|
Sample Questions for Math
Placement Exams
These are some sample
questions for the math placement exam. Use this as a guide for the level
of difficulty of the exam and for the breadth of the material covered.
Calculators may be used. The real math placement exam has more questions
and you will have 90 minutes to finish each section. The percentages
earned for each correct response are listed on the answer sheet so that you can
grade yourself on each section. At the end of this document there is an
explanation of what course you can expect to be placed in based on your score
and your major. It should be emphasized that these are just sample
questions. Your actual placement will be based on the placement exam you
take during the summer. It is available at:
http://danielwebster.placementtester.com/classes/mathplacement
SECTION A: INTRODUCTORY ALGEBRA
1. Do the indicated operations.
Remember the rules for the order of operations. Your results should be
either an integer or a fraction, but not a decimal.
a)
b) 
2. Simplify the following algebraic
expressions.
a)
b) 
3. Expand:
a)
b) 
4. Solve the following equations
for x.
a)
b)
5. Graph the linear equation 5x
+ 3y + 15 = 0 in the xy-plane.
6. Tickets for a basketball
tournament were $6.00 for students and $9.00 for non-students; and 250 more
student tickets were sold than non-student tickets. Total sales were
$10,500. How many of each type of ticket were sold?
SECTION B: COLLEGE ALGEBRA
1. Do the indicated operations.
Your results should be either an integer or a fraction, but not a decimal.
2. Simplify the following
expressions.
3. If
 find
f
(x+h) =
4. Find the equation of the line
passing through P(-2, 3) and Q(1, 5).
5. Let x, y and z
be positive real numbers, find w if
6. Sketch the graphs of:
a)
b) 
7. Solve the following equations
for x.
a)
b) 
c) 
8. The population of a certain
country grows exponentially. The population
P, after t years with current population P0
can be found using the formula
 What
will be the population of this country 5 years from now if the current
population
P0 = 10 million? In how many years will the population
of this country be doubled?
SECTION C: TRIGONOMETRY
1. Convert the measurement of the
given angle.
a)
°
b) -293.5° = _____________rad
2. Use a calculator to evaluate the
given expression.
a) csc(118.7°)
=
b) sec-1(2.31) =
3. Find the values of all the six
trigonometric functions (in exact form) of the angle (in standard position)
whose terminal side passes through the point (2, -5).
4. Find the resultant vector of
vectors A and B using horizontal and vertical components if
A=18cm Ð35° and
B=13cm Ð210°.
Express your result in magnitude and direction angle form.
5. Use the sum or difference
identities and the fact that
75°=45°+30°
to evaluate the exact value of sin(75°).
Leave your result in the form of radicals
and fractions, not in decimals.
6. Show the trigonometric identity
 .
7. Solve the trigonometric equation
 .
8. Two observers A and B sight a
helicopter due east. The observers are 7,540 ft apart, and the angles of
elevation they each measure to the helicopter are 32.0°
and 44.0°,
respectively. How far is observer A from the helicopter?
9. A plane left an airport A and
traveled 739 km to a city B, then turned toward another city C and traveled 424
km to reach city C. Finally, the plane made another turn at city C and
traveled 925 km back to the airport A. Draw a sketch of the triangle ABC
and find the angle at city C.
10. Sketch the graph of
. Also find the magnitude A, period T, and displacement D of the function.
answers to sample questions for math placement exam
Note that the value in percentage of each
problem is shown in ( )
SECTION A: INTRODUCTORY ALGEBRA
1. a)
(16%)
b) 5 (8%)
2. a) a4
(8%)
b) -3x3
+ 5x2 – 10x + 19 (8%)
3. a) 6x2
+ 5xy – 6y2(8%) b) 16x2
+ 24x + 9 (8%)
4. a) x =
 (10%)
b) x =
 , -2
(10%)
5. Graph of linear equation
5x + 3y + 15 = 0 in the xy-plane (8%)
6.
Student Tickets = 850, Non-student Tickets = 600 (16%)
SECTION B: COLLEGE ALGEBRA
1.
 (8%)
2. a2
– a
 (8%)
3. -3x2
– 6xh – 3h2 + 2x
+ 2h –5 (8%)
4.
OR
(8%)
5.
(8%)
6. a) (5%)
b) (10%)
7. a) x
= 5 (10%)
b) x =
 (10%)
c) x =
,
y =  (10%)
8. 14.19 million people, 9.9 years
(15%)
SECTION C: TRIGONOMETRY
1. a)
150° (4%)
b) -5.1225 (4%)
2. a) 1.1401
(4%)
b) 64.35° (4%)
| 3. |
sin
 =
(4%) |
csc
=
 (4%) |
|
cos
=
(4%) |
sec
=  (4%) |
|
tan
=
(4%) |
cot
=  (4%) |
4. 5.1750
47.65° (8%)
5.
(8%)
6. (8%)
7.
 ,
 ,
(8%)
8. 25,192 feet
(8%)
9. 51.41° (8%)
|
10.
A = 2, T =
 , D =
0 (12%)
|
 |
Click Here - for an explanation of where
you would be placed based on your score and your major.
|
