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

Solve for x: 6(x + 14) = 120.

6(x + 14) = 120
x =
2.Pre-nursing math (entrance exam)Hard

Solve for x: 7(x − 2) = 2x + 1.

7(x − 2) = 2x + 1
x =
3.Nursing math & unit conversionsMedium
116.1318 kg? kground to 0.1 kg

Practice exercise (made-up values, not clinical guidance). A weight conversion gives 116.1318 kg. The rule in this exercise is that weights are rounded to the nearest tenth of a kilogram. What value x do you record?

116.1318 kg
x = kg
4.Nursing math & unit conversionsHard
18.9 mmol/L? mg/dL1 mmol/L = 18 mg/dL

Practice exercise (made-up values, not clinical guidance). A blood glucose result is 18.9 mmol/L. Using 1 mmol/L = 18 mg/dL for glucose, find c in mg/dL to the nearest whole number.

18.9 mmol/L1 mmol/L = 18 mg/dL
c = mg/dL

3Solutions

1.Pre-nursing math (entrance exam)

Answer: x = 6

Solving equations: do the same thing to both sides until x stands alone. Undo operations in reverse order: first undo addition or subtraction, then multiplication or division. Clear parentheses with the distributive property, a(x + b) = ax + ab, and collect the x terms on one side. Check the answer by substituting it back.

Divide both sides by 6 (or multiply out the parentheses).

x + 14 = 20

Subtract 14 from both sides.

x = 6

Check

6·(6 + 14) = 120

Answer

x = 6
2.Pre-nursing math (entrance exam)

Answer: x = 3

Solving equations: do the same thing to both sides until x stands alone. Undo operations in reverse order: first undo addition or subtraction, then multiplication or division. Clear parentheses with the distributive property, a(x + b) = ax + ab, and collect the x terms on one side. Check the answer by substituting it back.

Distribute

7x − 14 = 2x + 1

Collect terms

5x = 15

Divide

x = 15/5 = 3

Answer

x = 3
3.Nursing math & unit conversions

Answer: x = 116.1 kg

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 tenths place

116.1318 → 1

Only the next digit decides

116.1318 → 3
3 is 4 or less, so 1 stays.
The digits after it (18) are ignored: round once, never step by step.

Round

x = 116.1 kg

Answer

x = 116.1 kg
4.Nursing math & unit conversions

Answer: c = 340 mg/dL

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.

Convert

c = 18.9·18 = 340.2 ≈ 340 mg/dL

Answer

c = 340 mg/dL

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