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

Use the order of operations to find the value of x: x = 5² − 2 × (12 − 11) + 4.

x = 5² − 2 × (12 − 11) + 4
x =
2.Pre-nursing math (entrance exam)Hard
5 65/1873 187/10003 187/100004 87/100

Which fraction or mixed number in lowest terms equals the decimal 3.187? Click it.

3.187
  1. 15 65/187
  2. 23 187/1000
  3. 33 187/10000
  4. 44 87/100
3.Nursing math & unit conversionsMedium
4.5427 mL? mLround to 0.1 mL

Practice exercise (made-up values, not clinical guidance). A dose calculation for an injection gives 4.5427 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?

4.5427 mL
x = mL
4.Nursing math & unit conversionsHard
00:0018:3502:35t = ?

Practice exercise (made-up values, not clinical guidance). An infusion starts at 18:35 and finishes at 02:35 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.

18:3502:35
t = h

3Solutions

1.Pre-nursing math (entrance exam)

Answer: x = 27

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

5² means 5 × 5, not 5 × 2.

x = 5² − 2 × (12 − 11) + 4
= 5² − 2 × 1 + 4
= 25 − 2 × 1 + 4
= 25 − 2 + 4
= 23 + 4

Result

x = 27

Answer

x = 27
2.Pre-nursing math (entrance exam)

Answer: 3 187/1000

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

0.187 = 187/1000

Simplify

187/1000
3.187 = 3 187/1000

Answer

3 187/1000
3.Nursing math & unit conversions

Answer: x = 4.5 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

4.5427 → 5

Only the next digit decides

4.5427 → 4
4 is 4 or less, so 5 stays.
The digits after it (27) are ignored: round once, never step by step.

Round

x = 4.5 mL

Answer

x = 4.5 mL
4.Nursing math & unit conversions

Answer: t = 8 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

18:35 → 24:00 = 325 min

After midnight

00:00 → 02:35 = 155 min

Total

325 + 155 = 480 min
t = 480/60 = 8 h

Answer

t = 8 h

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