Placement Exam

About the Exam

Who must take the exam? ALL incoming freshmen MUST take the exam.

Transfer students without a transferable course in College Algebra or higher must plan to take the Math Placement Exam to determine the appropriate place to begin their math sequence in Pre-Calc and Calculus are going to be required for their major.

Do I have to take the exam if I know the mathematics course I need?
Yes. The "obvious" choice for your first mathematics class at UM-Dearborn might be an inappropriate choice for several reasons. If there has been a gap of even as little as 6 months since your last mathematics course, you may have become rusty. Your previous mathematics course(s) may have been taught at an easier, more relaxed pace than you will find in a UM-Dearborn classroom, or your previous course may have had a misleading title when compared to the terminology used at UM-Dearborn  (many high school classes called "Pre-Calculus" only cover half of what is covered in UM-Dearborn's Pre-Calculus class).We have created the placement exam as the means of placing you in the most appropriate class, giving you the greatest likelihood of success with the least possible expenditure of time or tuition dollars.

What is the format and content of the math placment exam (Accuplacer)?
Each of the ACCUPLACER tests is adaptive. This means that the computer automatically determines which questions are presented to you based on your responses to prior questions. This technique selects just the right questions to ask without giving you questions that are too easy or too difficult. Because the ACCUPLACER tests are adaptive, you do not have to answer as many questions as you would on a traditional paper-and-pencil test.

Since ACCUPLACER tests are adaptive and since the questions are chosen for you based on your answers to previous questions, you must answer wevery question when it is first given. You cannot leave a question and come back to it later. You must answer a question in order to go to the next question. Once you go on to the next question, you cannot return to previous questions.

If you do not know the answer to a question, you should try to eliminate one or more of the choices. Then pick from the remaining choices. There are no calculators allowed on the exam.

What kinds of questions are on Accuplacer?

You will be asked to enter some background information such as Social Security number, name and address. The background information screen is illustrated below.

Fields with an asterisk (*) must be completed. Carefully listen to the test administrator for instructions on how to complete this page.

After completing the background information screen click contiue.

The arithmetic test measures your skills in three primary categories. The first is operations with whole numbers and fractions. This includes addition, subtraction, multiplication, division and recognizing equivalent fractions and mixed numbers. The second category involves operations with decimals and percents. It includes addition, subtraction, multiplication, and division as well as percent problems, decimal recognition, fraction and percent equivalences, and estimation problems. The last category tests applications and problem solving. Questions include rate, percent, and measurement problems, geometry problems, and distribution of a quantity into its fractional parts. A total of sixteen questions are asked.

Solve the following provlems and select you answer from the alternatives giv

1. 2.75 + .003 + .158 =

A. 4.36
B. 2.911
C. 0.436
D. 2.938

2. 7.86 X 4.6 =

A. 36.156
B. 36.216
C. 351.56
D. 361.56

3. 7/20 =

A. 0.035
B. 0.858
C. 0.35
D. 3.5

4. Which of the following is the least?

A. 0.105
B. 0.501
C. 0.015
D. 0.15

5. All of the following are ways to write 25 percent of N EXCEPT

A. 0.25 N
B. 25N/100
C.1/4 N
D. 25 N

6. Which of the following is closest to 27.8 X 9.6
A. 280
B. 300
C. 2,800
D. 3,000

7. A soccer team played 160 games and won 65 per cent of them. How many games did to win?

A. 94
B. 104
C. 114
D. 124

8. 32 is 40% of what number?

A. 12.8
B. 128
C. 80
D. 800

9. 3 1/3 - 2 2/5=

A. 1 1/2
B. 1/15
C. 14/15
D. 1 1/15

10. Three people who work full time are to work together on a project, but their total time on the project is to be equivalent to that of only one person working full time. If one of the people is budgeted for 1/2 of his time to the project and a second person for 1/3 of her time, what part of the third worker's time should be budgeted to this project?

A. 1/3
B. 3/5
C. 1/6
D. 1/8

Answers to the  Arithmetic problems above.

