Loyola University Chicago

Mathematics and Statistics

Math Placement Assessment



Why must I take the Math Placement Assessment (MPA)? Is Loyola University Chicago alone in requiring such a test?

National mathematics associations in the United States have found that roughly 30% to 40% of graduating high school seniors planning to attend college are not ready for college level mathematics courses. The goal of Loyola's Math Placement Assessment (MPA) is to place each new student in a math course in which the student will excel: one for which you are well prepared yet not so well equipped that you will find the course to be too easy or perhaps boring. Loyola is committed to helping every incoming student develop proficiency and self-confidence in using mathematics. This is particularly important for students planning to study science, or prepare for a career in the health professions. Basic math skills are also quite important for all social science majors since statistics is an indispensable tool in psychology, anthropology, economics, political science, and sociology. Furthermore, for the many Loyola students who apply to graduate school, admission tests for law school, MBA programs, and graduate programs in the humanities and other disciplines rely upon standardized tests (LSAT, GRE, and GMAT) that measure logical and quantitative reasoning. These are intellectual abilities which improve with the study of math.

Therefore, all first-year students and most transfer students (with specific exceptions detailed below) are required to take the MPA for placement. You will find that this is standard practice at colleges and universities across the country.

High school math grades are significant, but the value of, for example, a grade of B in Algebra 1 depends upon the high school that the student has attended as well as the level of the course (Honors or regular). Furthermore, some students who excelled in Algebra 1 in their first year of high school may have forgotten the material by their senior year, particularly if the student has stopped taking mathematics after three years. Nationally 30% to 40% of all students, regardless of the universities they are attending, find out after taking their college's math placement test that they are not ready for the level of college math that they expected.

Are you saying all the math that I took in high school doesn't matter?

Not at all. What we have learned is that everything depends upon how much math students take and when they take it. We have known students who have worked very hard on math during their first three years in high school to prepare for the ACT and SAT exams. But if these students do not follow up with math in their senior year, they tend not to be as ready for college math. In other words, they forget a great deal during the time when they are not taking math at all. Students who take math all four years tend to be far better prepared for college-level placement tests.

The main purpose of the MPA is to make certain that students are placed into a math class that is at the right level for them. No one should enroll in a class that is at too high a level and then do poorly in it (and be stressed, perhaps study so hard for this class that one neglects one's other courses, and lower one's GPA) because it is too hard. And it is vital to have the right mathematics background to succeed in Chemistry, Computer Science, and Physics courses. No one wants to do poorly in science courses as a result of taking them too soon without the appropriate foundation in math.

Why not use my scores from a standardized test: AP, SAT-II, SAT or ACT? I thought that ACT and SAT scores were good predictors of my success in college.

We do use scores from the standardized tests:

AP Exam

Students who earn a grade of 4 or 5 on either the AB or the BC advanced placement exam in calculus are exempt from the MPA.


We have learned over the years that the SAT-II exams do a good job of measuring a student's command of high school mathematics, and for this reason Loyola University will waive the MPA if the SAT-II score is sufficiently high.

SAT II - Math 1C:
  • If score is greater than 635, student is placed into Math 118 (and may take the MPA to place into Calculus).
  • If score is between 535 and 635, student is placed into Math 117 (and may take the MPA to place into a higher level).
  • If score is lower than 535, student must take the MPA.
SAT II - Math 2C:
  • If score is greater than 635, student is placed into Calculus.
  • If score is between 535 and 635, student is placed into Math 118 (and may take the MPA to place into Calculus).
  • If score is lower than 535, student must take the MPA.

ACT and SAT Exams

While ACT and SAT scores are good predictors of academic success, in general, we have found over the years that they do not offer a completely reliable way of placing students into their first math course at Loyola. The SAT math test attempts to measure math aptitude rather than determine how much algebra and precalculus the student has mastered. Nor are the ACT and SAT exams tailored to fit the curriculum of any particular college or university. However, students who earn a score of at least 26 on the ACT math test or at least 560 on the SAT math test will be not be placed below Math 117.

What if I am enrolled in an AP calculus class now?

Many students who take AP Calculus courses also take the AP Calculus exam. If you take the AP calculus exam and earn a grade of 4 or 5 on either the AB or BC test, you are not required to take Loyola's MPA. In fact, such students will be given one or two semesters of credit in calculus based upon their AP scores and the test that they have taken (AB or BC). If you are not taking an AP Calculus exam, keep in mind that Loyola does not count your high school grade in an AP Calculus class - as opposed to an AP Calculus test - as proof of your level of achievement in math. High schools across the United States teach calculus courses at a wide range of levels and with a wide spectrum of expectations.  Some students who have had calculus in high school place into Precalculus (Math 118) or College Algebra (Math 117) if, for example, their algebra skills are rusty. 

If I have taken a placement test at another college can I use those results?

