and B?

a. 4

b. 2

c. 8

d. 7

The union of sets A and B involves “bringing the elements of both sets together”. Thus, doing that will give you 8.

#### Question 5. Which of the following sets is the biggest?

a. Rational numbers

b. Real numbers

c. Irrational numbers

d. Complex numbers

You will quickly go for option A). But it probably did not come quickly to your mind that complex numbers are composed of two parts- the real part and the imaginary part. So, you see. All the other options are real numbers and real numbers are a part of complex numbers. This thus crowns the set of complex numbers the largest set of numbers.

#### Question 6. Two fair coins are tossed at the same time. What is the probability of getting just one head?

a. 1/4

b. 1

c. 1/8

d. 1/2

When 2 coins are tossed, the possible outcomes are (TH, HT, TT, HH), where H is Head and T is Tail. So, the total number of outcomes are 4. To get just one head will mean having either HT or TH outcomes. Thus, the desired number of outcomes becomes 2. So, the probability of getting just one head will be gotten by dividing the total number of outcomes by the desired number of outcomes. Doing that gives you 2/4 which results to 1/2.

#### Question 7. Jane had the following scores in ten different mathematics tests she wrote during the first semester: 14.5, 12, 08, 06, 15, 18, 12.5, 20, 16, 15.

What is her mean score?

a. 13.7

b. 10

c. 17

d. 15

This type of questions should be the questions you smile when you read through. You just need to get the mean of those set of values given by sum of values divided by total number of values. The sum of values is 137 and the total number of values (total number of test scores) is 10. Doing a division of 137 by 10 gives you 13.7. Easy, right? More also you have the scientific calculator which will be a matter of seconds to input the data and punch to get your answer.

#### Question 8. Two circles A and B have radii r and 2r respectively. What can you say about the two circles?

a. The circumference of B is two times the circumference of A

b. They have the same areas.

c. They have the same circumferences

d. The area of B is two times the area of A

This question simply tests your knowledge of the formula for the area and circumference of a circle. The radius of B is twice that of A. So, fitting that into the formulas for circumference and area of a circle, B has twice the circumference of A and four times the area of A.

#### Question 9. A sum of $25000 became $27250 at the end of 3 years when calculated at simple interest. What was the rate of interest?

a. 7%

b. 10%

c. 3%

d. 72%

Again, just an application of formula. Simple interest is given by principal x rate/100. So, in this question, you just need to make “rate” the subject of the formula. So, deducing the simple interest to be $27250-$25000 gives $2250. Then you just do some little manipulations getting the rate as the subject of the formula and having your result to be 3%.

#### Question 10. Batman and Superman took five hours to smash a building to pieces. How long will it take Batman and Superman do smash five buildings similar to the one they first smashed?

a. They will take 2 seconds

b. They will take 5 hours

c. They would not be able to smash 5 buildings

d. They will take 25 hours

## More CLEP Study Resources

Looking for a study guide to fill a couple gaps, or just want a full length practice exam? You can find a few of my favorite resources below. Note that some of the links are affiliate – meaning I’ll make a few dollars if you purchase, but I’m only sharing those resources that were genuinely helpful during my own CLEP journey.

**Official CLEP Study Guide**: It’s quite short on the study side of things, but this is the go-to practice test bank. I don’t think I’ve done a single CLEP test without taking the practice test in this book first.

**REA CLEP College Mathematics**: I’m not huge on reading, but this book series is fantastic if you’re into that kind of thing. It also includes some nifty online practice tests, though I always found the official practice tests more reassuring.

**InstantCert Academy**: The website looks like it was made before the internet, but it’s legitimately the single most useful study guide I’ve found. Basically it’s a series of flashcards that help you learn about College Mathematics in a fast paced and fun way.

Plenty of other resources exist – just do a quick internet search – but these are the three that I’ve personally found the most helpful back when I did CLEP.

Congrats on starting your CLEP study journey! Study hard, earn credit, and most of all remember to have fun.