1. B
2. A
3. C
4. C
5. D
6. A
7. B
8. C
9. C

Elementary Algebra
There are also three categories in the Elementary Algebra Test. The first category, operations with integers and rational numbers, includes computation with integers and negative rationals, the use of absolute values, and ordering. The second category is operations with algebraic expressions. It tests your skills in evaluating simple formulas and expressions, and in adding and subtracting monomials and polynomials. Both of these categories include questions about multiplying and dividing monomials and polynomials, evaluating positive rational roots and exponents, simplifying algebraic fractions, and factoring. The third category tests skill in solving equations, inequalities, and word problems. These questions include solving systems of linear equations, quadratic equations by factoring, verbal problems presented in algebraic context, geometric reasoning, the translation of written phrases into algebraic expressions, and graphing. Twelve questions are presented.

Solve the following problems and choose your answer from the alternatives given.

1. (2)^1/2*(15)^(1/2)= ?

A. 17
B. 30
C. (30)^2
D. (17)^2

2. What is the value of the expression 2x^2 + 3xy - 4y^2 when x = 2 and y = - 4?

A. -80
B. 80
C. -32
D. 32

3. (3x - 2y)^2 =

A. 9x2 - 4y2
B. 9x2 + 4y2
C. 9x2 + 4y2 - 6xy
D. 9x2 + 4y2 - 12xy

4. (x^2 - x - 6)/(x^2 - 4) =

A. (x-3)/2
B. (x-3)/(x-2)
C. (x-3)/(x+2)
D. 3/2

5. (4 - (- 6))/(-5) =

A. 2/5
C. 2
D. - 2

6. If 2x - 3(x + 4) = - 5, then x =

A. 7
B. - 7
C. 17
D. -17

7. - 3(5 - 6) - 4(2 - 3) =

A. -7
B. 7
C. -1
D. 1

8. If 20 - x > 16, then

A. X < 5
B. X > 5
C. X > 32
D. X < 32


9. If A represents the number of apples purchased at 15 cents each and B represents the number of bananas purchased at 10 cents each, which of the following represents the total value of the purchases?

A. A + B
B. 25(A + B)
C. 10A + 15B
D. 15A + 10B

10. In the figure below, both circles have the same center, and the radius of the larger circle is R. If the radius of the smaller circle is 3 units less than R, which of the following represents the area of the shaded region?

A. Pi R^2
B. Pi (R - 3)^2
C. Pi R^2 - Pi . 3^2
D. Pi R^2 - Pi (R - 3)^2

Answers to the Elementary Algebra problems above.

1. C
2. A
3. D
4. B
5. D
6. B
7. B
8. A
9. D


College-Level Mathematics
The College-Level Mathematics test assesses proficiency from intermediate algebra through pre-calculus. Five categories are covered. The first category, algebraic operations, includes simplifying rational algebraic expressions, factoring, expanding polynomials, and manipulating roots and exponents. The second category, solutions of equations and inequalities, includes the solution of linear and quadratic equations and inequalities, equation systems, and other algebraic equations. Coordinate geometry asks questions about plane geometry, the coordinate plane, straight lines, conics, sets of points in the plane, and graphs of algebraic functions. Applications and other algebra topics asks about complex numbers, series and sequences, determinants, permutations and combinations, fractions, and word problems. The last category, functions and trigonometry, presents questions about polynomial, algebraic, exponential, logarithmic and trigonometric functions. Twenty questions are asked.

1. Solve for x: | 7x - 2 | = x + 4

2. Simplify: (x - 1) / (2x - x - 1)

3. If g(x) = x + 1, then g(a) + g(a + 2) = ?

4. Factor: 16x - y

5. If f(x) = x - 4x - x + 1, then f(-x) = ?

6. Evaluate: SUM( 2^n + 1), for n = 0 to n = 3

7. Where defined, simplify: (x - 1/x) /(1 + 1/x)

8. If f(x) = 3/(x + 2) and g(x) = x/(x - 4), find f(x) + g(x)

9. Solve: x + 3x - 10 < 0

10. If f(x) = 3x and g(x) = 1 + x , then f(g(x)) = ?

11. Factor: 3x(4x + 2) + 4x + 2

12. Solve: x + 5x - 3 = 0

13. Find the solution set of: (x + 2)^(1/2) = -4

14. Factor: 5x - 20x + 15

15. Find all roots of: x4 - 10x + 9 = 0


16. If the domain D of the function f is the set of all real numbers x for which
f(x) = 3/(2x - 8) is a real number, then D is what set of numbers?

