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Free clep college math practice problems, all clep college math resources.

Our free CLEP College Math Practice Tests are each a selection of 10 to 12 questions, which will give you a cross-section of topics from the CLEP College Math exam. You might think of them as little quizzes, which you can use to hone your skills.

Free CLEP College Math Practice Tests

The CLEP College Mathematics exam tests students on general mathematics courses such as algebra, probability, statistics, and geometry. It does not cover specialized and advanced math courses. The examination consists of 60 questions, and students are given 90 minutes to complete the exam.

Varsity Tutors’ Learning Tools provide a variety of free CLEP College Mathematics study material to assist you as you prepare for your mathematics test. On Varsity Tutors’ Learning Tools for CLEP College Mathematics website, you have access to over a thousand flashcards related to CLEP College Mathematics, daily questions covering content, and practice tests. Varsity Tutors’ Learning Tools Practice Tests for CLEP College Mathematics provides you with free College Mathematics practice by offering practice tests for the CLEP College Mathematics exam. Each practice test has a number of questions that emulate the questions that will appear on the actual exam. By completing the practice tests, you better your chances of preparing for the actual exam.

After completing the CLEP Math practice test, you can read a detailed explanation of each problem’s solution in the question overview section at the bottom of the page. In this explanation, you are given a comprehensive breakdown of how the correct answer was reached, along with important formulas and key definitions. In addition, you are told the difficulty of the question and the percentage of students who have correctly answered the problem. Here, you can also see how long it took you to answer the question, and compare that to how long it has taken the average user. With the help of Varsity Tutors’ Learning Tools, CLEP College Mathematics preparation has become simple and efficient.

The practice tests are an excellent way for you to estimate how well you will do on the actual CLEP College Math exam. Varsity Tutors’ Learning Tools provide you with a number of detailed charts and diagrams at the end of the practice test. Along with being able to check your percentile rank, you are able see the percentage of questions you answered correctly and compare that with the percentage of other people who answered each question correctly. Furthermore, you can share your results on a number of social media platforms, so that you can compare results with your study partners. By completing the free CLEP Mathematics practice tests online, you may develop a deeper understanding of the material covered. The practice tests also allow you to track your results and customize your study plan.

While the CLEP College Mathematics test can be daunting and overwhelming, the material available on Varsity Tutors’ Learning Tools website can help improve your study experience. By utilizing the College Mathematics example questions from the practice tests, you will be able to prepare for a number of topics. The free test questions online cover subsections of the CLEP College Mathematics test, including probability, prime and composite number, algebra, and geometry.

Varsity Tutors’ Learning Tools Practice Tests for CLEP Mathematics are an excellent way for you to build your confidence before the test. The practice tests give you a great deal of College Mathematics study help. Not only do Varsity Tutors’ Learning Tools Practice Tests help you review mathematics, but they can also help you prepare yourself for your CLEP Mathematics test day.

Practice Quizzes

Clep college math problem set 1, clep college math problem set 2.

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CLEP College Mathematics Practice Test

Prepare for your test with realistic questions.

The College Board administers the College-Level Examination Program (CLEP), which offers affordable exams that help students receive college credits. This article covers the CLEP College Mathematics exam, which covers topics that are generally taught in courses for non-math majors in college.

Click “Start Test” above to take a free CLEP College Mathematics practice test!

What is the CLEP College Mathematics Exam?

As mentioned previously, CLEP exams can be taken to earn college credits for the things you already know. If you have learned the exam material through on-the-job training, previous studies, or simple life experience, you can take this one exam and receive college credit as if you took the one-semester course!

By taking and passing the CLEP College Mathematics exam, you can skip the algebra class at college. This will potentially:

• Allow you to earn three or more college credits
• Save you money because the test is cheaper than a semester at college
• Allow you to graduate on time or possibly to graduate ahead of schedule
• Add flexibility to your degree program

Taking the CLEP College Mathematics exam can save you from hours of classwork and all of the hours of homework that professors assign. You should check with your college before taking this exam to make sure they will accept it.

CLEP College Mathematics Exam Eligibility

Anyone has the ability to take a CLEP exam at any time they wish! There are no age restrictions or educational requirements.

