Mathematics Placement Exam Spring 2003
This is a placement examination to be taken on the first day of class. This exam is to help you and your instructor see if you are adequately prepared to take the course for which you have registered. Please do the best that you can on this exam, but the results will not have any impact on your grade for the course. If you find yourself unable to do any of these questions, you should seriously consider switching to a more elementary course and taking this course when you have a more solid background. However, do not be concerned if you cannot do all of the problems.
This exam must be the results of your own efforts. You may use a calculator. To avoid disturbing other students, you must remain seated until the end of the examination period.
Please fill in the following information:
Name: ______________________________ Email: __________________________
Please answer as many of the following questions as possible on the examination paper. Blue books will be provided for scratch work. The blue books must be returned.
1. For each of the following problems you will be combining fractions by addition, subtraction, multiplication, or division. Your answer must be a fraction reduced to lowest terms. Fill in the answer after the equals sign.
2. Perform the indicated arithmetic operations. Give the answer as an integer or as a fraction with the smallest possible denominator. Do not give your answer as a decimal fraction.
4832198 + 6897875 = _________
358 - 427 = _________
468 * 827 = _________
865 / 35 = _________
(43/87) + (29/137) = _________
(11/12) - (23/24) = _________
(19/21) * (7/8) = _________
(11/13) / (18/19) = _________
3. Perform the indicated set operations. Give the resulting set for the following operations. Assume all sets are drawn from the universe of non-negative integers. Write your answer after the equals sign.
4. The straight-line distance from city A to city B is 325 miles. The straight-line distance from city B to city C is 217 miles. What are the smallest and the largest possible values of the straight-line distance from city A to city C.
Smallest: __________ Largest: ________________
5. Consider the point (3.5,2.8). Apply the translation that shifts points (x,y) to (x+0.21,y-.75). What is the image of the original point? ______________
6. Solve the following equations for x. Use decimal fractions to no more than 6 places.
x + 26 = 5 x = __________
-5*x = 26 x = __________
298*x + 497 = 1024 x = __________
5*x + 3 = 7x + 5 x = __________
7/x + 5 = 1 x = __________
7. Perform the indicated operations on polynomials and restate in simplest terms.
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8 .Solve the following quadratic equations for x.
x
= __________
x
= __________
x =
__________
9. If you
graph the function, 
,
the slope of the line will be _________, the x-intercept will be ________, and
the y-intercept will be __________.
10. A social club has 120 members. Each member is either a Democrat or a Republican. Each member is either male or female. Of the members, 35 are male Democrats, 50 are Republicans (male or female), and 60 are female. How many male Republicans are there in the club? _________
11. If a treasure of 3000 gold pieces is divided into 15 equal shares, and the captain
5 shares, how many gold pieces does the captain get? ________.
12. If sin(x) = 3/5, then cos(x) = _______ or _________.
13. If the base of a triangle is 12 inches and the height of the triangle is 6 inches, what s the area of the triangle in square feet? ___________
14. If a bank offers you 2% interest compounded quarterly and you deposit $100 dollars at the start of a quarter, how many dollars will be in your account at the end of 2 years? _________
15. Assume you live on a planet that is perfectly round, and has a radius of 8000 miles. Suppose you put a string around the equator of that planet and pull it nice and tight. How long will the string be? ____________. Suppose you now make the string 3.14159 miles longer and hold it up a uniform distance above the equator in a perfect circle. How high above the surface of your planet will the longer string ride?_________
16.
For what values of real numbers 
is it true that 
?
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