Prairie State Achievement Exam

WorkKeys: Applied Math Section

The Applied Mathematics assessment measures a person's skill in using mathematics reasoning to solve work-related problems. As a test taker, you will have to set up and solve problems like those that actually occur in a workplace. Calculators are permitted. A formula sheet will be provided.

The assessment contains 33 multiple choice questions at five levels of complexity with Level 7 being the most complex. Although Level 3 is the least complex, it still assesses a level of mathematical skill well above no skill at all. The levels build on each other by incorporating the skills assessed at the preceding levels.

Regardless of the skill level, most of these problems will involve one or more of the following applications.

    Quantity: Employees often need to determine the number of items sold, produced, or purchased, or to figure totals on a per unit basis.

    Money: Working with monetary units is a central part of business and is tangential to virtually every job, if in no other way than to understand a paycheck. Tasks involving monetary units include figuring sales, costs, wages and expenses.

    Time: Some tasks involve figuring elaspsed time. Other problems are also frequently figured in terms of time ( e.g., production, sales, costs, distance, area). In many of these tasks, employees must be familiar with conversion of time units.

    Measurement: Calculating distance, area, weight, and volume is crucial to most work situations. Again, employees must be familiar with conversions, as well as the appropriate degree of accuracy needed for different situations.

    Proportions and Percentages: Proportions can be used in many tasks that require making predictions (e.g., if this is the amount for X units, how much is needed for Y units?). Percentages are used in the workplace to calculate commisions, dicounts, taxes, price increases, changes in sales, and wage changes.

    Averages: Many records in the workplace are expressed in terms of averages (e.g., those involving sales records, wages, costs, hours worked). These averages become tools in the decision making processes of the business.

    What follows are sample questions for each of the Levels 3-7.

For additional problems, 3 questions each per level, click here.

Level 3

This level measures a person's skill in performing basic mathematical operations (addition, subtraction, multiplication, division) and conversions from one form to another using whole numbers, fractions, decimals or percentages.

1. In your job as a cashier, a customer gives you a $20 bill to pay for a can of coffee that costs $3.84. How much change should you give back?

A) $15.26
B) $16.16
C) $16.26
E) $17.16


2. It took you 1 hour to unpack, price and shelve 3 boxes of jeans at work. On the average, how many minutes did it take to unpack, price and shelve 1 box of jeans?

A) 15
B) 20
C) 30
D) 40
E) 50


3. You work in a music shop and a customer wants to purchase 3 cassette tapes costing $8.99 each. Excluding any taxes, how much does the customer owe?

A) $27.00
B) $26.97
C) $26.98
D) $27.03
E) $27.99


4. A customer in the music shop where you work purchases 3 cassette tapes. One costs $8.99, one costs $7.99, and one is on sale for $3.99. Excluding taxes, how much does the customer owe?

Calculate on your own. Check answer below.

5. Calculate the missing values so as to complete the chart.





crate of items


12 items per crate


purchased item


$__?__ per item


distance (mile)


2 hrs per mile

__?__ hrs


6. You must keep track of inventory in an office supply warehouse. This week, 8 computers of a particular model have been shipped out of the warehouse to a local store, while 4 more computers of the same model have been received by the warehouse from the factory. What is the overall change in the number of these computers in inventory this week?

A) down 8
B) up 4
C) down 4
D) up 8
E) down 12

7. Calculate the missing values so as to complete the chart.













Level 4

This level measures a person's skill in performing one or two mathematical operations, such as addition, subtraction, or multiplication, on several positive or negative numbers. Problems may require adding commonly known fractions, decimals or percentages or adding three fractions that share a common denominator. The test taker is also required to calculate averages, simple ratios, proportions, and rates, using whole numbers and decimals.

8. In the hospital where you work, one of your duties is to take pulse counts. One patient has a pulse count of 21 beats in 15 seconds. At this rate, what should this patient's pulse count be for 60 seconds?

A) 84
B) 315
C) 126
D) 42
E) 105

9. You use 3 gallons of concentrated cleaner to mix 10 gallons of usable solution. How much concentrated cleaner should be used to make 30 gallons of usable solution?