Here are some examples of who takes the CLEP College Mathematics exam:

• College students
• High school students who are preparing to graduate
• Homeschool students
• Adults who are returning to school
• Professionals who want to use the exam results to help advance their careers
• Applicants to master’s degree programs that still have undergraduate prerequisites they need to fulfill

CLEP College Mathematics Exam Outline

The CLEP College Mathematics exam contains 60 questions and has a time limit of 90 minutes.

About half of the questions will focus on your ability to solve simple, straightforward problems, while the other half of the questions are centered on more complex problems that require you to fully understand the concepts at hand.

The questions are split into seven categories:

Algebra and Functions (20%)

The knowledge and skills tested in this section include:

• Solving equations
• Solving linear inequalities and systems of linear equations
• Interpretation and evaluation of functions
• Graphs of functions
• Linear and exponential growth

The types of functions covered in this category are linear, polynomial, exponential, radical, piecewise defined, and logarithmic.

Counting and Probability (10%)

• Multiplication rules
• Intersection
• Complementary events
• Conditional probability
• Expected value

Data Analysis and Statistics (15%)

• Data interpretation and representation
• Numerical summaries of data
• Standard deviation
• Normal distribution

Financial Mathematics (20%)

• Present value
• Future value

Geometry (10%)

• Properties of triangles
• Properties of quadrilaterals
• Parallel and perpendicular lines
• Properties of circles

Logic and Sets (15%)

• Logical operations and statements
• Set relationships
• Disjoint sets
• Equality of sets
• Venn diagrams
• Operations on sets

Numbers (10%)

• Properties of numbers
• Elementary number theory
• Measurements
• Absolute value

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CLEP College Mathematics Exam Registration

The CLEP College Mathematics exam is administered on a flexible schedule throughout the year, and you can register online via the College Board website.

Before you can register, you will need to create a College Board account on their website. This account will allow you to manage your profile, see the exams you have taken, and view the grades of the exams you have taken.

During the registration process, you will need to pay the $90 exam fee. You will also choose whether to take the exam at a testing center or remotely.

Testing In-person

Once you have selected the test center and time that you want to take the exam, you will need to return to the portal of the CLEP website and print your ticket. You will not be admitted into the testing center without this printed ticket.

Testing Remotely

Before registering to take the exam remotely, you should ensure that you meet the technical requirements:

• You must have a PC desktop or laptop (Macs, Chromebooks, and tablets are not supported).
• Your computer must be using the Windows 10 operating system (Windows 11 is not supported).
• Your computer must have the most recent version of Google Chrome installed.
• You must have a speaker of some kind, internal or external (headphones are not allowed).
• You must have a camera and microphone, internal or external.
• You must have a reliable internet connection.

Once you have selected the day and time that you want to take the exam, you will need to return to the portal of the CLEP website and download the ETS Online Test application. This application is what allows you to take the exam on your computer at home.

In-person Testing

You should arrive at the testing center 15-30 minutes earlier than your scheduled exam time. After you arrive, you will be asked to provide a valid form of photo ID and your printed registration ticket.

Before you enter the testing room, you will be asked to leave all personal items behind. These include your cell phone, pencils, books, notes, calculators, bags, and food items.

Because you cannot bring your own calculator, a TI-30XS MultiView scientific calculator will be made available within the testing software throughout the entire exam:

Remote Testing

You should log in to your CLEP account 15-30 minutes prior to the scheduled time. Once you have logged in, you will need to download and install the Proctortrack desktop app. Within this app, you will be asked to verify your identity with a face scan and a scan of a valid photo ID. You will also be instructed to scan your testing room with your webcam so the proctor can determine that there are no prohibited items in your testing area.

Once the verification process is complete, you will need to open the ETS Online Test application, where the proctor will get you set up and begin the exam.

During the exam, you must ensure that no one enters your testing room. If someone does enter, you must ask them to leave, and you cannot say anything else to them.

How the CLEP College Mathematics Exam is Scored

the CLEP College Mathematics exam is scored on a point system, with each correct answer adding one point to your score. You will not have points taken away for any incorrect answers. If you skip a question, you will not have points taken away.

