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 pair of shoes costs $114.99. It is on sale at 40% off, and a sales tax of 5% is added to the sale price. What is the final price P? Round to the nearest cent.

$114.99−40%+5%
P = $
2.Pre-nursing math (entrance exam)Hard

Your first 5 exam scores are 88, 90, 80, 86, 71. What score x do you need on the next exam for a mean of exactly 85 over all 6 exams?

88, 90, 80, 86, 71x̄ = 85
x =
3.Nursing math & unit conversionsMedium
76.562 gtt/min? gtt/minround to 1 gtt/min

Practice exercise (made-up values, not clinical guidance). A drip-rate calculation gives 76.562 gtt/min. The rule in this exercise is that drip rates are rounded to the nearest whole drop. What value x do you record?

76.562 gtt/min
x = gtt/min
4.Nursing math & unit conversionsHard
0.5 mg/h? mcg/min1 mg = 1000 mcg1 h = 60 min

Practice exercise (made-up values, not clinical guidance). An infusion delivers 0.5 mg/h. Express this dose rate D in mcg/min. Round to one decimal place.

0.5 mg/h1 mg = 1000 mcg1 h = 60 min
D = mcg/min

3Solutions

1.Pre-nursing math (entrance exam)

Answer: P = 72.44 $

Discounts and sales tax: a discount of d% leaves (100 − d)% of the price; a tax of t% adds t% of the discounted price. Work in that order: price × (1 − d/100), then × (1 + t/100). Round money to the nearest cent only at the end.

Sale price

$114.99 × 0.6 = 68.994 ≈ $68.99

Add the tax

P = $68.99 × 1.05 = 72.4395 ≈ $72.44

Answer

P = $72.44
2.Pre-nursing math (entrance exam)

Answer: x = 95

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

85 × 6 = 510

Score needed

x = 510 − 415 = 95

Answer

x = 95
3.Nursing math & unit conversions

Answer: x = 77 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

76.562 → 6

Only the next digit decides

76.562 → 5
5 is 5 or more, so round 6 up.
The digits after it (62) are ignored: round once, never step by step.

Round

x = 77 gtt/min

Answer

x = 77 gtt/min
4.Nursing math & unit conversions

Answer: D = 8.3 mcg/min

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.

Set up the chain

D = 0.5 mg/h × (1000 mcg/1 mg) × (1 h/60 min)

Calculate

D = 500/60 = 8.333 ≈ 8.3 mcg/min

Answer

D = 8.3 mcg/min

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