Mathematics Placement Information
All entering students, regardless of major or area of interest, are required to complete a short
online questionnaire and mathematics assessment prior to attending the SOAR program.
Information supplied on your questionnaire will be reviewed together with your score on the
assessment to determine the best first mathematics course for you.
The Questionnaire
In the questionnaire component of the placement process, you will be asked to provide
information about your past background in mathematics (including courses you took or are
currently taking, and grades you have earned). You will also be asked to tell us about your
interests and plans for after graduation. This information helps us understand your experiences
with mathematics before Albion and your goals after Albion, so we can tailor our advice to your
particular situation.
The Assessment
The math placement assessment consists of 55 multiple choice questions. The questions cover
topics in three areas: Algebra, Precalculus, and Calculus. Each student will take a 55-question
test covering the entire range of topics, but the exact questions on each test will be different
for each individual student.
Algebra
There will be about 25 questions covering topics typically covered in the high school Algebra 1 –
Algebra 2 sequence. Topics include, but are not limited to, the following:
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Order of operations
Solving equations and inequalities
Simplifying expressions involving radicals or exponents
Performing operations with algebraic expressions
Evaluating formulas and expressions
Factoring
Simplifying rational expressions
Solving linear equations and systems of linear equations
Geometric reasoning and graphing
Solving word problems
Precalculus
There will be about 16 questions covering topics typically covered in a high school Precalculus
class. These questions will cover such topics as
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Working with polynomial, rational, exponential, logarithmic and trigonometric functions
Solving inequalities involving absolute value
Reasoning from a graph or diagram
Solving equations using factoring
Working with function composition
Solving word problems
Calculus
The remaining 14 questions on the assessment will consists of topics typically covered in an AP
calculus course. Both AB and BC topics appear on our assessment. These questions will help us
give you the best possible advice about which calculus course would be the best first course for
you. Topics on this part of the assessment include
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Finding limits
Computing derivatives
Understanding derivative as limit of difference quotient
Computing indefinite and definite integrals
Determining volumes of revolution
Convergence of series, including Taylor series
Solving initial value problems
Solving word problems
Preparing For the Assessment
We recommend that you spend some time making sure that your skills are up to speed before
taking the assessment. Even for students who have done well in previous math studies, we find
that it helps when students take time to “knock the rust off” some skills. In particular, we find
that students who have been away from the traditional college-prep mathematics courses for a
period of time, or those who have been heavily reliant on calculator use, tend to lose some
proficiency with algebra. As you prepare for the assessment, please consult the following
resources.
 Khan Academy, http://www.khanacademy.org/ . You can create a free account
on this site, which provides tutorials and practice problems in various areas.
 To prepare for the Algebra portion of the assessment, we recommend
that you master the topics covered under “Arithmetic and Pre-Algebra”,
“Algebra”, and “Geometry”
 To help you prepare for the Precalculus portion of the assessment, we
recommend that you master the topics covered in “Trigonometry and
Precalculus”
 The topics covered under “Calculus” will provide a good calculus
refresher for students who have already completed at least one semester
of calculus study
 Practice Problems and solutions are available on the following pages. The
problems presented here are not meant to be inclusive of all covered topics or
possible problems. These problems are for practice only and do not necessarily
reflect problems actually on the assessment.
The Results
Your questionnaire and assessment will be reviewed prior to SOAR, and you will receive your
results at your first academic planning session at SOAR. At that time, you will have the
opportunity to discuss your placement results with your SOAR adviser as well as members of
the Department of Mathematics and Computer Science. Students are strongly encouraged to
enroll in the recommended mathematics course within one year of completing the placement
process. If you delay studying mathematics at Albion until your second or third year, you may
find that time and distance from the subject have a negative effect on your skills. If you have
questions about your math placement, please contact Dr. Paul Anderson, Chair of the
Department of Mathematics and Computer Science, at [email protected] .
Mathematics Placement Practice Problems
Algebra – Practice Problems
2x2  8
, for x  2.
3x  6
2x  2
a.
3
2x  4
b.
3
2
c.
x2
3
3x  6
d.
2
1. Simplify
2. Simplify
x
x

x 3 x  2
2 x2
x2  6
2 x
b.
x  6
1
c.
3
a.
2 x2  x
x2  x  6
d.
3. Simplify
8x 6 y 2
z0
a. Cannot be simplified due to the term z 0 in the denominator.
b. 4x3 y
c.
2 2x 3
y
d. 2 2x3 y
4. Solve for x : 4 x  1 
2x
3
3
10
1
b.
10
c. 1
d. There is no real solution to this equation.
a.
5. The length of a rectangle is three more than twice its width. The perimeter of the
rectangle is 42 inches. Find the length of the rectangle.
a. 20 inches
b. 3 inches
c. 6 inches
d. 15 inches
Precalculus – Practice Problems
1. If log 2 x  5 , find log 2 (8 x).
a.
b.
c.
d.
10
8
40
16
2. State the domain of the function f ( x) 
a.
b.
c.
d.
x
.
3 x
x0
x3
0 x3
x3
3. Determine the range of the function f ( x)  4cos(5x   ) .
a. 1  y  1
b.   y  
c. 5  y  5
d. 4  y  4
4. If two lines intersect at a right angle, determine the product of their slopes.
a. 0

b.
2
c. -1
d. 1
5. If f ( x)  2 x  1 , determine a formula for f 1 ( x).
a. 2 x  1
2x 1
x 1
c.
2
1
d.
2x 1
b.
Calculus – Practice Problems
1. Determine the derivative of the function y  4cos( x 2  1).
a. 4sin(2 x)
b. 8x sin( x2  1)
c. 4 x sin( x 2  1)
d. 4( x2  1)sin(2 x)
2x2  2x
x 1 5 x  5
2. Determine the limit : lim
a. 0
b. ∞
2
c.
5
d. This limit cannot be determined.
3. Determine the value of the indefinite integral:
 xe
x2
dx
a. x 2e x  C
3
b. xe x  e x  C
2
c. 2e x  C
2
2
ex
d.
C
2
4. Write a definite integral representing the volume generated by revolving the area under
the graph of y  e x from x  0 to x  1 about the x  axis.
1
a.   e x dx
2
0
1
b.   e 2 x dx
0
e
c.   e 2 x dx
1
1
d. 2  xe x dx
0

5. Determine the interval of convergence for the series:
k 0
 3 3
a.   , 
 2 2
b.
c.
 3,3
 ,  
d. x  3 only
2k
 k ! ( x  3)
k
Answers to Math Placement Practice Problems
Algebra
1.
2.
3.
4.
5.
B
D
C
A
D
Precalculus
1.
2.
3.
4.
5.
B
B
D
C
C
Calculus
1.
2.
3.
4.
5.
B
C
D
B
C