The number of correct answers you have will be your raw score. The raw score that you receive will be converted into a scaled score. A scaled score is typically in numeric form ranging from 20 to about 80.

Your unofficial score report will be available on your screen as soon as you finish the exam, and an official report will be made available the next day when you log in to your CLEP account.

Passing Score

There is no set passing score for this exam. The college of your choice will have its own score requirements. You can generally find this score requirement on the college website.

According to the American Council on Education, a score of 50 or higher on the scaled score is often what colleges require.

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How to Study for the CLEP College Mathematics Exam

How to study effectively.

Your success on CLEP test day depends not only on how many hours you put into preparing but also on whether you prepared the right way. It’s good to check along the way to see whether your studying is paying off. One of the most effective ways to do this is by taking CLEP College Mathematics practice tests to evaluate your progress. Practice tests are useful because they show exactly where you need to improve. Every time you take a free CLEP College Mathematics exam practice test, pay special attention to these three groups of questions:

• The questions you got wrong
• The ones you had to guess on, even if you guessed right
• The ones you found difficult or slow to work through

This will show you exactly what your weak areas are and where you need to devote more study time. Ask yourself why each of these questions gave you trouble. Was it because you didn’t understand the material? Was it because you didn’t remember the vocabulary? Do you need more repetitions on this type of question to build speed and confidence? Dig into those questions and figure out how you can strengthen your weak areas as you go back to review the material.

Answer Explanations

Additionally, many CLEP practice tests have a section explaining the answer choices. It can be tempting to read the explanation and think that you now have a good understanding of the concept. However, an explanation likely only covers part of the question’s broader context. Even if the explanation makes sense, go back and investigate every concept related to the question until you’re positive you have a thorough understanding.

Comprehend Each Topic

As you go along, keep in mind that the CLEP College Mathematics practice test is just that: practice. Memorizing these questions and answers will not be very helpful on the actual test because it is unlikely to have any of the same exact questions. If you only know the right answers to the sample questions, you won’t be prepared for the real thing. Study the concepts until you understand them fully, and then you’ll be able to answer any question that shows up on the test.

Strategy for CLEP College Mathematics Practice

When you’re ready to start taking practice tests, follow this strategy:

• Remove Limitations. Take the first test with no time constraints and with your notes and CLEP College Mathematics study guide handy. Take your time and focus on applying the strategies you’ve learned.
• Time Yourself. Take the second practice test “open book” as well, but set a timer and practice pacing yourself to finish in time.
• Simulate Test Day. Take any other practice tests as if it were test day. Set a timer and put away your study materials. Sit at a table or desk in a quiet room, imagine yourself at the testing center, and answer questions as quickly and accurately as possible.
• Keep Practicing. Keep taking practice tests on a regular basis until you run out of practice tests or it’s time for the actual test. Your mind will be ready for the schedule and stress of test day, and you’ll be able to focus on recalling the material you’ve learned.

Can I use a calculator on the CLEP College Mathematics exam?

Yes, a digital calculator will be provided for you to use on this exam.

How many questions are on the CLEP College Mathematics exam?

There are 60 questions on this exam.

How long is the CLEP College Mathematics exam?

The time limit for this exam is 90 minutes (1.5 hours).

Are formulas given on the CLEP College Mathematics exam?

No, there will not be a list of formulas provided for this exam.

What is the passing score for the CLEP College Mathematics exam?

There is no set passing score for this exam.

How much does the CLEP College Mathematics exam cost?

The examination fee is $90.

By Peter Rench

Peter Rench joined Mometrix in 2009 and serves as Vice President of Product Development, responsible for overseeing all new product development and quality improvements. Mr. Rench, a National Merit Scholar, graduated magna cum laude with a Bachelor of Science in Mechanical Engineering and a minor in mathematics from Texas A&M University.

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by Mometrix Test Preparation | This Page Last Updated: October 31, 2023

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Free Practice Test: CLEP College Mathematics

Rea clep college mathematics.

*At the time of publishing.

• Exam Study Guide
• Free Practice Test
• Recommended Study Tools

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.