A) 3 1/3 gallons
B) 8½ gallons
C) 10 gallons
D) 5 gallons
E) 9 gallons


10. On July 1, you opened a new checking account for your lawn-care business. Based on the check register below, how much is in the account on August 1?

 Check #



Check Amount

Deposit Amount





Rake yard



Van Repair



New Mower





Deposit   $330.67 $

A) $330.67
B) $356.52
C) $555.37
D) $581.22
E) $911.89

11. If it takes 2 yards of interfacing to make 4 suits, how many yards of interfacing should it take to make 20 suits?

Calculate the result and check your answer below.

12. If you can print 800 copies of a letter in 16 minutes, how long should it take to print 2400 copies of the same letter?

Calculate the result and check your answer below.

13. A customer purchased clothing totaling $54.00 from the clothing store you work for. The state sales tax rate is 5%. How much tax should you charge the customer for this purchase?

Calculate the result and check your answer below.

14. During a routine inspection, a quality control officer found three defective parts out of every 150 parts inspected. If 24 defective parts were found, how many parts were inspected?

A) 72
B) 450
C) 1200
D) 2200
E) 3600

15. Over the last five days, you made the following number of sales calls: 8, 7, 9, 5, and 7. To help in planning staff time, you track the average number of calls you make each day. What was your average over the last 5 days?

A) 4.1
B) 7.0
C) 7.2
D) 9.0
E) 36.0

16. The discount store where you work is selling a video game for 15% off the regular price of $21.00. You have to change the price tags for the sale. How much should you take off from the regular price?

A) $4.15
B) $1.50
C) $0.15
D) $3.15
E) $6.00

17. You need about 1½ hours to set up a computer workstation. At this rate, how many hours should it take you to set up 7 of these workstations?

A) 4 2/3
B) 8½
C) 10
D) 10½
E) 11 2/3

Level 5

Questions at Level 5 require the test taker to look up and calculate single-step conversions within the English or non-English system of measurement (e.g. converting from ounces to pounds or from centimeters to meters) or between systems of measurement (e.g. centimeters to inches) Problems at this level contain several steps of logic and calculations. The test taker must determine what information, calculations, and unit conversions are needed to find a solution.


18. Quik Call charges 18¢ per minute for long distance calls. Econo Phone totals your phone usage each month and rounds the number of minutes to the nearest 15 minutes. It then charges $7.90 per hour of phone usage, dividing this into 15-minute segments if you used less than a full hour. If your office makes 5 hours 3 minutes worth of calls this month using the company with the lower price, how much will these calls cost?

A) $39.50
B) $41.48
C) $41.87
D) $54.00
E) $54.54

19. The drug store where you work marks up the price of batteries by 35%. You must price some batteries that cost the store $1.80 per package. What price should you put on each package?

A) $0.63
B) $2.15
C) $2.43
D) $2.77
E) $3.50

20. In your job at the kennel, you groom dogs. It takes you 1 hour 15 minutes to groom an average sized dog. Large dogs, however, take 1 hour 45 minutes to groom. Today you have to groom 3 average sized dogs and 2 large dogs. How much time should it take you to groom all 5 dogs?

A) 3 hours
B) 3 hours 45 minutes
C) 6 hours 15 minutes
D) 7 hours 15 minutes
E) 7 hours 45 minutes

21. You are the new maintenance person for the local school and need to calculate how much wax will be required for the cafeteria floor based on its square footage. The cafeteria is 120 feet by 45 feet. What is the square footage you should use to figure the amount of wax needed for the cafeteria floor?

Calculate and check your result below.

22.You have been asked to ship a package that weighs 41 pounds; however, the freight company wants to know the weight in kilograms. What is the closest approximation of the package's weight in kilograms?

A) 18.64
B) 43.20
C) 82.00
D) 90.20
E) 100.00

23. You must set up tables for a wedding reception in the restaurant where you work. There will be 24 individuals and 40 couples attending. Each table seates 8 persons. How many tables should you set up?

Calculate and check your result below.

24. The shoe store where you work is having a ¼ off sale. A customer purchases a pair of shoes that regularly costs $48.50. How much should you deduct from the regular price?

Calculate and check your result below.

