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

Read the last sentence first: what exactly is asked, and in which unit or form (lowest terms, nearest cent, one decimal place)?
Write the numbers in one form: turn mixed numbers into improper fractions, percents into decimals, and hours and minutes into one unit.
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.
Work one step at a time and write each line down; round only at the very end.
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

Write the given quantity with its unit and the unit you want.
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.
Write it as a fraction so that the unwanted unit cancels; for a rate, use one fraction per unit that changes.
Check the direction: a smaller unit gives a bigger number.
Round only the final answer, to the precision the question names.

2Practice problems

1.Pre-nursing math (entrance exam)Medium

Calculate x = 0.33 ÷ 0.22 without a calculator. Give the exact value.

x = 0.33 ÷ 0.22

x =

2.Pre-nursing math (entrance exam)Hard

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 A? Round to the nearest whole number.

p = %

3.Nursing math & unit conversionsMedium

Practice exercise (made-up values, not clinical guidance). A newborn weighs 8 lb 9 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 9 oz1 lb = 16 oz1 kg = 2.2 lb

m = kg

4.Nursing math & unit conversionsHard

Practice exercise (made-up values, not clinical guidance). An order reads 0.5 mcg/kg/min for a patient who weighs 75 kg. Express the dose rate D in mg/h. Round to two decimal places.

0.5 mcg/kg/min75 kg

D = mg/h

3Solutions

1.Pre-nursing math (entrance exam)

Answer: x = 1.5

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 100 so that the divisor is a whole number.

x = 0.33 ÷ 0.22 = 1.5

Answer

x = 1.5

2.Pre-nursing math (entrance exam)

Answer: p = 37 %

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

245 + 195 + 230 = 670

Percent

p = 245/670 × 100 = 36.57 ≈ 37%

Answer

p = 37%

3.Nursing math & unit conversions

Answer: m = 3.89 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

9 oz/16 = 0.5625 lb

8 + 0.5625 = 8.563 lb

Pounds to kilograms

m = 8.563/2.2 = 3.892 ≈ 3.89 kg

Answer

m = 3.89 kg

4.Nursing math & unit conversions

Answer: D = 2.25 mg/h

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 = 0.5 mcg/kg/min × 75 kg × (60 min/1 h) × (1 mg/1000 mcg)

Calculate

D = 0.5·75·60/1000 = 2.25 mg/h

Answer

D = 2.25 mg/h

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