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 Free Practice Test

Question 1: a sum of $25000 became $27250 at the end of 3 years when calculated at simple interest. what was the rate of interest, click for answer.

Correct Answer: A. 0.03

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

Correct Answer: D. 8

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

Question 3: 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?

Correct Answer: C. 13.7

Explanation: 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 .

Question 4: Two fair coins are tossed at the same time. What is the probability of getting just one head?

Correct Answer: B. 2-Jan

Explanation: 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 5: Which of the following is the converse to the statement “All footballers are rich people”

• Rich people must not be footballers
• All rich people are footballers
• Some poor people are footballers
• Some footballers are poor

Correct Answer: B. All rich people are footballers

Explanation: 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 6: Which of the following sets is the biggest?

• Complex numbers
• Irrational numbers
• Real numbers
• Rational numbers

Correct Answer: A. Complex numbers

Explanation: You will quickly go for 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 s 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 7: Two circles A and B have radii r and 2r respectively. What can you say about the two circles?

• The circumference of B is two times the circumference of A
• The area of B is two times the area of A
• They have the same circumferences
• They have the same areas.

Correct Answer: A. The circumference of B is two times the circumference of A

Explanation: 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 8: What is the largest real number less than 20?

• There is no largest real number less than 20
• None of the above

Correct Answer: A. There is no largest real number less than 20

Explanation: Very tricky a question. At the first glance, you might want to choose 19. Then on a second thought you might think it's 19.9999.... But hey! The largest real number less than 20 and 19.9999... says it continues on and on. That simply tells you it goes on to infinity and thus there is really no real number less than 20.

Question 9: 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?

• They will take 2 seconds
• They would not be able to smash 5 buildings
• They will take 25 hours
• They will take 5 hours

Correct Answer: C. They will take 25 hours

Explanation: Well this is just common sense. ;) If they took 5 hours to smash into pieces a building, then it is very obvious that the will take 5×5 hours to smash five similar buildings. That will be 25 hours.

Question 10: What are the X- and the Y- intercepts of this equation: 4X + 16Y = 32

Correct Answer: B. X=8 Y=2

Explanation: 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.

More CLEP College Mathematics Study Resources

Official clep study guide.

While quite short on the study side of things, the official CLEP book is the go-to final practice test. Since this is the only official practice test available, I normally use it as my final spot check before taking the test.

REA offers a great combination of CLEP study tips, exam study materials, and detailed practice tests. This book functions well as the central pillar of a strong CLEP prep strategy, with resources like the Official CLEP Study Guide (above) providing a great final practice test at the end.

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 yet. Basically it’s a series of flashcards that help you study in a fast paced and fun way.

• Online Practice Tests

Mathematics Practice Questions 1

1. an instrument store gives a 10% discount to all students off the original cost of an instrument. during a back to school sale an additional 15% is taken off the discounted price. julie, a student at the local high school, purchases a flute for $306. how much did it originally cost, 2. if y(x-1)=z then x=, 3. which of the following values is not equal to 34(58+9).

• 34 * 58 + 34 * 9
• 1,972 + 306
• (9 + 58) 34

4. Two angles of a triangle measure 15° and 85 °. What is the measure for the third angle?

5. if 5 ounces is equal to 140 grams, then 2 pounds of ground meat is equal to how many grams, 6. which year did the most children take swimming lessons.

7. Between which year did the largest decrease in children taking swimming lessons occur?

8. what was the average number of children taking swim lessons from 1990 to 1995, 9. which of the following is equal to 5.93 * 10-2, 10. on a map, 1 inch represents 20 miles. the distance between 2 towns is 6 1/5 inches. how many miles are actually between the two towns, 11. which of the following is a correct graph of x>1, x<4 .

12. How many cubed pieces of fudge that are 3 inches on an edge can be packed into a Christmas tin that is 9 inches deep by 12 inches wide by 9 inches high with the lid still being able to be closed?