17. The graph of which of the following equations is a straight line parallel to the graph of
y = 4x ? (a) x - y = 4; (b) 4x + y = 2; (c) y - x = 3; (d) y = -4x

18. The ground floor of the John Hancock building in Chicago is a rectangle whose perimeter is 860 feet. The length is 100 feet more than the width. Find the length and width.

19. The first and third terms of a geometric sequence are 75 and 3. The second term could be: (a) 25; (b) 15; (c) -25; (d) 36

20. If f(x) = 2x + 1 and f -1 denotes the inverse of f, then f -1(0) = ?

Answers to the College-Level Mathematics problems above.

1. x = - or x = 1

2. (x + 1) / (2x + 1)

3. 2a + 4 or 2(a + 2)

4. (4x + y)(4x - y)

5. -x - 4x + x + 1

6. 19

7. x - 1

8. (x+ 5x -12) / (x - 2x - 8)

9. -5 < x < 2

10. 3 + 3x or 3(1 + x)

11. (3x + 1)(4x + 2)

12. (-5 v37 ) / 2

13. No solution

14. 5(x - 1)(x - 3)

15. x = 1 and x = 3

16. {x: x ? 2}

17. (c)

18. width = 165 feet,
length = 265 feet

19. (b)

20. -


How do I prepare for the exam?
Review your last mathematics test as well as the notes and text you used. There are mathematics textbooks and videos in the UM-Dearborn Mardigian Library that may be helpful. Review "familiar" sections and problems if it has been more than a few years since your last mathematics course, also review the problems at one level below the last course that you completed. Time yourself doing a practice test.

Some materials for exam preparation:

What are the possible outcomes of the examination, and how are the results related to mathematics requirements?
The results of the exam will be evaluated along with your previous mathematics background and your ACT or SAT scores (when available), and you will be placed in the appropriate algebra, Pre-Calculus, or Calculus I course. Algebra courses (Math 080 and Math 090) at UM-Dearborn award additive credit only (credit which is in addition to credit requirements for graduation, and will not count toward graduation or toward fulfilling requirements). For many concentrations, completing one mathematics course will fulfill your mathematics requirement (it must be a course for degree credit, not additive credit). Other majors require much more mathematics. Please consult the Undergraduate Announcement or speak with your academic advisor concerning the requirement in your specific situation.

Placement into Math 080/090 (Introductory/Intermediate Algebra):
If you have had only one year of algebra, you will probably place in one of our review algebra courses. You may also need to take one of these algebra classes to upgrade your skills in preparation for Math 105.

Placement into Math 105 (Pre-Calculus):
This placement allows you to take Math 104 (Precalculus without Trigonometry) or Math 105 (Precalculus with Trigonometry) depending on your major. Please talk to your advisor regarding the appropriate course to take. If you are undecided about your major, taking Math 105 will keep all your options open. If you are placed into Pre-Calculus, be prepared to work very hard; even the well-prepared students report spending 3-4 hours per night on homework. This is a jam-packed course with no time for a significant review of background algebra. There is brief, superficial coverage of some algebra topics. You should be concerned if much of that material seems unfamiliar. Be conservative about deciding to stay in the course while reviewing algebra. We are conservative about placing you into Pre-Calculus, and you should be equally protective of your own best interests.

Placement into Math 113/115 (Calculus I):
If you have never had trigonometry, you will not be able to take the Calculus I (Math 115) course that is designed for mathematics, science, and engineering majors, You may, however, be prepared to take the  Calculus I (Math 113) designed for business and social science majors. The course that you choose will depend on your academic goals; discuss this with your advisor.

Placement into Math  116/215 (Calculus I and II):
If you have had some calculus and are hoping to place into Calculus II or above, you must either:

  • Take the AP (Advanced Placement) Exam given by the Educational Testing Service, or
  • Receive transfer credit for the appropriate prerequisite(s), or
  • Contact the Department Chair for special circumstances.


Is it possible to retest if I am not satisfied with the results? Yes, retesting is possible. However, you must wait at least 2 weeks before you retest. We recommend that you use this time to review. The Orientation Office has a schedule of dates when mathematics placement retesting will be available. If you wish to retest, please contact the Orientation Office at (313) 593-5100 immediately upon receiving the results of your first exam.