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 = 11.4 ÷ 0.6 without a calculator. Give the exact value.

x = 11.4 ÷ 0.6
x =
2.Pre-nursing math (entrance exam)Hard

A gym charges a one-time sign-up fee of $40 plus $15 per month. Maria has paid $205 in total. For how many months n has she been a member?

$40$15/month$205
n = months
3.Nursing math & unit conversionsMedium
12345678910111211:15?11:15 AM10:15 AM11:15 PM1:15 AM

Practice exercise (made-up values, not clinical guidance). A dose is charted at 11:15 (24-hour clock). Which entry is the same time on the 12-hour clock? Click it.

11:15
  1. 111:15 AM
  2. 210:15 AM
  3. 311:15 PM
  4. 41:15 AM
4.Nursing math & unit conversionsHard
25 mcg/min? mg/h1 h = 60 min1 mg = 1000 mcg

Practice exercise (made-up values, not clinical guidance). An infusion delivers 25 mcg/min. Express this dose rate D in mg/h.

25 mcg/min1 h = 60 min1 mg = 1000 mcg
D = mg/h

3Solutions

1.Pre-nursing math (entrance exam)

Answer: x = 19

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 10 so that the divisor is a whole number.

x = 11.4 ÷ 0.6 = 19

Answer

x = 19
2.Pre-nursing math (entrance exam)

Answer: n = 11 months

Word problems: name the unknown (for example x = number of months), write the facts as one equation, solve it, and check that the answer makes sense in the story. A fixed fee plus a rate per unit gives total = fee + rate × units.

Equation

40 + 15n = 205

Solve

15n = 165
n = 165/15 = 11

Answer

n = 11 months
3.Nursing math & unit conversions

Answer: 11:15 AM

24-hour clock: from 1 PM onwards add 12 to the hour (3:45 PM = 15:45). Midnight to 12:59 AM is 00:00–00:59, and 12:00–12:59 PM stays 12:00–12:59. Going back, subtract 12 from hours 13–23 and add PM; hours 00 become 12 AM. Count time across midnight in two parts: up to 24:00 (00:00), then from 00:00 on.

Convert the hour

11 → 11 AM

Answer

11:15 AM

Answer

11:15 AM
4.Nursing math & unit conversions

Answer: D = 1.5 mg/h

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 = 25 mcg/min × (60 min/1 h) × (1 mg/1000 mcg)

Calculate

D = 25·60/1000 = 1.5 mg/h

Answer

D = 1.5 mg/h

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