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 = 2.05 × 2.2 without a calculator. Give the exact value.

x = 2.05 × 2.2
x =
2.Pre-nursing math (entrance exam)Hard

After a 15% pay rise, a nursing assistant earns $276 a week. What was the weekly pay x before the rise, in dollars?

$276+15%
x = $
3.Nursing math & unit conversionsMedium
230.697 gtt/min? gtt/minround to 1 gtt/min

Practice exercise (made-up values, not clinical guidance). A drip-rate calculation gives 230.697 gtt/min. The rule in this exercise is that drip rates are rounded to the nearest whole drop. What value x do you record?

230.697 gtt/min
x = gtt/min
4.Nursing math & unit conversionsHard
½ tsp · 3/day · 5 d? mL1 tsp = 5 mL

Practice exercise (made-up values, not clinical guidance). A prescription reads ½ tsp of an oral suspension three times a day for 5 days. Using 1 tsp = 5 mL, how many mL V are needed for the whole course?

½ tspthree times a day5 days1 tsp = 5 mL
V = mL

3Solutions

1.Pre-nursing math (entrance exam)

Answer: x = 4.51

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.

Multiply and place the point

The factors have 3 decimal places together.

x = 2.05 × 2.2 = 4.51

Answer

x = 4.51
2.Pre-nursing math (entrance exam)

Answer: x = 240 $

Reverse percentages: when a value has already been increased or decreased by a percent, the new value is a percent of the original, not the other way round. After a 20% discount the price is 80% of the original, so original = new price ÷ 0.80. Never add the 20% back on to the new price.

Set up the equation

1.15 · x = 276

Solve

x = 276/1.15 = $240.00

Answer

x = $240.00
3.Nursing math & unit conversions

Answer: x = 231 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

230.697 → 0

Only the next digit decides

230.697 → 6
6 is 5 or more, so round 0 up.
The digits after it (97) are ignored: round once, never step by step.

Round

x = 231 gtt/min

Answer

x = 231 gtt/min
4.Nursing math & unit conversions

Answer: V = 37.5 mL

Dimensional analysis: write the given quantity, then multiply by conversion factors written as fractions (for example 60 min/1 h or 1 mg/1000 mcg) so that each unwanted unit appears once on top and once underneath and cancels. When only the wanted unit is left, calculate. Use the equivalents the question gives and round only the final answer.

Volume per dose

½ tsp = 0.5·5 = 2.5 mL

Whole course

V = 2.5 mL × 3/day × 5 = 37.5 mL

Answer

V = 37.5 mL

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