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 walking trail is 0.25 miles long. How many feet x is that?

0.25 mi1 mi = 5280 ft
x = ft
2.Pre-nursing math (entrance exam)Hard

Use the order of operations to find the value of x: x = −3² + 4 × 7.

x = −3² + 4 × 7
x =
3.Nursing math & unit conversionsMedium
1234567891011126:20 AM?05:2018:2007:2006:20

Practice exercise (made-up values, not clinical guidance). A dose is charted at 6:20 AM. Which entry is the same time on the 24-hour clock? Click it.

6:20 AM
  1. 105:20
  2. 218:20
  3. 307:20
  4. 406:20
4.Nursing math & unit conversionsHard
00:0020:4003:45t = ?

Practice exercise (made-up values, not clinical guidance). An infusion starts at 20:40 and finishes at 03:45 the next morning (24-hour clock). How many hours t did it run? Give the answer in hours as a decimal, rounded to two decimal places.

20:4003:45
t = h

3Solutions

1.Pre-nursing math (entrance exam)

Answer: x = 1320 ft

Unit conversions: multiply by a factor that equals 1, written so that the old unit cancels: 3 ft × 12 in/1 ft = 36 in. Metric length: 1 km = 1000 m, 1 m = 100 cm = 1000 mm, 1 cm = 10 mm. US customary: 1 ft = 12 in, 1 yd = 3 ft, 1 mi = 5280 ft; 1 gal = 4 qt, 1 qt = 2 pt, 1 pt = 2 cups; 1 ton = 2000 lb. Time: 1 h = 60 min, 1 min = 60 s, 1 day = 24 h, 1 week = 7 days. A smaller unit gives a bigger number.

Miles to feet

x = 0.25 × 5280 = 1320 ft

Answer

x = 1320 ft
2.Pre-nursing math (entrance exam)

Answer: x = 19

Order of operations (PEMDAS/BODMAS): work inside parentheses first, then exponents (powers), then multiplication and division from left to right, and last addition and subtraction from left to right. Multiplication does not come before division, and addition does not come before subtraction: each pair is done in the order it appears. A negative number in parentheses keeps its sign when squared: (−3)² = 9, but −3² = −9.

One operation at a time

−3² means −(3²) = −9: the exponent comes before the minus sign.

x = −3² + 4 × 7
= −9 + 4 × 7
= −9 + 28

Result

x = 19

Answer

x = 19
3.Nursing math & unit conversions

Answer: 06:20

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

6 AM → 06

Answer

06:20

Answer

06:20
4.Nursing math & unit conversions

Answer: t = 7.08 h

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.

Before midnight

20:40 → 24:00 = 200 min

After midnight

00:00 → 03:45 = 225 min

Total

200 + 225 = 425 min
t = 425/60 = 7.083 ≈ 7.08 h

Answer

t = 7.08 h

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