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
2 4/135 5/365/63 13/18

Work out 3 1/4 + 1 8/9. Click the answer in lowest terms.

3 1/4 + 1 8/9
  1. 12 4/13
  2. 25 5/36
  3. 35/6
  4. 43 13/18
2.Pre-nursing math (entrance exam)Hard
4 2/32 1/21 11/218

Work out 2 2/3 × 1 3/4. Click the answer in lowest terms.

2 2/3 × 1 3/4
  1. 14 2/3
  2. 22 1/2
  3. 31 11/21
  4. 48
3.Nursing math & unit conversionsMedium
215.852 gtt/min? gtt/minround to 1 gtt/min

Practice exercise (made-up values, not clinical guidance). A drip-rate calculation gives 215.852 gtt/min. The rule in this exercise is that drip rates are rounded to the nearest whole drop. What value x do you record?

215.852 gtt/min
x = gtt/min
4.Nursing math & unit conversionsHard
1½ tbsp? mL3 fl oz? mL1 cup? mL1½ tsp? mLΣ = ? mL

Practice exercise (made-up values, not clinical guidance). During a shift a patient takes 1½ tbsp of liquid supplement, 3 fl oz of juice, 1 cup of tea, 1½ 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: 5 5/36

Adding and subtracting fractions: the denominators must be the same. Find the least common denominator (LCD), rewrite each fraction with it by multiplying top and bottom by the same number, then add or subtract the numerators only. Simplify by dividing top and bottom by their greatest common factor, and write an improper fraction as a mixed number.

Improper fractions

3 1/4 = 13/4
1 8/9 = 17/9

Common denominator

The least common multiple of 4 and 9 is 36.

13/4 = 117/36
17/9 = 68/36

Add the numerators

117/36 + 68/36 = 185/36

Simplify

185/36 = 5 5/36

Answer

5 5/36
2.Pre-nursing math (entrance exam)

Answer: 4 2/3

Multiplying and dividing fractions: first turn mixed numbers into improper fractions (2 1/3 = 7/3). To multiply, multiply the numerators and the denominators. To divide, keep the first fraction, change ÷ to ×, and flip the second fraction (multiply by its reciprocal). Cancel common factors and write the result in lowest terms as a mixed number.

Improper fractions

2 2/3 = 8/3
1 3/4 = 7/4

Multiply

8/3 × 7/4 = 56/12

Simplify

56/12 = 4 2/3

Answer

4 2/3
3.Nursing math & unit conversions

Answer: x = 216 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

215.852 → 5

Only the next digit decides

215.852 → 8
8 is 5 or more, so round 5 up.
The digits after it (52) are ignored: round once, never step by step.

Round

x = 216 gtt/min

Answer

x = 216 gtt/min
4.Nursing math & unit conversions

Answer: V = 360 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

1½ tbsp = 1.5·15 = 22.5 mL
3 fl oz = 3·30 = 90 mL
1 cup = 1·240 = 240 mL
1½ tsp = 1.5·5 = 7.5 mL

Add

V = 22.5 + 90 + 240 + 7.5 = 360 mL

Answer

V = 360 mL

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