Hollins University
Department of Mathematics and Statistics
Placement Examination

This placement exam is required of every student who enrolls at Hollins. Your performance on this exam will determine whether you are q-proficient, or will be required to enroll in Math 100, Math 105 or Math 130. 

(1) Math 100 - Introduction to Quantitative Reasoning (Fall 2008)

    This course is for students who need practice in applying fundamental mathematical skills (algebra, graphing, data analysis and linearity) to real-life applications.  The goal of the course is to develop the quantitative skills that promote problem-solving with confidence.

 

(2) Math 105 - Quantitative Reasoning in Today's World (Fall 2008 and Spring 2009)

    This course focuses on the application of mathematics to personal and social issues.  It is designed to prepare students for the mathematics they will encounter in other college courses, particularly in the social and natural sciences.  It stresses problem solving, financial management and growth and will provide students with critical thinking and quantitative reasoning skills needed to understand major life issues.

 

(3) Math 130 - Mathematical Modeling with Precalculus I (Fall 2008 and Spring 2009)

    This is a gentle introduction to mathematics in today's world with an emphasis on the application of algebra and precalculus to real world problems.  Recommended for prospective teachers and non-mathematicians.

 

 

If you are q-proficient, there are several beginning mathematics/statistics courses offered at Hollins during the 2008-2009 academic year that you may wish to consider.  You and your advisor will receive a recommendation for one or more of the courses listed below, based on your mathematical background and your performance on this placement exam.

 

(1) Math 140 - Mathematical Modeling with Precalculus II (Spring 2009) 

        Applications of functions and mathematical models to real-world problems.  Provides a minimal preparation for calculus. Recommended for prospective teachers.

 

(2) Stat 140 - Introductory Statistics (Fall 2008 and Spring 2009)  Q

        All students are strongly encouraged to take at least one statistics course while at Hollins! 

 

(3) Math 241 - Calculus I (Fall 2008)  Q

        Required for mathematics majors and minors. Strongly recommended for all students interested in veterinary science, medicine, science, mathematics, business or economics.

 

(4) Math 242 - Calculus II  (Spring 2009) Q

        Required for mathematics majors and minors.  Recommended for all students interested in veterinary science, medicine, science, mathematics, business, or economics.

 

(5) Math 246 - Laboratories in Mathematical Experimentation (Spring 2009)

        Required for mathematics majors and minors.

 

(6) Stat 251 - Statistical Methods I (Fall 2008) Q

        Recommended for students who have AP statistics credit, or a strong mathematical background.   Appropriate for students with college credit for Calculus I.   Required for mathematics majors and minors. 

 

(7) Math 255 - Linear Algebra (Fall 2008) Q

        Particularly appropriate for students with college credit for Calculus I.

Background Survey

Please answer the following questions before you begin the exam.

A. What is your last name? (Please type it in the text box below.)

B. What is your first name?

C.  What is your middle name or initial?

 

D. When did you graduate from high school?

E. Which, if any, of the following math courses did you take during high school ? (Select all that apply.)

Algebra I     Algebra II     Geometry     PreCalculus   

Analysis     Integrated Math     Statistics    Calculus

F. Do you have any college credit for mathematics or statistics courses?  If so,  please list the courses and where you took them.

G.  Which, if any, of the Hollins mathematics or statistics courses listed at the top of this page, are you most interesting in taking at Hollins during the 2008-2009 school year?

Thank you!

On to the placement test...

Exam Questions

The exam consists of 40 multiple choice questions. There is only one best answer to every question. You may use a calculator if you like.  If you have computer problems and need to restart the test, please send an email to jclark@hollins.edu .  Include your name and a brief explanation.

1.  A company announces that it must lay off 30% of its 30,000 employees, effective immediately.  Further, it will lay off 20% of its remaining employees at the end of one year.  Assuming that no other employees join or leave the company, then after both rounds of layoffs, how many employees will remain with the company?

13,200          15,000      16,800     28,200      none of these     

2.  What percent of the 30,000 employees will have been laid off?

44%         50%     56%     94%      none of these    

3.  Suppose that for the past several years, the population of Tukeytown has grown by 5% every year.  If the population is  8,500 in the year 2000, what will its population be in 2002?

8,925         9,000      9,350    9,371      42,500     

4.  The following data set contains batting averages for 20 players randomly selected from an online Baseball Almanac. 

player

Batting

Average

player

Batting

Average

AA

0.143

MD

0.125

BC

0.301

MH

0.108

BH

0.305

MM

0.167

CR

0.115

RC

0.085

DH

0.136

RL

0.267

GV

0.333

RS

0.261

HA

0.229

SU

0.27

HK

0.341

TC

0.097

JB

0.27

TO

0.218

JS

0.281

WG

0.054

 Which of the following graphs is a legitimate histogram of the distribution of batting averages?

none of these  

5. The chart below shows the currency exchange rates between several countries as of September 23rd, 2008.  Use this chart to find the value of 90 British pounds in Euros.

 

244.25      113.77    71.20     33.16     none of these     

6. A certain 6-year old Mazda Miata is worth $11,500.  For every year since it was first sold, the car has gone down (depreciated) in value by $1,900.  How much was the car worth when it was new?

$100          $12,900      $13,400    $22,900    $23,000     

The following histogram displays the results of a survey that asked college students how many hours they spent studying each week.

7.  What was the total number of students surveyed?

7        35      40    245   none of these     

8.  What percentage of the students survey studied an average of 35 or more hours per week?

57%       66%    67%    80%  none of these     

9. Suppose you need to buy enough carpet to cover a room that is 9 ft by 20 ft.  The carpet costs $15 per square yard.  How much will you have to spend for the carpet? 

