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

Two volunteers share $220 in the ratio 6 : 5. How much x does the person with the larger share get, in dollars?

$2206 : 5
x = $
2.Pre-nursing math (entrance exam)Hard

Your first 4 exam scores are 69, 94, 93, 72. What score x do you need on the next exam for a mean of exactly 84 over all 5 exams?

69, 94, 93, 72x̄ = 84
x =
3.Nursing math & unit conversionsMedium
6 lb 2 oz? kg1 lb = 16 oz1 kg = 2.2 lb

Practice exercise (made-up values, not clinical guidance). A newborn weighs 6 lb 2 oz. Using 1 lb = 16 oz and 1 kg = 2.2 lb, find the weight m in kilograms. Round to two decimal places.

6 lb 2 oz1 lb = 16 oz1 kg = 2.2 lb
m = kg
4.Nursing math & unit conversionsHard
1 fl oz? mL1 cup? mL4 tbsp? mLΣ = ? mL

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

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

3Solutions

1.Pre-nursing math (entrance exam)

Answer: x = 120 $

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.

Value of one part

220/(6 + 5) = 20

Larger share

x = 6 × 20 = $120.00

Answer

x = $120.00
2.Pre-nursing math (entrance exam)

Answer: x = 92

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.

Total needed

84 × 5 = 420

Score needed

x = 420 − 328 = 92

Answer

x = 92
3.Nursing math & unit conversions

Answer: m = 2.78 kg

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.

Ounces to pounds

2 oz/16 = 0.125 lb
6 + 0.125 = 6.125 lb

Pounds to kilograms

m = 6.125/2.2 = 2.784 ≈ 2.78 kg

Answer

m = 2.78 kg
4.Nursing math & unit conversions

Answer: V = 330 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

1 fl oz = 1·30 = 30 mL
1 cup = 1·240 = 240 mL
4 tbsp = 4·15 = 60 mL

Add

V = 30 + 240 + 60 = 330 mL

Answer

V = 330 mL

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