All students in courses numbered Math102 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 MATH100 Problem Solving Strategies. If she completes MATH100 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).
A Sample test (with solutions) is at the bottom of this page.
The test consists of ten problems to be solved by the student, using a calculator as approproiate 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. 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 medecine costs $6.99 for 200 tablets. The name brand of this medecine 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)
Set-ups:
Maintained by cpeltier@saintmarys.edu1.) 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 arithmentic 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.
Last corrected 8/27/99