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
2 1/46 2/72 1/163 2/3

Work out 2 3/4 × 1 1/3. Click the answer in lowest terms.

2 3/4 × 1 1/3
  1. 12 1/4
  2. 26 2/7
  3. 32 1/16
  4. 43 2/3
2.Pre-nursing math (entrance exam)Hard
20242025A270215B280265C125185

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 A over the two years?

x̄ =
3.Nursing math & unit conversionsMedium
8 lb 13 oz? kg1 lb = 16 oz1 kg = 2.2 lb

Practice exercise (made-up values, not clinical guidance). A newborn weighs 8 lb 13 oz. Using 1 lb = 16 oz and 1 kg = 2.2 lb, find the weight m in kilograms. Round to two decimal places.

8 lb 13 oz1 lb = 16 oz1 kg = 2.2 lb
m = kg
4.Nursing math & unit conversionsHard
00:0019:1503:00t = ?

Practice exercise (made-up values, not clinical guidance). An infusion starts at 19:15 and finishes at 03:00 the next morning (24-hour clock). How many hours t did it run? Give the answer in hours as a decimal, rounded to two decimal places.

19:1503:00
t = h

3Solutions

1.Pre-nursing math (entrance exam)

Answer: 3 2/3

Multiplying and dividing fractions: first turn mixed numbers into improper fractions (2 1/3 = 7/3). To multiply, multiply the numerators and the denominators. To divide, keep the first fraction, change ÷ to ×, and flip the second fraction (multiply by its reciprocal). Cancel common factors and write the result in lowest terms as a mixed number.

Improper fractions

2 3/4 = 11/4
1 1/3 = 4/3

Multiply

11/4 × 4/3 = 44/12

Simplify

44/12 = 3 2/3

Answer

3 2/3
2.Pre-nursing math (entrance exam)

Answer: x̄ = 242.5

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 A

270 + 215 = 485

Mean

x̄ = 485/2 = 242.5

Answer

x̄ = 242.5
3.Nursing math & unit conversions

Answer: m = 4.01 kg

Household measures and weight: nursing exams use rounded equivalents: 1 teaspoon (tsp) = 5 mL, 1 tablespoon (tbsp) = 15 mL = 3 tsp, 1 fluid ounce (fl oz) = 30 mL = 2 tbsp, and 1 cup = 8 fl oz = 240 mL. For weight, 1 kg = 2.2 lb and 1 lb = 16 oz; for length, 1 inch = 2.54 cm. Set the conversion up so that the unit you do not want cancels out.

Ounces to pounds

13 oz/16 = 0.8125 lb
8 + 0.8125 = 8.813 lb

Pounds to kilograms

m = 8.813/2.2 = 4.006 ≈ 4.01 kg

Answer

m = 4.01 kg
4.Nursing math & unit conversions

Answer: t = 7.75 h

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.

Before midnight

19:15 → 24:00 = 285 min

After midnight

00:00 → 03:00 = 180 min

Total

285 + 180 = 465 min
t = 465/60 = 7.75 h

Answer

t = 7.75 h

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