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
d = 6 m

A circle has a diameter of 6 m. Using π ≈ 3.14, find its circumference C.

d = 6 mπ ≈ 3.14
C = m
2.Pre-nursing math (entrance exam)Hard
20242025A280230B255270C115110

The table shows the number of volunteers at centres A, B and C in 2024 and 2025. What percent p of all 2025 volunteers were at centre B? Round to the nearest whole number.

p = %
3.Nursing math & unit conversionsMedium
94969810010210410635363738394041°F°C97.9 °F? °C

Practice exercise (made-up values, not clinical guidance). A patient’s temperature is 97.9 °F. Convert it to degrees Celsius T with °C = (°F − 32) × 5/9. Round to one decimal place.

97.9 °F
T = °C
4.Nursing math & unit conversionsHard
1 mg/h? mcg/min1 mg = 1000 mcg1 h = 60 min

Practice exercise (made-up values, not clinical guidance). An infusion delivers 1 mg/h. Express this dose rate D in mcg/min. Round to one decimal place.

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

3Solutions

1.Pre-nursing math (entrance exam)

Answer: C = 18.84 m

Perimeter, area and volume: the perimeter is the distance around a shape (rectangle: 2l + 2w). Area is measured in square units: rectangle l × w, triangle ½ × base × height, circle π·r². The circumference of a circle is π·d = 2π·r. Volume is in cubic units: box l × w × h, cylinder π·r²·h. Use the value of π the question gives.

Circumference

C = 3.14 × 6 = 18.84 m

Answer

C = 18.84 m
2.Pre-nursing math (entrance exam)

Answer: p = 44 %

Percent means per hundred: p% of a number is (p/100) × the number. To find what percent A is of B, divide A by B and multiply by 100. A percent change compares the change with the original value: percent change = (new − original)/original × 100.

Total 2025

230 + 270 + 110 = 610

Percent

p = 270/610 × 100 = 44.26 ≈ 44%

Answer

p = 44%
3.Nursing math & unit conversions

Answer: T = 36.6 °C

Temperature: °C = (°F − 32) × 5/9 and °F = °C × 9/5 + 32. Subtract 32 before you multiply when going from °F, and add 32 after you multiply when going from °C. A quick check: 37 °C is 98.6 °F, and every 1 °C is 1.8 °F.

Subtract 32

97.9 − 32 = 65.9

Multiply by 5/9

T = 65.9·5/9 = 36.61 ≈ 36.6 °C

Answer

T = 36.6 °C
4.Nursing math & unit conversions

Answer: D = 16.7 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 = 1 mg/h × (1000 mcg/1 mg) × (1 h/60 min)

Calculate

D = 1000/60 = 16.67 ≈ 16.7 mcg/min

Answer

D = 16.7 mcg/min

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