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
25/348 1/21 9/252 3/10

Work out 3 2/5 ÷ 2 1/2. Click the answer in lowest terms.

3 2/5 ÷ 2 1/2
  1. 125/34
  2. 28 1/2
  3. 31 9/25
  4. 42 3/10
2.Pre-nursing math (entrance exam)Hard
ABCA: 30%B: 5%C: 65%

The pie chart shows how a hospital’s 240 employees are split between departments A to C. What is the angle θ of the sector for department C, in degrees?

θ = °
3.Nursing math & unit conversionsMedium
94969810010210410635363738394041°F°C97.7 °F? °C

Practice exercise (made-up values, not clinical guidance). A patient’s temperature is 97.7 °F. Convert it to degrees Celsius T with °C = (°F − 32) × 5/9. Round to one decimal place.

97.7 °F
T = °C
4.Nursing math & unit conversionsHard
4 mcg/kg/min? mg/h65 kg1 h = 60 min1 mg = 1000 mcg

Practice exercise (made-up values, not clinical guidance). An order reads 4 mcg/kg/min for a patient who weighs 65 kg. Express the dose rate D in mg/h. Round to two decimal places.

4 mcg/kg/min65 kg
D = mg/h

3Solutions

1.Pre-nursing math (entrance exam)

Answer: 1 9/25

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

3 2/5 = 17/5
2 1/2 = 5/2

Multiply by the reciprocal

17/5 ÷ 5/2 = 17/5 × 2/5 = 34/25

Simplify

34/25 = 1 9/25

Answer

1 9/25
2.Pre-nursing math (entrance exam)

Answer: θ = 234 °

Reading charts and tables: read the title, the categories and the scale first. On a bar chart or line graph, follow the top of the bar or the point across to the vertical axis; every gridline is one step of the scale. A pie chart shows parts of a whole: a sector of p% stands for p% of the total and has an angle of p% of 360°.

Share of 360°

θ = 0.65 × 360° = 234°

Answer

θ = 234°
3.Nursing math & unit conversions

Answer: T = 36.5 °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

97.7 − 32 = 65.7

Multiply by 5/9

T = 65.7·5/9 = 36.5 °C

Answer

T = 36.5 °C
4.Nursing math & unit conversions

Answer: D = 15.6 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 = 4 mcg/kg/min × 65 kg × (60 min/1 h) × (1 mg/1000 mcg)

Calculate

D = 4·65·60/1000 = 15.6 mg/h

Answer

D = 15.6 mg/h

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