No. Loyola's MPA is designed to place students into a Loyola University Chicago math course. How one college designs its math courses may be different from the way another college designs them. What Loyola covers in Precalculus may not coincide with what another college or university covers in a course with the same name. (For example, logarithms and exponential functions may be covered in College Algebra at one institution and in Precalculus at another college.) Thus, our placement recommendations pertain only to our Loyola courses. A student who has taken a placement test at another school may be calculus ready for that institution but not calculus ready for Loyola; or vice versa. In addition, placement tests taken a year or more ago (even at the same school) gradually lose their validity since a student who does not use mathematics begins to forget what was once learned.

What is meant by math placement?

Loyola University has a sequence of courses which prepare one for Calculus.  A student must either successfully complete the sequence or must score high enough on the MPA in order to enroll in calculus. The MPA tries to determine which course is most appropriate, neither too difficult nor too easy, for each incoming student to Loyola University Chicago.

We describe placement below:

  • Math 100 (Intermediate Algebra)
  • Math 117 (College Algebra) which is a prerequisite to Chem 101 (General Chemistry A) and Chem 105 (Chemical Principles)
  • Math 118 (Precalculus) which is a co-requisite to Comp 170 (Object-Oriented Programming), Chem 101 (General Chemistry A)
  • Math 131 (Applied Calculus I), Math 161 (Calculus I)


What does the MPA cover?

The MPA primarily covers Algebra I, Algebra II, Trigonometry and Precalculus. Here is a list of topics covered within each of the four sections:

PART A: Elementary Algebra and Logical Reasoning

  • Prime factorization of an integer
  • Rounding an integer
  • Laws of exponents, particularly for integer exponents
  • Radicals
  • Simplify expressions
  • Evaluate an expression
  • Distance formula (Pythagorean theorem)
  • Scientific notation
  • Simple linear equations
  • Simple story problems: age, area, cost, constant speed, average of a set of numbers, business (tax, profit, discount)
  • Recognizing the value of a million, a billion, a trillion
  • Understanding perimeter and area of simple figures
  • Triangles: number of degrees in the sum of the angles; obtuse and acute angles; Pythagorean theorem; finding area of a right triangle
  • Circles: finding area and circumference
  • Percentages
  • Straight lines: slope, y-intercept, x-intercept
  • Linear inequalities
  • Parallel and perpendicular lines

PART B: Intermediate Algebra

  • Factoring polynomials
  • Division of polynomials
  • Absolute value
  • Simple inequalities
  • Language of functions
  • Quadratic formula
  • Meaning of the discriminant: number of real roots, number of complex roots
  • Finding the vertex of a parabola; finding maximum and minimum values of quadratics
  • Systems of two equations in two unknowns
  • Direct and inverse variation
  • Story problems

PART C: Advanced Algebra

  • Complex numbers, simplifying complex expressions
  • Factoring sum and difference of two cubes
  • Inverse functions and composition of functions
  • Quadratic-like equations (e.g., x4 - 7x2 + 12 = 0, or 1 + 2/x - 15/x2 = 0)
  • Theory of Equations
    • Remainder and factor theorems
    • Descartes' rule of signs
    • Polynomial division
    • Finding rational roots of polynomials with integer coefficients
    • Conjugate pairs theorem
    • Recognizing the sum and product of roots by looking at coefficients
  • Equations of circles: recognizing the center and the radius
  • Linear systems in two unknowns; recognizing inconsistent equations
  • Rational functions
    • Analyzing graphs: zeros, singularities, horizontal and vertical asymptotes
  • Systems of non-linear equations
  • Formulas for area of basic shapes and surface area and volume of basic solids (for example, cylinders or cubes)
  • Symmetry of functions (with respect to origin, or with respect to the y-axis)
  • Story problems revisited
  • Log and exponential functions
    • Properties of logs
    • Exponential growth and decay; doubling time for a growing population, half-life for decay
    • Compound interest
  • Limiting behavior of functions: how does y behave as x approaches plus or minus infinity

PART D: Precalculus

  • Recognizing linear functions from a table of data
  • Piecewise defined functions
  • Inverse functions
  • Composition of functions
  • Average rate of change of a function
  • Polynomial and Rational functions revisited
    • Power functions
    • Graphs of rational functions
    • Limiting behavior of functions
    • Understanding rate of growth of functions
  • Domain and range
  • Trigonometry
    • Definition of sine, cosine, tangent, cot, sec, csc
    • Laws of sines and cosines
    • Trig identities
    • Radian vs. degree measure
    • Periodicity of a function
    • Inverse trig functions
  • Logs and exponential functions revisited
    • Recognizing exponential growth from a table of data
    • Graphs
    • Compounding of interest
    • Properties of the log function; change of base formula
    • Limiting behavior of functions
    • Comparison of growth rates of power functions with exponential functions
  • Transformations of functions
    • Vertical and horizontal shifts
    • Reflections and symmetry
    • Vertical stretches and compressions
    • Horizontal stretches and compressions
  • Sequences and Series
    • Finite geometric series

Tell me about the format of the test! What is a passing grade?

