WorkKeys Applied Math Exam Flashcards

Q: What is the ACT WorkKeys Applied Math assessment?

It is a 34-question, 55-minute multiple-choice exam that measures workplace mathematical reasoning across 5 difficulty levels (Level 3 to Level 7). It is one of three required assessments for earning the ACT National Career Readiness Certificate (NCRC), alongside Workplace Documents and Graphic Literacy.

Q: Can I use a calculator on the WorkKeys Applied Math test?

Yes. Any 4-function, scientific, or graphing calculator is permitted. ACT also provides a formula sheet during the exam, so memorizing formulas is not necessary, but knowing when to apply each one is.

Q: What score do I need to earn an NCRC?

A Level 3 or higher earns a Bronze NCRC, Level 4 earns Silver, Level 5 earns Gold, and Level 6 or higher earns Platinum. Scores are reported as both a scale score (65-90) and a level score (3-7). Your employer or school may require a specific level.

Q: What math topics are tested on WorkKeys Applied Math?

All questions are realistic workplace scenarios. Topics include basic operations, money and time, percentages, proportions and ratios, measurement and conversions (US and metric), averages, area and volume, and multi-step workplace problems that increase in complexity at Levels 6-7.

Q: What is the NCRC and why does it matter?

The ACT National Career Readiness Certificate (NCRC) is a portable credential recognized by more than 29,300 U.S. employers that verifies foundational workplace skills. Earning it can support job applications, college placement, and workforce development programs.

Q: How can I retake the WorkKeys Applied Math test?

You may retake the assessment as many times as needed, but there is a mandatory 30-day waiting period between attempts. Check with your testing center for local scheduling and any fees, which vary and are often covered by schools or workforce programs.

Question 1

Order of operations (PEMDAS)

Accepted Answer

Workplace calculations with multiple operations must follow Parentheses, then Exponents, then Multiplication and Division (left to right), then Addition and Subtraction (left to right). Skipping this order changes the answer: 2 + 3 x 4 is 14, not 20, because multiplication precedes addition.

Question 2

Fraction multiplication (a/b x c/d)

Accepted Answer

Multiply numerators together and denominators together: (a x c)/(b x d). You do NOT need a common denominator for multiplication; the common-denominator rule applies only to addition and subtraction of fractions.

Question 3

Division with a remainder: when to round up

Accepted Answer

When a problem asks how many containers, batches, or shifts are needed, round UP, because a partial container still must be purchased or scheduled. When it asks how many whole units fit, round DOWN, because the remainder cannot be used.

Question 4

Decimal addition and subtraction alignment

Accepted Answer

Line up the decimal points vertically before adding or subtracting, and pad shorter numbers with trailing zeros. Misaligning by one place shifts the answer by a factor of 10, the most common arithmetic error in workplace bookkeeping.

Question 5

Mixed number to improper fraction

Accepted Answer

Multiply the whole number by the denominator and add the numerator: 3 1/4 = (3 x 4 + 1)/4 = 13/4. Convert mixed numbers before multiplying or dividing; leaving them mixed forces error-prone two-step arithmetic.

Question 6

Converting a fraction to a decimal

Accepted Answer

Divide the numerator by the denominator: 3/8 = 3 / 8 = 0.375. This conversion is required whenever a workplace answer must be in decimal form, such as money, measurements, or calculator output.

Question 7

Regular hourly wage calculation

Accepted Answer

Multiply the hourly rate by the number of hours worked: pay = rate x hours. Verify decimal placement: a $14.50 rate over 40 hours is $580.00, not $58.00 or $5,800.

Question 8

Overtime pay (time-and-a-half)

Accepted Answer

Under FLSA-style rules, hours worked beyond 40 in a week are paid at 1.5 x the regular rate. Compute regular pay for the first 40 hours and overtime pay for the remainder, then add; never apply 1.5x to all hours.

