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 student’s quiz scores are 88, 86, 87, 85, 94. What is the mean score x̄?

88, 86, 87, 85, 94
x̄ =
2.Pre-nursing math (entrance exam)Hard

A home-care nurse drives 110 miles in 2 h 45 min. What is the average speed v in miles per hour?

110 mi2 h 45 min
v = mph
3.Nursing math & unit conversionsMedium
94969810010210410635363738394041°F°C? °F35.5 °C

Practice exercise (made-up values, not clinical guidance). A patient’s temperature is 35.5 °C. Convert it to degrees Fahrenheit T with °F = °C × 9/5 + 32. Round to one decimal place.

35.5 °C
T = °F
4.Nursing math & unit conversionsHard
½ tbsp? mL1½ fl oz? mL2 cups? mL2 tsp? mLΣ = ? mL

Practice exercise (made-up values, not clinical guidance). During a shift a patient takes ½ tbsp of liquid supplement, 1½ fl oz of juice, 2 cups of tea, 2 tsp of cough syrup. Using the equivalents given, find the total oral intake V in mL.

1 tbsp = 15 mL1 fl oz = 30 mL1 cup = 8 fl oz = 240 mL1 tsp = 5 mL
V = mL

3Solutions

1.Pre-nursing math (entrance exam)

Answer: x̄ = 88

Mean, median, mode and range: the mean (average) is the sum divided by the number of values. The median is the middle value once the values are in order; with an even number of values it is the mean of the two middle ones. The mode is the value that occurs most often. The range is the largest value minus the smallest.

Sum

88 + 86 + 87 + 85 + 94 = 440

Divide by the count

x̄ = 440/5 = 88

Answer

x̄ = 88
2.Pre-nursing math (entrance exam)

Answer: v = 40 mph

Rates and scales: speed = distance ÷ time, with the time in the unit of the answer (2 h 15 min = 2.25 h, because 15 min = 15/60 h). A map scale is a proportion: 1 cm on the map stands for a fixed distance on the ground, so multiply the map distance by it.

Time in hours

2 + 45/60 = 2.75 h

Speed

v = 110/2.75 = 40 mph

Answer

v = 40 mph
3.Nursing math & unit conversions

Answer: T = 95.9 °F

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.

Multiply by 9/5

35.5·9/5 = 63.9

Add 32

T = 63.9 + 32 = 95.9 °F

Answer

T = 95.9 °F
4.Nursing math & unit conversions

Answer: V = 542.5 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

½ tbsp = 0.5·15 = 7.5 mL
1½ fl oz = 1.5·30 = 45 mL
2 cups = 2·240 = 480 mL
2 tsp = 2·5 = 10 mL

Add

V = 7.5 + 45 + 480 + 10 = 542.5 mL

Answer

V = 542.5 mL

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