TEAS-style math practice: cram pack

Formula sheets, the key method steps for every topic and 4 practice problems, with full solutions at the back.

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1Formulas and methods

Pre-nursing math (entrance exam)

Order of operations
parentheses → exponents → × ÷ (left to right) → + − (left to right)
Fractions
a/b + c/d = (ad + bc)/bd, a/b × c/d = ac/bd, a/b ÷ c/d = a/b × d/c
Percent
p% of N = (p/100)·N; percent = part/whole × 100
Percent change
(new − original)/original × 100
Discount, then tax
price × (1 − d/100) × (1 + t/100)
Proportion
a/b = c/d → ad = bc
Mean, median, mode, range
sum/count; middle of ordered list; most frequent; max − min
Length, capacity, time
1 km = 1000 m, 1 m = 100 cm, 1 ft = 12 in, 1 yd = 3 ft, 1 mi = 5280 ft, 1 gal = 4 qt = 16 cups, 1 h = 60 min
Temperature
°F = °C·9/5 + 32, °C = (°F − 32)·5/9; a change of 1 °C = 1.8 °F
Area
rectangle l·w, triangle ½·b·h, circle π·r²
Perimeter and circumference
rectangle 2l + 2w, circle π·d = 2π·r
Volume
box l·w·h, cylinder π·r²·h; 1000 cm³ = 1 L
Speed
distance ÷ time (time in hours for mph or km/h)

Method

  1. Read the last sentence first: what exactly is asked, and in which unit or form (lowest terms, nearest cent, one decimal place)?
  2. Write the numbers in one form: turn mixed numbers into improper fractions, percents into decimals, and hours and minutes into one unit.
  3. Pick the method: PEMDAS for expressions, a common denominator for adding fractions, part ÷ whole × 100 for percents, cross-multiplying for proportions, inverse operations for equations.
  4. Work one step at a time and write each line down; round only at the very end.
  5. Check the size of the answer with an estimate, and put an equation’s answer back in.

Nursing math & unit conversions

Metric steps
1 kg = 1000 g, 1 g = 1000 mg, 1 mg = 1000 mcg, 1 L = 1000 mL
Weight and length
1 kg = 2.2 lb, 1 lb = 16 oz, 1 in = 2.54 cm, 1 ft = 12 in
Household measures
1 tsp = 5 mL, 1 tbsp = 15 mL, 1 fl oz = 30 mL, 1 cup = 8 fl oz = 240 mL
Temperature
°C = (°F − 32)·5/9, °F = °C·9/5 + 32
24-hour clock
PM hours 1–11: add 12; 12 AM = 00:xx; 12 PM = 12:xx
Dose rate
mcg/min × 60/1000 = mg/h
Laboratory factors
glucose 1 mmol/L = 18 mg/dL; creatinine 1 mg/dL = 88.4 µmol/L; Hb 1 g/dL = 10 g/L

Method

  1. Write the given quantity with its unit and the unit you want.
  2. Pick the equivalent: 1000 between kg, g, mg and mcg or L and mL; 1 kg = 2.2 lb; 1 tsp = 5 mL, 1 tbsp = 15 mL, 1 fl oz = 30 mL, 1 cup = 240 mL.
  3. Write it as a fraction so that the unwanted unit cancels; for a rate, use one fraction per unit that changes.
  4. Check the direction: a smaller unit gives a bigger number.
  5. Round only the final answer, to the precision the question names.

2Practice problems

1.Pre-nursing math (entrance exam)Medium

Calculate x = 8.4 ÷ 0.4 without a calculator. Give the exact value.

x = 8.4 ÷ 0.4
x =
2.Pre-nursing math (entrance exam)Hard
20242025A280150B50240C280170

The table shows the number of volunteers at centres A, B and C in 2024 and 2025. What was the mean number of volunteers per year x̄ at centre B over the two years?

x̄ =
3.Nursing math & unit conversionsMedium
1234567891011129:10 AM?09:1008:1010:1021:10

Practice exercise (made-up values, not clinical guidance). A dose is charted at 9:10 AM. Which entry is the same time on the 24-hour clock? Click it.

9:10 AM
  1. 109:10
  2. 208:10
  3. 310:10
  4. 421:10
4.Nursing math & unit conversionsHard
10 mg/h? mcg/min1 mg = 1000 mcg1 h = 60 min

Practice exercise (made-up values, not clinical guidance). An infusion delivers 10 mg/h. Express this dose rate D in mcg/min. Round to one decimal place.

10 mg/h1 mg = 1000 mcg1 h = 60 min
D = mcg/min

3Solutions

1.Pre-nursing math (entrance exam)

Answer: x = 21

Decimals: to add or subtract, line up the decimal points. To multiply, multiply as whole numbers and give the product as many decimal places as the two factors have together. To divide by a decimal, move the decimal point of both numbers the same number of places to the right until the divisor is a whole number.

Move the decimal points and divide

Multiply both numbers by 10 so that the divisor is a whole number.

x = 8.4 ÷ 0.4 = 21

Answer

x = 21
2.Pre-nursing math (entrance exam)

Answer: x̄ = 145

Mean, median, mode and range: the mean (average) is the sum divided by the number of values. The median is the middle value once the values are in order; with an even number of values it is the mean of the two middle ones. The mode is the value that occurs most often. The range is the largest value minus the smallest.

Row B

50 + 240 = 290

Mean

x̄ = 290/2 = 145

Answer

x̄ = 145
3.Nursing math & unit conversions

Answer: 09:10

24-hour clock: from 1 PM onwards add 12 to the hour (3:45 PM = 15:45). Midnight to 12:59 AM is 00:00–00:59, and 12:00–12:59 PM stays 12:00–12:59. Going back, subtract 12 from hours 13–23 and add PM; hours 00 become 12 AM. Count time across midnight in two parts: up to 24:00 (00:00), then from 00:00 on.

Convert the hour

9 AM → 09

Answer

09:10

Answer

09:10
4.Nursing math & unit conversions

Answer: D = 166.7 mcg/min

Dimensional analysis: write the given quantity, then multiply by conversion factors written as fractions (for example 60 min/1 h or 1 mg/1000 mcg) so that each unwanted unit appears once on top and once underneath and cancels. When only the wanted unit is left, calculate. Use the equivalents the question gives and round only the final answer.

Set up the chain

D = 10 mg/h × (1000 mcg/1 mg) × (1 h/60 min)

Calculate

D = 10000/60 = 166.7 mcg/min

Answer

D = 166.7 mcg/min

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