Question 9

Converting minutes to a fractional hour

Accepted Answer

Divide minutes by 60: 20 min = 20/60 = 1/3 hour (about 0.333), and 45 min = 0.75 hour. Use this conversion whenever a labor charge or wage problem gives time in hours and minutes, because hourly rates multiply only by hours.

Question 10

Elapsed time across the AM/PM boundary

Accepted Answer

Convert both times to 24-hour format (add 12 to PM hours except 12 itself) and subtract: 7:45 AM to 4:15 PM becomes 07:45 to 16:15, or 8 hours 30 minutes. Mixing AM/PM subtraction directly is the most common time-clock error.

Question 11

Subtracting unpaid breaks from elapsed time

Accepted Answer

Calculate gross elapsed time first, then subtract only the unpaid break minutes to get paid work hours. A 30-minute unpaid lunch means 8h30m elapsed becomes 8h paid; forgetting to subtract overstates pay, and subtracting twice understates it.

Question 12

Making change (count-up method)

Accepted Answer

Start at the purchase price and count up to the cash tendered using the fewest denominations: price $13.65, tendered $20.00 means add $0.35 to reach $14.00, then $1 and $5 bills to reach $20. Counting up avoids subtraction errors and gives the customer the correct bills and coins.

Question 13

Gross pay vs net pay

Accepted Answer

Gross pay is total earnings before deductions; net (take-home) pay is what remains after taxes, insurance, retirement, and other withholdings. Workplace math problems specify which one to calculate; computing gross when net is asked, or vice versa, is a frequent miss.

Question 14

Converting weekly, monthly, and annual wages

Accepted Answer

Annual is approximately weekly x 52, and monthly is approximately annual / 12. Use 52 weeks (not 4.33 weeks) for weekly-to-annual conversions, because the extra fraction of weeks per month accumulates across the year.

Question 15

Percent change formula

Accepted Answer

Percent change = (amount of change / original amount) x 100. The ORIGINAL (starting) value is always the denominator; using the new value as the denominator is the most common percent-change error.

Question 16

Percent increase vs percent decrease

Accepted Answer

Both use (change / original) x 100; the sign of the change tells the direction. A price rising from $24 to $30 is a 25% increase; falling from $30 to $24 is a 20% decrease, because the same $6 difference gives a different percentage when the base differs.

Question 17

Discount (percent off)

Accepted Answer

Discount amount = discount percent x original price; sale price = original minus discount. Always compute the discount amount first and subtract; multiplying by (1 - percent) in one step risks dropping a place value when working by hand.

Question 18

Markup vs profit margin

Accepted Answer

Markup is added to COST: selling price = cost x (1 + markup percent). Margin is taken from SELLING PRICE: profit = price x margin percent. A 50% markup on a $10 cost yields $15, which is only a 33% margin on the $15 selling price, so the two terms are not interchangeable.

Question 19

Successive discounts (do not add percentages)

Accepted Answer

Two discounts applied in sequence multiply, not add: 20% off then 10% off yields a final price of 0.80 x 0.90 = 0.72 of original (28% off), not 30% off. Add the percentages only if both discounts are taken off the same original base.

Question 20

Sales commission

Accepted Answer

Commission = commission rate x sales amount. A 5% commission on $18,000 in sales is $900; total compensation adds this to any base salary. Distinguish the commission rate (percent per dollar of sales) from the commission amount (the dollar result).

Question 21

Sales tax application order

Accepted Answer

Sales tax applies to the discounted (sale) price, not the original price, and is added AFTER the discount is subtracted. Computing tax on the original price overcharges the customer and is a frequent register-error cause.

Question 22

Percent of a whole vs part-to-whole percent

Accepted Answer

X percent of a whole multiplies the percent by the whole (15% of 200 = 30). Part is what percent of whole divides part by whole (30/200 = 15%). The two operations are inverses; recognizing which one the prompt asks for sets up the correct calculation.

Question 23

Feet and inches conversion (1 ft = 12 in)

Accepted Answer

Multiply feet by 12 to get inches; divide inches by 12 to get feet. For mixed measurements like 5 ft 8 in, convert the feet portion to inches and add, or convert everything to one unit before any further arithmetic.

