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: 2x − 5 = 3.

2x − 5 = 3
x =
2.Pre-nursing math (entrance exam)Hard

Solve for x: 6(x − 9) = x + 11.

6(x − 9) = x + 11
x =
3.Nursing math & unit conversionsMedium
209.401 gtt/min? gtt/minround to 1 gtt/min

Practice exercise (made-up values, not clinical guidance). A drip-rate calculation gives 209.401 gtt/min. The rule in this exercise is that drip rates are rounded to the nearest whole drop. What value x do you record?

209.401 gtt/min
x = gtt/min
4.Nursing math & unit conversionsHard
4 fl oz? mL½ tbsp? mL1 tsp? mLΣ = ? mL

Practice exercise (made-up values, not clinical guidance). During a shift a patient takes 4 fl oz of juice, ½ tbsp of liquid supplement, 1 tsp of cough syrup. Using the equivalents given, find the total oral intake V in mL.

1 fl oz = 30 mL1 tbsp = 15 mL1 tsp = 5 mL
V = mL

3Solutions

1.Pre-nursing math (entrance exam)

Answer: x = 4

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.

Add 5 to both sides.

2x = 8

Divide both sides by 2.

x = 4

Check

2·4 − 5 = 3

Answer

x = 4
2.Pre-nursing math (entrance exam)

Answer: x = 13

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

6x − 54 = x + 11

Collect terms

5x = 65

Divide

x = 65/5 = 13

Answer

x = 13
3.Nursing math & unit conversions

Answer: x = 209 gtt/min

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 ones place

209.401 → 9

Only the next digit decides

209.401 → 4
4 is 4 or less, so 9 stays.
The digits after it (01) are ignored: round once, never step by step.

Round

x = 209 gtt/min

Answer

x = 209 gtt/min
4.Nursing math & unit conversions

Answer: V = 132.5 mL

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.

Each item in mL

4 fl oz = 4·30 = 120 mL
½ tbsp = 0.5·15 = 7.5 mL
1 tsp = 1·5 = 5 mL

Add

V = 120 + 7.5 + 5 = 132.5 mL

Answer

V = 132.5 mL

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