$300         $900      $2700    $8100     none of these   

10. A recipe for pasta salad that serves 6 calls for 1 package of ranch flavored party dip, ½ cup of sour cream, 1 cup of mayonnaise, 1 pound pasta shells and 2½ cups of mixed vegetables. You want to make enough pasta salad for 32 people. How many cups of sour cream will you need?

3 cups        2.7 cups     2 ⅔ cups    4 ⅞  cups     none of these   

11. Which is larger -- the distance between the earth and the sun (approximately 93 million miles) or the federal debt ($8.7×1011) ?

distance between the earth and sun      federal debt     neither -they are roughly the same size   

12. There are approximately 132 million births worldwide in a year.  Express this quantity in births per minute.

0.25 births/minute        4.19 births/minute    593 births/minute    2511births/minute     none of these   

13. The following table tallies the amounts of 111 withdrawals from an automated teller machine.  For example, 17 withdrawals were for the amount of $20 and 3 were for the amount of $50; no withdrawals were made of $40.  The total amount withdrawn was $12,180.  Find the median and the mode of these withdrawal amounts.

median = $100,  mode =$100  

median = $111.17,  mode = $100

median = $111.17,   no mode

median = $140,  mode = $20

none of these

14. The distribution of individual incomes in the US is strongly skewed to the right. In 1997, two measures of center for the top 1% of individual incomes were $330,000 and $675,000. Which of these numbers represents the mean income of the top 1% and which number represents the median income of the top 1%?

$330,000 is the mean and $675,000 is the median. It depends on which argument you want to make.
$330,000 is the median and $675,000 is the mean. There is not enough information in this problem to be able to tell which is which.

15.  Suppose you go out for a nice dinner and the total bill is $81.76.  If you leave the waitress a $100 bill, approximately what percent tip did you leave?

15%       17%    18%    22%  25%    

16. In a certain city, the cost to rent a car is a flat fee of $70 plus $0.40 per mile.  Find a linear function to represent the cost C as a function of the mileage m.

C = $70 + $0.4m      m = $70 + $0.4C      C = $0.4 + $70m     m =$0 .4 + $70C      none of these

17.  How far can you travel for $250?

72 miles     180 miles    250 miles     400 miles    none of these

18. In  2005 the enrollment at a certain university was 5100 students and was decreasing at a rate of 0.8% per year.  Assuming that enrollment continues to decline in this manner, what will enrollment be in 2006?

1020    4080    5059   5141     none of these

19. Find the relative change in organic fruit and vegetable sales from 1997 to 2003 using the table below.

Year Organic Fruit & Vegetable Sales
1997 $1.5 billion
1998 $1.8 billion
1999 $2.1 billion
2000 $2.5 billion
2001 $3.1 billion
2002 $3.6 billion
2003 $4.3 billion
2.8%    18.7%    65%     186.7%    none of these

20.   Let  .  Solve for  x. 

                                        2

21.  Consider y = x2 + 2kx + 2.  If y = 2 when x = 3, solve for k.

-2           -3/2              -1         3/2           2

22.

                                       

23. The graph of 5x - y + 4 = 0 crosses the y-axis at y =

-4          -5/4          -4/5          4/5          4

24. The expression    is equivalent to

                                       

25. The solution set of 3x2 + x = 4 is

                                       

26. The equation of the line passing through (-6,5) having slope = - ⅓ is

3y - x-9 = 0            x +3y - 9 = 0            x -3y = 9           3y + x + 21 = 0              y - x - 21 = 0

27.  Solve (1+ x) / x  = 7 for x.

1/6       1           8/7       6        none of these

28. Determine the equation of a third degree polynomial whose graph has x intercepts at (-3,0), (-1,0), (2,0) and y intercept is (0,-12).

-2(x-3)(x-1)(x+2)           2(x-3)(x-1)(x+2)          2(x+3)(x+1)(x-2)           -2(x+3)(x+1)(x-2)          none of these

29. One sunny day, Galileo hurled himself into the air.  His height above the ground (in feet) was given by h(t) = -9t2 + 18t + 27.  What was the highest point of his jump ?

18 ft          27 ft          36 ft           45 ft          none of these

30.  When did he reach this highest point?        After . . .

1 second           2 seconds          3 seconds           4 seconds          none of these

31.  Find the horizontal asymptote of  .

y = -3            x = -3          x = 2           y = 2          none of these

32.  Find the vertical asymptote of .

y = -3            x = -3          x = 2           y = 2          none of these

33. If  log3(x+4) = 1, then x =

-1        1        3        4        7

34. A bacteria population is initially 50 and doubles every hour.  When will the population reach 700?

2 hours       2.6 hours        3.8 hours        4.0 hours        none of these

35. If  f(x) = ex+1,  then f -1(y) =

                                       

36. The sketch below best represents the graph of which function?

                                    

37.  Let f(x) = |x-1| .  The graph of y = f(x) is best represented by which of the following?

                         

           

38. If f(x) = x2-1, then f(x+h) =

x2+ h2 +1                x2+ h-1          (x+h-1)2             (x2-1)(h2-1)                x2 +2xh + h2-1

39. The sketch below represents a portion of the graph of which function?

y = 1 + sin(x/2)               y = 1 + cos(x/2)          y = 1 + sin(2x)            y = 1+ cos(2x)                none of these

40. Solve sin(x/2) = ½ for x  in [0, 2p].

{p/6, 5p/6}               {p/3, 5p/3}        {p/3, 2p/3}            p                none of these

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