25. As a teacher's aide, you must figure percentage scores on student tests. If a student has 72 points out of 87 possible points, what percent of the total points possible did this student obtain?

Calculate and check your result below.

26. You work in the gift wrap section of a department store. You can wrap 15 average-sized packages in 2 hours. About how many of these packages should you be able to wrap in 5 hours?

Calculate and check your result below.

Level 6

Questions at Level 6 measure a person's skill in using negative numbers, fractions, ratios, percentages, and mixed numbers in calculations. The test taker may have to find the areas of rectangles or circles and volumes of rectangular solids or to solve problems that compare production rates and pricing schemes. Questions may require considerable translation from verbal to mathematical expression and require considerable setup with multiple step calculations.

27. You are preparing to tile the floor of a rectangular room that is 15½ feet by 18½ feet in size. The tiles you plan to use are squares, measure 12 inches on each side, and are sold in boxes that contain enough tiles to cover 25 square feet. How many boxes of tiles should you order to complete the job?

A) 11
B) 12
C) 34
D) 59
E) 287

28. The production line where you work can assemble 5 amplifiers every 30 minutes. At this rate, how long should it take the line to assemble 125 amplifiers?

A) 4 hours 10 minutes
B) 12 hours 30 minutes
C) 12 hours 50 minutes
D) 20 hours 50 minutes
E) 25 hours

29. You must figure the amount of fabric necessary to make a drape for an office window. The finished drape must be 7½ feet long and 5 feet wide. The fabric is wide enough to allow for side hems, but you must determine the length needed. You must allow 8 inches extra at the top and at the bottom to fold under for the hems. How many linear yards of fabric should you need to make the drape?

Calculate and check your result below.

30. As a cosmetologist, you must schedule you own appointments, so you need to know how long one haircut takes. Today you gave 7 haircuts between 1:45 and 4:15 and had no breaks. Approximately how long did it take you to give each haircut?

Calculate and check your answer below.

31. In the machine shop where you work, you are required to keep production records on each part for each day. On Wednesday, 45 pieces of a particular part were machined in 3 hours. On Thursday, 52 pieces of the same part were machined in 3.5 hours. On Friday, 112 pieces of the same part were machined in 7 hours. On which day did the shop have the best production rate (the most pieces machined per hour)?

Calculate and check your answer below.

Level 7

Questions at Level 7 require multiple steps of logic and calculations. Questions may involve more than one unknown, nonlinear functions and applications of basic statistical concepts. At this level, question content or format may be unusual, and the information presented may be incomplete or implicit, requiring the test taker to derive the information needed to solve the problem from the setup.

32. You operate a machine that stamps bottle caps out of 2-inch-by-2-inch aluminum squares. Occasionally, the machine produces an unusable cap, a reject, that must be recycled. The number of rejects made at different production rates is shown below. Today you have been told to produce 600 caps per hour. Approximately how many caps total should you have to produce to end up with your quota of 2,400 good ones?

A) 2,400
B) 2,448
C) 2,500
D) 2,548
E) 2,616

33. In your job at a company that makes bowling balls, you are doing a quick check of how much plastic resin has been used this week by the machine that molds the balls. Each ball is a sphere with a radius of 4 inches (the finger holes are drilled out after the ball has been molded). Production records show that 1,200 balls were made this week. Ignoring waste, about how many cubic feet of resin were used in the machine this week?

A) 46
B) 186
C) 268
D) 2,233
E) 321,536

34. The farm where you just started working has a vertical cylindrical oil tank that is 2.5 feet across on the inside. The depth of the oil in the tank is 2 feet. If 1 cubic foot of space holds 7.48 gallons, about how many gallons of oil are left in the tank?

A) 37
B) 59
C) 73
D) 230
E) 294

35. Your job with the Department of Parks and Recreation requires you to plant Ginkgo trees along the streets of your city. You have 500 of the trees that are ready for planting. You are to plant the trees along the blocks as shown by the dashed lines on the map below. The trees must be planed 30 feet apart. Each block is 3/8 mile long. How many trees, if any, do you need to complete the job?

A) None; you have 236 extra trees
B) None; you have exactly enough
C) You need 20 more trees.
D) You need 908 more trees.
E) You need 15,340 more trees.

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