13. sarah is twice as old as her youngest brother. if the difference between their ages is 15 years. how old is her youngest brother, 14. which of the following fractions is equal to 5 / 6 , 15. what will it cost to tile a kitchen floor that is 12 feet wide by 20 feet long if the tile cost $8.91 per square yard, 16. in a writing competition, the first place winner receives ½ of the prize money. the second runner up receives ¼ of what the winner won. what was the total amount of prize money distributed if the winner receives $6,000, 17. you are lying 120 ft away from a tree that is 50 feet tall. you look up at the top of the tree. approximately how far is your hear from the top of the tree in a straight line, 18. a cyclist bikes x distance at 10 miles per hour and returns over the same path at 8 miles per hour. what is the cyclist’s average rate for the round trip in miles per hour, 19. if edging cost $2.32 per 12-inch stone, and you want a double layer of edging around your flower bed that is 6 yards by 1 yard. how much will edging you flower bed cost, 20. if 3x=6x-15 then x + 8=, 21. the number of milliliters in 1 liter is, 22. the cost to ride on a ferry is $5.00 per vehicle and driver with an additional cost of 50 cents per passenger. if the charge to get on the ferry is $6.50, how many people were in the vehicle, 23. what is 1 / 9 of 9, 24. in his pocket, a boy has 3 red marbles, 4 blue marbles, and 4 green marbles. how many will he have to take out of his pocket to ensure that he has taken out at least one of each color, 25. which fraction is equal to 0.20%, 26. find the missing term in the following sequence: 4, 9, 19, __, 79, 27. how much money did jessica’s budget allow for housing in april of 2001.

28. What was the average amount of money that Jessica’s budget allowed for clothing the first six months of 2001?

29. if jessica only spent 20% instead of the 25% allotment for food in may of 2001, how much did she save, 30. jonathan can type a 20 page document in 40 minutes, susan can type it in 30 minutes, and jack can type it in 24 minutes. working together, how much time will it take them to type the same document, 31. of the following fractions, which is less than 2 / 3 , 32. a hockey team won 6 games and lost 8. what is the ratio of wins to number of games, 33. sue receives a base salary of $90 weekly plus a 12% commission on all sales. sue had $3,000 in sales this week. how much did she make total, 34. if the perimeter of a rectangular house is 25 1 / 3 yards, and the length is 22 feet. what is the width, 35. jimmy made a 15% profit on the sale of a custom designed boat, and the original cost of the boat was $15,000. the boat sold for how much, 36. a recent study showed that an increase in body weight by 10 kilograms resulted in a 0.15% increase in heart disease. what fraction is equal to 0.15%, 37. 6.334 * 10 4 =, 38. if 3x + 5x = -8, then x + 1 =, 39. two angle in a triangle equal 120°. what is the measure of the third angle, 40. which of the following would be an appropriate unit to measure sugar for a cookie recipe, answers & explanations.

1.  C:  The equation,  x -0.10 x -0.15( x -0.10 x )=306, may be used to solve the problem. Solving for  x  gives 0.90 x  – 0.15 x  + 0.015 x  = 306, where  x  = 400. Thus, the original price was $400.

2.  B:  The equation may be solved by first distributing the  y  across the expression,  x  – 1, on the left side of the equation. Doing so gives:  x y  –  y  =  Z . Adding  y  to both sides of the equation gives:  x y  =  Z  +  y . Finally, division of both sides of the equation by  y  gives:  x =( Z + y )/ y  or  x = Z / y +1.

3.  B:  This problem illustrates the distributive property of multiplication over addition. The factor being distributed may not change.

4.  D:  The measure of the third angle of the triangle is equal to 180°-(15° + 85°), or 80°.

5.  C:  Since there are 32 ounces in 2 pounds (16 ounces = 1 pound), the following proportion may be written: 5/140=32/ x  . Solving for  x  gives  x  = 896. Thus, there are 896 grams in 2 pounds of meat.

6.  E:  The largest number of children taking swimming lessons, in one year, was 500, in 1995.

7.  C:  The only decrease in number of children taking swimming lessons was from 1992 to 1993, with a decrease of 200 children.