Question 24

Pounds and ounces conversion (1 lb = 16 oz)

Accepted Answer

Multiply pounds by 16 for ounces; divide ounces by 16 for pounds. Mixed weights like 3 lb 8 oz must be converted to a single unit (56 oz) before applying a per-ounce rate; keeping mixed units through a multiplication produces a wrong answer.

Question 25

Mixed-unit arithmetic: convert first

Accepted Answer

Whenever a problem gives measurements in two related units (feet and inches, pounds and ounces, hours and minutes), convert both to the smaller unit before adding, subtracting, multiplying, or dividing. Operating on mixed units directly is the leading source of measurement errors on the test.

Question 26

Metric prefix relationships (kilo, centi, milli)

Accepted Answer

Kilo- means 1,000, centi- means 1/100, and milli- means 1/1,000 of the base unit. Moving between prefixes shifts the decimal three places per step: 2.5 kg = 2,500 g = 2,500,000 mg. The decimal-shift pattern makes metric conversion faster than US-unit conversion.

Question 27

Pounds and kilograms conversion

Accepted Answer

1 kilogram is about 2.2046 pounds, and 1 pound is about 0.4536 kilograms. To convert 5 kg to pounds, multiply by 2.2046 (about 11.02 lb). Use the precise factor in shipping and medical contexts, because rounding to 2.2 introduces compounding error.

Question 28

Temperature conversion (F and C)

Accepted Answer

C = (F - 32) x 5/9 and F = (C x 9/5) + 32. Subtract 32 first when going from Fahrenheit to Celsius; multiplying before subtracting gives a wrong result. Water freezes at 0C / 32F and boils at 100C / 212F.

Question 29

Unit pricing for comparison shopping

Accepted Answer

Divide total price by quantity to get price per single unit (per ounce, per pound, per item) and compare across package sizes. The lowest total price is not always the lowest unit price; bulk packages sometimes cost more per unit than smaller ones.

Question 30

Speed, distance, and time relationship

Accepted Answer

Speed = distance / time, distance = speed x time, and time = distance / speed. Identify which two values are given and which is unknown; the formula rearranges to isolate whichever variable the problem asks for.

Question 31

Cross-multiplication to solve proportions

Accepted Answer

For a/b = c/d, multiply diagonally: a x d = b x c, then solve for the unknown. Cross-multiplication converts a proportion into a single algebraic equation and is the fastest way to solve rate and ratio problems on the test.

Question 32

Map scale problems

Accepted Answer

A map scale like 1 inch = 10 miles means 1 map unit represents 10 real units; multiply map distance by the scale factor for real distance. Keep the units straight: a 3.5-inch map distance at 1 in = 10 mi is 35 miles, not 3.5 miles.

Question 33

Unit rate (price or quantity per single unit)

Accepted Answer

A unit rate expresses one quantity per 1 unit of another, such as $0.45 per ounce, 50 miles per hour, or 12 widgets per minute. Divide the numerator by the denominator so the denominator equals 1; comparing unit rates is the standard way to choose between options.

Question 34

Mixing ratios (paint, chemicals, recipes)

Accepted Answer

A 3:1 mixing ratio means 3 parts of one component to 1 part of another (4 total parts). To make 20 gallons of a 3:1 mix, split it as 15 gallons of the first and 5 of the second; multiply the total by (part / total parts) for each component.

Question 35

Combined work-rate formula

Accepted Answer

For two workers with individual rates 1/a and 1/b (jobs per unit time), the combined rate is 1/a + 1/b = 1/combined; take the reciprocal to find the combined time. A worker who finishes in 4 hours and another in 6 hours together finish in 1/(1/4 + 1/6) = 2.4 hours.