The MPA is divided into four sections. Each section contains 12 problems (randomly selected from a large pool of questions). Each question is multiple choice; there is only one correct answer. You will have one hour to complete the test. There is no penalty for guessing. To place into Math 117, you need to answer 7 questions correctly from each of Parts A and B. To place into Math 118, you need to answer 7 questions correctly from each of Parts A, B, and C. To place into Calculus, you need to answer 7 questions correctly from each of the four parts of the test.

There is no passing grade for the MPA! This is a placement test, and your math placement is critical for your college success. Students preparing for careers in medicine or any of the health sciences, business, law, pre-engineering, and any of the physical, life and social sciences need the correct math placement to succeed.

How can I best prepare for the MPA?

If you have not taken mathematics in your senior year of high school, then you will certainly want to review thoroughly Algebra I and II, Trigonometry, and Precalculus (assuming you have taken these courses in high school). You may use your high school texts to review. If your course books are not available, then we recommend...

Online Resources:

Purple Math, Regents Exam Prep (stay with the math topics on LU's exam), and Khan Academy.


Print Resources:

Part A: Elementary Algebra and Logical Reasoning

Angel, Allen and Dennis Runde. Intermediate Algebra for College Students, 8th ed. Upper Saddle River, NJ: Pearson-Prentice Hall, 2010.

Part B: Intermediate Algebra

Angel, Allen and Dennis Runde. Intermediate Algebra for College Students, 8th ed. Upper Saddle River, NJ: Pearson-Prentice Hall, 2010.

Part C: Advanced Algebra

Axler, Sheldon, Algebra and Trigonometry, 1st edition, Hoboken, NJ: Wiley, 2012.

Part D: Precalculus

Axler, Sheldon, Algebra and Trigonometry, 1st edition, Hoboken, NJ: Wiley, 2012.

Are calculators permitted?

When you take the MPA online, you may use any calculator with which you are comfortable. Calculators must be of the hand-held variety, and must not have a keyboard or a wireless connection. In particular, laptops are not permitted. The online test includes an on-screen scientific calculator that has only basic functionality. (The inverse trigonometric functions, for example, are not supported.) Consequently, most students will prefer to use their own calculators.

In our introductory courses at Loyola, most students use a TI-84+ graphing calculator.

Can you show me sample questions for each of the four parts of the MPA?

What are the requirements for my computer?

Minimum hardware/software requirements to take the online test:

  • 640 x 480 256-color display
  • Cookies and Javascript must be enabled on your browser

Recommended hardware/software requirements to take the online test:

  • 800 x 600 16-color display or greater
  • Cookies and Javascript must be enabled on your browser

Is there a fee required to take the test?

There is no fee to take this test the first time. Online test takers will be given 70 minutes to complete the MPA to compensate for possible slowness with their internet connection. If a student wishes to repeat the test, a fee of $10 will be charged.

What if I am taking the MPA online and the system crashes or my internet connection fails?

If you experience a system failure or other technical problem while taking the MPA, email the Placement Testing Team at  placementtest@luc.edu explaining the nature of the problem.  If you are not able to use the internet for email, then call the Office of First-Year Experience at (773) 508-7410 to report the problem. You should receive a response within 24 to 48 hours.

Is my placement in Chemistry, Physics, or Computer Science dependent upon my MPA scores?

Both the Department of Chemistry and the Department of Computer Science believe that proficiency in basic mathematics is essential for success in their entry level courses.

Inorganic Chemistry requires proficiency in algebra and an understanding of logarithmic functions. Introductory Programming (Computer Science 125) and Introduction to Object-Oriented Programming (Computer Science 170) also require that the student possess excellent logical reasoning skills as well as an understanding of basic algebra and functions.

To register for Chemistry 101 or Chemistry 105, the student is expected to test into at least Math 118 (or to have completed Math 117 with a grade of C- or better). To register for Chemistry 102 or Chemistry 106, the student is expected to have tested into Calculus (or to have completed Math 118 with a grade of C- or better).

To register for Computer Science 170, the student is expected to test into at least Math 118 (or to have completed Math 117 with a grade of C- or better).

Physics courses have math prerequisites but do not rely upon the MPA.

If I am not happy with my math placement, what are my options?

Remember that it may be in your best long term interest to begin with a course that allows you to build a strong foundation for your future studies in math rather than trying to rush. If you are not pleased with your placement, you may repeat the test. Although the placement results are usually accurate, occasionally they fail to represent a student's true mathematical ability. If you wish to appeal the result of your MPA, please email the Freshman Placement Coordinator John Houlihan.

If I don't feel ready for calculus, should I deliberately try not to do well on the MPA?

Heavens, no! Unfortunately, every year several incoming students try not to do well on the MPA and, as a result, place into a course (Math 100) which is far below their desired goal. At Loyola University, you are not compelled to begin with a mathematics course that corresponds precisely to your MPA placement level. You may decide to begin with a lower-level course if that makes you more comfortable. If, for example, you place into Calculus and do not feel ready to take calculus, you may certainly choose to begin with a class such as Precalculus or College Algebra.