8.  B:  The average may be written as (200+250+400+200+300+500)/6, which is approximately 308.

9.  A:  Movement of the decimal point two places to the left gives 0.0593.

10.  C:  The following proportion may be used to solve the problem: 1/20=6.2/ x . Solving for  x  gives  x  = 124, so there are actually 124 miles between the two towns.

11.  A:  The correct graph should show a line segment between 1 and 4, including the points, 1 and 4.

12.  D:  The volume of the tin is 972 in”. The volume of each piece of fudge is 27 in”. 972 ÷ 27 = 36.

13.  B:  The following system of equations may be used to solve the problem: ( s =2 b @ s – b =15). Substituting 2 b  for  s , in the second equation, gives: 2 b  –  b  = 15, where  b  = 15. The younger brother is 15 years old.

14.  C:  Multiplying the numerator and denominator of the given fraction by 5 gives the fraction, 25/30, which is equivalent.

15.  B:  Converting feet to yards, the dimensions may be rewritten as 4 yards by 6 2/3 yards. Thus, the area of the floor is 26 2/3 yd’. Multiplication of this area by the cost per square yard gives the expression, 26 2/3?8.91, which equals 237.6. Thus, the cost is $237.60.

16.  C:  The following equation may be solved for  x : 6000=1/2  x . Solving for  x  gives  x  = 12,000. Thus, the amount of prize money distributed equaled $12,000.

17.  D:  The distance may be determined by writing and solving the following equation for  c : 50 2 +120 2 = c 2 .  c  = 130, thus the distance is 130 feet.

18.  D:  The average rate for the round trip is the total distance traveled divided by the total travel time. Distance traveled=2x. Travel time=x/10+x/8=4x/40+5x/40=9x/40. Average Rate=2xx9x/40=(2xx40)/9x=80/9 = approximately 8.9 mph.

19.  E:  The length is equal to 216 inches. The width is equal to 36 inches. So, the length may be covered by 18 12-inch stones, while the width may be covered by 3 12-inch stones. A total of 42 stones is needed for one layer, and 84 stones need for two layers. Multiplication of 84 by $2.32 gives 194.88. Thus, the total cost is $194.88.

20.  E:  The equation may be solved for  x  by first subtracting 6 x  from both sides of the equation. Doing so gives -3 x  = -15, where  x  = 5. Substituting 5 for  x  into the second expression gives 5 + 8, which equals 13.

21.  B:  There are 1,000 milliliters in 1 liter.

22.  D:  The problem may be modeled with the equation, 6.50 = 5.00 + 0.50 x , where  x  represents the number of passengers. Solving for  x  gives  x  = 3. Thus, there were 3 passengers, plus 1 driver, for a total of 4 people in the vehicle.

23.  C:  This problem may be represented as 1/9 . 9, which equals 1.

24.  D:  Taking out 3 of each color will ensure that he has 1 of each color. Thus, he needs to take out 9 marbles, in all.

25.  E:  0.20% = 0.002, and 1/500=0.002.

26.  D:  The increase from term to term is twice the increase from the previous two terms. Thus, the increase from 19 to the missing term will be 20, or twice the increase of 10. Thus, the missing term is equal to 19 + 20, or 39.

27.  C:  The solution may be modeled by the expression, 0.25(2490). Thus, her budget allowed $622.50 for housing in April of 2001.

28.  E:  The average may be represented as (0.10(2578)+0.10(2432)+0.10(2668)+0.10(2490)+0.10(2622)+0.10(2555))/6, which simplifies as (257.80+243.20+266.80+249.00+262.20+255.50)/6, or 255.75. The average budget amount for clothing in the first six months of 2001 was $255.75.

29.  A:  The amount she saved may be represented by the expression, 0.25(2622) – 0.20(2622), which equals 131.10. Thus, she saved $131.10.

30.  B:  The problem may be modeled with the equation, 1/40+1/30+1/24=1/ t . Solving for  t  gives  t  = 10. Thus, working together, they can type the same document in 10 minutes.

31.  D:  The fraction, 3/5, equals 0.6, which is less than 2/3.

32.  C:  The ratio may be written as 6/14, which reduces to 3/7.

33.  B:  The amount of money she made may be represented by the expression, 90 + 0.12 x , where  x  represents the amount of sales. Substituting 3000 for  x  gives 90 + 0.12(3000), which equals 450. So, she made $450 this week.

