Mathematics Proficiency Test

All students in courses numbered Math 102 through Math 114, and Math 118 and Math 302, must pass this test on basic mathematics by the deadline announced each semester (usually two weeks into the semester) or withdraw from the course. There are ten questions; at least eight must be answered correctly for a pass. A student who is unable to pass the test within this time will have the option to enroll in a two-credit non-core [does not fulfill general education requirement] course MATH 100: Problem Solving Strategies. If she completes MATH 100 with a grade of B or above, this will excuse her from the proficiency test in subsequent mathematics courses (She will be responsible for presenting documentation to the instructor in the subsequent course).

 

Description

The test consists of ten problems to be solved by the student, using a calculator as appropriate but with no other assistance.

The problems will come from the following categories. Most will be in verbal format (require reading and understanding). Sample questions are given for each type.

  1. Percentage in which the base is known
    What would you pay for a $32 item if it is on sale at 30% off and the sales tax is 5% ?

  2. Percentage in which the base is not known
    A company "downsizes" by laying off 12% of its workers. If 324 workers are laid off, how many remain?

  3. Ratio - direct and simple or with interpretation needed
    If a roofer can cover a 225 square foot roof with 80 bundles of shingles, how large a roof can she cover with 24 bundles? (round to nearest tenth of a square foot)

  4. Formula evaluation
    Evaluate the expression {5A - 2[A - 5(2B - 3A) + 4] } for A = -2 and B = 2

  5. Area/Multiplication
    A hallway is to be covered with tiles that have the shape of a 4 inch square. How many tiles will be needed to cover the hallway if its dimensions are 28 feet by 36 inches?

  6. Problems solvable with linear equations - with or without need for algebraic manipulation

    A. A local pizza restaurant charges $10.75 for the first large pizza and $5.50 for each additional large pizza. The math club has budgeted $60 for tonight's pizza party. What is the largest number of large pizzas they could buy without going over budget?

    B. A company makes a Halloween candy mix that costs $1.50 per pound. The mix is made up of 3 kinds of candy. Sweet Tarts cost $1.50 per pound, gum costs $1.00 per pound, and candy corn costs $2.25 per pound. The candy mix has equal amounts (by weight) of Sweet Tarts and gum. How many ounces of gum are in a pound of the mix?

  7. Patterns
    A florist sells 42 flowers on Monday, 51 flowers on Tuesday, 60 on Wednesday and 69 on Thursday. If this pattern continues, how many can she expect to sell on Friday?

  8. Averages
    Jean bought three CD's at $12.99 each, five at $16.99 each , and one for $10.99. What was the average price of the CD's she bought?

  9. Price comparison
    Missy earned $225 working 35 hours for one company and Linda earned $250 working 40 hours for another company. Which person has the better hourly rate?

  10. Addition/ subtraction of signed numbers
    One night in South Bend the temperature was -17 degrees C. The temperature then rose 25 degrees C. What was the temperature then?

  11. Division
    At Rosy Rita's restaurant, 5 servers share equally all the tips they receive. If each server receives a $90 weekly salary plus the share of the tips, what is the total pay received by each for a week when the total of all tips is $583.75?

  12. Mixed number computation (exact answer required - in fraction/mixed number form, which is the form used to give the information in the question)

    A. Divide and reduce to lowest terms: 8 1/3 divided by 4 1/7

    B. The owners of a local hardware store estimated that 2/5 of the total income was spent for goods sold, 1/3 was spent for overhead, and the rest was profit. What fractional part did they estimate was profit?

 

Answers: [parts in brackets not required in answer]

  1. Pay $23.52 [Price $22.40 plus tax $1.12]

  2. 2376 workers remain [There were 2700 workers - 12% were laid off, 88% remain]

  3. 67.5 square feet [225 sq. ft/80 bundles = 67.5 sq. ft/24 bundles]

  4. 86 [{5(-2) - 2[(-2) - 5(2(2) - 3(-2)) + 4] } - keep careful track of the order of operations]

  5. 756 tiles [hall is 84 tiles long by 9 tiles wide]

  6. A. nine pizzas [$5.25 left over]

    B. 6 oz [Using g for amount of gum (in pounds) in a pound of mix, get cost of a pound of mix: 1.50*g + 1.00*g + 2.25*(1- 2*g) = 1.50, so that g = 3/8 LB - questions specifically asked for ounces and 3/8 lb. is 6 oz.]