Question 36

Inverse proportion (more workers, less time)

Accepted Answer

When total work is fixed, workers and time are inversely proportional: workers1 x time1 = workers2 x time2. Doubling the crew halves the time; cutting the crew by a third triples the time. Distinguish inverse proportion from direct proportion; using the wrong one flips the answer.

Question 37

Arithmetic mean (average)

Accepted Answer

Mean = sum of values / count of values. The sum and the count must use the same units, and every value must be included; skipping one value or counting it twice changes the mean. A workplace mean might be the average daily output, average wage, or average defect count.

Question 38

Finding a missing value when the mean is known

Accepted Answer

Multiply the mean by the count to get the required total sum, then subtract the sum of the known values. If 4 days must average 50 units and three days produced 45, 52, and 48, the fourth day needs 200 - 145 = 55 units.

Question 39

Weighted average

Accepted Answer

Multiply each value by its weight, sum those products, and divide by the total weight. A weighted average differs from a simple average when groups have different sizes; 80% on a 200-question section and 90% on a 50-question section averages to 82%, not 85%.

Question 40

Median vs mean (outlier resistance)

Accepted Answer

The median is the middle value when data is sorted; the mean is the arithmetic average. A single extreme value can shift the mean dramatically while leaving the median nearly unchanged, which is why income data and home prices are usually reported as medians.

Question 41

Area of a rectangle

Accepted Answer

Area = length x width, with both dimensions in the same unit. The result is in square units (sq ft, sq m). Adding the dimensions (length + width) gives the half-perimeter, not the area; this is a common confusion on basic geometry problems.

Question 42

Area of a triangle

Accepted Answer

Area = 1/2 x base x height, where height is perpendicular to the base (not the slant side). For a 10-foot base and 6-foot height, area = 30 sq ft. Using a slant length as the height inflates the area.

Question 43

Area of a circle

Accepted Answer

Area = pi x r^2, where r is the radius (half the diameter). Squaring the diameter by mistake gives 4x the correct area; always convert diameter to radius first. Use the calculator's pi key, not 3.14, for precision.

Question 44

Volume of a rectangular prism

Accepted Answer

Volume = length x width x height, all in the same unit. The result is cubic units (cubic feet, cubic meters). To find how many smaller boxes fit inside, divide the prism's volume by the smaller box's volume.

Question 45

Volume of a cylinder

Accepted Answer

Volume = pi x r^2 x h, where r is the radius of the circular base and h is the height. Calculate r^2 first (radius squared), multiply by height, then by pi. Confusing diameter with radius quadruples the volume.

Question 46

Border reduction in area problems

Accepted Answer

When an unplanted (or unwalked) border of width W runs along ALL edges of a rectangle, subtract 2W from BOTH the length and the width before multiplying. A 5-meter border on a 120 x 85 m field leaves a 110 x 75 m planted section; subtracting W only once or from only one dimension is the most common area error.

Question 47

Dilution equation (C1V1 = C2V2)

Accepted Answer

Concentration x Volume before dilution equals Concentration x Volume after. To dilute 200 mL of a 12% solution to 8%, solve 12 x 200 = 8 x V2, giving V2 = 300 mL (add 100 mL of solvent). Set up the equation before plugging in numbers to avoid sign and unit errors.

Question 48

Volume pricing and buying-tier strategy

Accepted Answer

When the same product is sold at different per-unit prices across quantity tiers, compute the total cost (including unused units) for the amount needed at each tier. The lowest per-unit price may still cost more overall if the tier forces buying more than you need.

Question 49

Rate-of-completion problems

Accepted Answer

Total work = workers x time x per-worker rate. To find the time for a different crew size, keep total work fixed and rearrange: time2 = (workers1 x time1 x rate) / (workers2 x rate). Recognize this as a proportion, not an addition problem.

Question 50

Profit margin analysis

Accepted Answer

Profit margin = (revenue - cost) / revenue, expressed as a percent. Margin is computed on the SELLING price, while markup is computed on the COST; a 25% margin on $100 revenue means $25 profit and $75 cost. Confusing the two bases is a common error in retail problems.

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