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

Calculate x = 0.068 ÷ 0.17 without a calculator. Give the exact value.

x = 0.068 ÷ 0.17
x =
2.Pre-nursing math (entrance exam)Hard
10 53/1001 247/7533 753/100003 753/1000

Which fraction or mixed number in lowest terms equals the decimal 3.753? Click it.

3.753
  1. 110 53/100
  2. 21 247/753
  3. 33 753/10000
  4. 43 753/1000
3.Nursing math & unit conversionsMedium
14.0181 mL? mLround to 0.1 mL

Practice exercise (made-up values, not clinical guidance). A dose calculation for an injection gives 14.0181 mL. The rule in this exercise is that volumes of 1 mL or more are rounded to the nearest tenth of a mL. What value x do you record?

14.0181 mL
x = mL
4.Nursing math & unit conversionsHard
2 cups? mL1 tbsp? mL6 fl oz? mLΣ = ? mL

Practice exercise (made-up values, not clinical guidance). During a shift a patient takes 2 cups of tea, 1 tbsp of liquid supplement, 6 fl oz of juice. Using the equivalents given, find the total oral intake V in mL.

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

3Solutions

1.Pre-nursing math (entrance exam)

Answer: x = 0.4

Decimals: to add or subtract, line up the decimal points. To multiply, multiply as whole numbers and give the product as many decimal places as the two factors have together. To divide by a decimal, move the decimal point of both numbers the same number of places to the right until the divisor is a whole number.

Move the decimal points and divide

Multiply both numbers by 100 so that the divisor is a whole number.

x = 0.068 ÷ 0.17 = 0.4

Answer

x = 0.4
2.Pre-nursing math (entrance exam)

Answer: 3 753/1000

Fractions, decimals and percents are three ways to write the same number. Fraction → decimal: divide the numerator by the denominator. Decimal → percent: multiply by 100 (move the point two places right). Percent → decimal: divide by 100. Decimal → fraction: write the digits over 10, 100 or 1000 (one zero per decimal place) and simplify.

Over a power of ten

0.753 = 753/1000

Simplify

753/1000
3.753 = 3 753/1000

Answer

3 753/1000
3.Nursing math & unit conversions

Answer: x = 14 mL

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

14.0181 → 0

Only the next digit decides

14.0181 → 1
1 is 4 or less, so 0 stays.
The digits after it (81) are ignored: round once, never step by step.

Round

x = 14 mL

Answer

x = 14 mL
4.Nursing math & unit conversions

Answer: V = 675 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

2 cups = 2·240 = 480 mL
1 tbsp = 1·15 = 15 mL
6 fl oz = 6·30 = 180 mL

Add

V = 480 + 15 + 180 = 675 mL

Answer

V = 675 mL

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