  7. 78 flowers on Friday [Number of flowers sold increases by 9 each day]

  8. Average price $14.99 each [She bought 9 CD's for a total of $134.91]

  9. Missy [She makes about $6.43 per hour, Linda makes $6.25 per hour]

  10. 8 degrees C

  11. $206.75 for each server [$90 salary + $116.75 in tips]

  12. A. 175/87 [equivalent correct answer: 2 1/87]

    B. 4/15 of income is profit

 

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Sample Test

(From Fall 1999) Setups of problems follow the list of answers

1. A couple stayed at a Florida condominium where the daily rate was $265.00 plus 15% tax. If the total bill was $3352.25, how many days did the couple stay?

2. The Roberts family pays $435 a month for rent. If rent represents 38% of their income, then what is the monthly income? (Round to the nearest cent)

3. Jones Realty received a commission of $1200 for selling a $140,000 home. At the same rate, what would be the commission for selling a $455,000 home?

4. Evaluate the expression  for a = -8 and b = 18.

5. A certain room has a length of 18 feet, a width of 16 feet, and a height of 9 feet. How many square feet of wallpaper will be required to cover the walls?

6. A local department store offered a special on tapes: five at the regular price and $3.99 for a sixth tape. What was the regular price for a tape if a student spent $38.94, before taxes, to purchase six of them?

7. Lisa found a course in which all students received a grade of A last semester. She registered for it and 12 minutes later told four friends. Twelve minutes later, each of them told four other friends, and twelve minutes later each of these friends told four of their friends. If the pattern continues, how many people besides Lisa will know Lisa's secret in only 60 minutes?

8. A student's scores on four tests are 72%, 79%, 87%, and 89%. What grade must the student score on the fifth test so that the average will be 84%?

9. The generic brand of medicine costs $6.99 for 200 tablets. The name brand of this medicine costs $8.50 for 160 tablets, but we can use a $2.00 off coupon for the name brand. Which brand is the better deal?

10. The day-to-day changes for the Dow-Jones stock average for the first three days of one week were recorded as follows: Monday +8 2/3; Tuesday -5 1/4; Wednesday +14 1/8. What was the net change for the three day period?

 

Numerical answers:

  1. 11 days
  2. $1144.74
  3. $3900
  4. 1936
  5. 612 square feet
  6. $6.99 each
  7. 1364 people (besides Lisa)
  8. 93%
  9. generic
  10. +17 13/24 (could also be written 421/ 24 - but can't be neatly written as a decimal, does require a fraction)

 

Setups:

  1. The cost each day was $265 + (.15)*(265) which is $304.75 so we can write an equation ($304.75)*(number of days) = $3352.25 . Solving gives number of days = (3352.25) / (304.75) = 11

  2. $435 = (.38)*(monthly income) so monthly income = ($435)/(.38) = $1144.7368... which rounds (nearest cent) to $1144.74

  3. rate = (commission) / (price). Since the rate is the same, we can write a proportion (commission) / (455000) = (1200) / (140000) so commission = (1200)*(455000)/(140000) = $3900 [If you calculate the rate first, don't round it off - keep all decimal places]

  4. (-8)^2 -4*(-8)*(18) + 4*(18)^2 = 64 + 576 + 1296 = 1936

  5. There are four walls: 2 walls each 18 ft long x 9 ft high, area 2*18*9 = 324 sq. ft and 2 walls each 16 ft long x 9 ft high, area 2*16*9 = 288 sq. ft, total area is 324 + 288 = 612 sq. ft.

  6. Using R for regular price, since we know the total price, we can say (5*R + 3.99) = $38.94 . Solving for R gives R = $6.99  [OR: 38.94 - 3.99 = $34.95 for 5 tapes at regular price, so each cost 34.95 / 5 = 6.99 - equation just sets up this arithmetic for you]

  7. This is easiest to set up with a table. At each 12 minute interval, the number of people increases by 4 times the number of people who found out at the previous step:


    Time since Lisa learned 12 min 24 min 36 min 48 min 60 min
    # people who find out at the time
    		 4 4*4 = 16 4*16 = 64 4*64 = 256 4*256 = 1024
    # people who know (besides Lisa) 4 4+16 = 20 20 + 64 = 84 84 + 256 = 340 340 + 1024 = 1364

     

  8. Using x for the score needed, since we know what the average must be, we have (72 + 79 + 87 + 89 + x) / 5 = 84.   Solving for x gives x = 93. [OR: to average 84, need a total score of 5*84 = 420 percentage points. The four tests so far give 327 points, so she needs 93 more - this is the same arithmetic that is set up by the equation]

  9. Cost for generic = $6.99 / 200 = $.03495 per tablet. Cost for name brand = ($8.50 - $2.00) / 160 = $.040625 per tablet, so the generic is still a better deal.

  10. Total change = (8 2/3) + (-5 1/4) + 14 (1/8) = (8 16/24) + (-5 6/24) + (14 3/24) = 17 13/24.