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

A recipe uses 10 cups of flour for 5 batches of muffins. At the same rate, how many cups of flour x are needed for 7 batches?

10 : 5x : 7
x = cups
2.Pre-nursing math (entrance exam)Hard
5 1/101 41/1002 18/411 41/1000

Which fraction or mixed number in lowest terms equals 141%? Click it.

141%
  1. 15 1/10
  2. 21 41/100
  3. 32 18/41
  4. 41 41/1000
3.Nursing math & unit conversionsMedium
0.22723 mL? mLround to 0.01 mL

Practice exercise (made-up values, not clinical guidance). A dose calculation for a small injection gives 0.22723 mL. The rule in this exercise is that volumes below 1 mL are rounded to the nearest hundredth of a mL. What value x do you record?

0.22723 mL
x = mL
4.Nursing math & unit conversionsHard
1 mcg/kg/min? mg/h104 kg1 h = 60 min1 mg = 1000 mcg

Practice exercise (made-up values, not clinical guidance). An order reads 1 mcg/kg/min for a patient who weighs 104 kg. Express the dose rate D in mg/h. Round to two decimal places.

1 mcg/kg/min104 kg
D = mg/h

3Solutions

1.Pre-nursing math (entrance exam)

Answer: x = 14 cups

Ratios and proportions: a ratio a : b compares two amounts. In a proportion two ratios are equal, a/b = c/d, and you solve it by cross-multiplying: a·d = b·c. To share an amount in the ratio m : n, divide it into m + n equal parts; one share is m parts, the other n parts.

Proportion

10/5 = x/7

Cross-multiply and solve

5·x = 70
x = 70/5 = 14 cups

Answer

x = 14 cups
2.Pre-nursing math (entrance exam)

Answer: 1 41/100

Fractions, decimals and percents are three ways to write the same number. Fraction → decimal: divide the numerator by the denominator. Decimal → percent: multiply by 100 (move the point two places right). Percent → decimal: divide by 100. Decimal → fraction: write the digits over 10, 100 or 1000 (one zero per decimal place) and simplify.

Percent to decimal

141% = 1.41

Over a power of ten

0.41 = 41/100

Simplify

41/100
1.41 = 1 41/100

Answer

1 41/100
3.Nursing math & unit conversions

Answer: x = 0.23 mL

Rounding: look at the digit just after the place you round to: 5 or more rounds up, 4 or less leaves the digit as it is. Round only the final answer, never the steps. Typical exam rules: volumes of 1 mL or more to the nearest tenth, volumes below 1 mL to the nearest hundredth, drip rates to whole drops and weights to one decimal place; always follow the rule the question states.

Digit in the hundredths place

0.22723 → 2

Only the next digit decides

0.22723 → 7
7 is 5 or more, so round 2 up.
The digits after it (23) are ignored: round once, never step by step.

Round

x = 0.23 mL

Answer

x = 0.23 mL
4.Nursing math & unit conversions

Answer: D = 6.24 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 = 1 mcg/kg/min × 104 kg × (60 min/1 h) × (1 mg/1000 mcg)

Calculate

D = 1·104·60/1000 = 6.24 mg/h

Answer

D = 6.24 mg/h

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