34.  A:  First, the perimeter measurement may be converted to feet. Multiplying 25 1/3 yards by 3 gives an equivalent measurement of 76 feet. Thus, the following equation may be written: 76 = 2(22) + 2 w , which simplifies to 76 = 44 + 2 w , where  w  = 16. The width of the house is 16 ft.

35.  A:  The problem may be modeled with the expression, 15,000 + 0.15(15,000), which equals 17,250. Thus, he sold the boat for $17,250.

36.  A:  3/2000=0.0015, which is equivalent to 0.15%.

37.  D:  Moving the decimal point 4 places to the right gives 63,340.

38.  C:  Solving the given equation for  x  gives  x  = -1. Substitution of -1 for  x , in the second equation, gives -1 + 1 = 0.

39.  A:  The interior angle measures of a triangle sum to 180°. Thus, the measure of the third angle is equal to the difference of 180° and 120°, or 60°.

40.  B:  Cups is an appropriate measure of capacity for sugar.

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Practice Problems

This page contains question sheets which are sent out to new students by many colleges before they arrive to start their undergraduate degree. These questions make suitable bridging material for students with single A-level Mathematics as they begin university - the material is partly revision, partly new material. All 11 sheets cover material relevant to the Mathematics, Mathematics & Statistics and Maths and Philosophy courses; sheets 8, 9 and 10 are not relevant to the Mathematics and Computer Science degree.

For each sheet the subject matter is briefly described, and there is some recommended reading material; the chapter numbers refer to the fourth edition of D.W.Jordan and P.Smith's book Mathematical Techniques, published by Oxford University Press in 2008.

• Sheet 1: Standard Functions and Techniques,  PDF Reading: §§ 1.3, 1.6-1.8, 1.10-1.16
• Sheet 2: Differentiation, PDF Reading: Chapter 2
• Sheet 3: Further Differentiation,  PDF Reading: §§ 3.1-3.5, 3.9-3.10
• Sheet 4: Applications of Differentiation, PDF Reading: §§ 4.1-4.4
• Sheet 5: Taylor Series, PDF Reading: §§ 5.1-5.4
• Sheet 6: Complex Numbers, PDF Reading: Chapter 6
• Sheet 7: Matrices, PDF Reading: Chapter 7
• Sheet 8: Vectors, PDF Reading: §§ 9.1-9.4, 9.6
• Sheet 9: The Scalar 'Dot' Product, PDF Reading: §§ 10.1-10.3, 10.9
• Sheet 10: The Vector 'Cross' Product, PDF Reading: §§ 11.1-11.2
• Sheet 11: Integration, PDF Reading: §§ 14.1-15.4, 15.8
• All the above 11 sheets as one file: PDF
• All the above 11 sheets as one webpage: Questions
• Induction 1: PDF Reading: R.B.J.T. Allenby Numbers and Proof , Chapter 7
• Induction 2:  PDF Reading: R.B.J.T. Allenby Numbers and Proof , Chapter 7
• Algebra 1: PDF Reading: No pre-requisites
• Algebra 2: PDF Reading: Chapters 7 and 8
• Calculus 1 - Curve Sketching: PDF Reading: §§ 4.1-4.4
• Calculus 2 - Numerical Methods and Estimation: PDF Reading: §4.6, §5.2
• Calculus 3 - Techniques of Integration: PDF Reading: §§17.5-17.7
• Calculus 4 - Differential Equations: PDF Reading: §§ 22.3-22.4, Chapter 18
• Calculus 5 - Further Differential Equations:  PDF Reading: Chapter 19, §22.5
• Complex Numbers: PDF Reading: Chapter 6
• Geometry: PDF Reading: §10.1, §10.9, §11.1, §16.1
• The second 11 sheets as one file:  PDF
• The second 11 sheets as one webpage: More challenging Questions
• Dynamics 1 - Basic Definitions. Newton's Second Law  PDF
• Dynamics 2 - Oscillations and Further Examples.  PDF
• These two sheets as one webpage: Further Sheets