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 = 4.6 × 0.8 without a calculator. Give the exact value.

x = 4.6 × 0.8
x =
2.Pre-nursing math (entrance exam)Hard

After a 15% pay rise, a nursing assistant earns $57.5 a week. What was the weekly pay x before the rise, in dollars?

$57.5+15%
x = $
3.Nursing math & unit conversionsMedium
94969810010210410635363738394041°F°C? °F37.6 °C

Practice exercise (made-up values, not clinical guidance). A patient’s temperature is 37.6 °C. Convert it to degrees Fahrenheit T with °F = °C × 9/5 + 32. Round to one decimal place.

37.6 °C
T = °F
4.Nursing math & unit conversionsHard
00:0022:5507:35t = ?

Practice exercise (made-up values, not clinical guidance). An infusion starts at 22:55 and finishes at 07:35 the next morning (24-hour clock). How many minutes t did it run?

22:5507:35
t = min

3Solutions

1.Pre-nursing math (entrance exam)

Answer: x = 3.68

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

Multiply 46 × 8 and then place the decimal point.

x = 4.6 × 0.8 = 3.68

Answer

x = 3.68
2.Pre-nursing math (entrance exam)

Answer: x = 50 $

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 = 57.5

Solve

x = 57.5/1.15 = $50.00

Answer

x = $50.00
3.Nursing math & unit conversions

Answer: T = 99.7 °F

Temperature: °C = (°F − 32) × 5/9 and °F = °C × 9/5 + 32. Subtract 32 before you multiply when going from °F, and add 32 after you multiply when going from °C. A quick check: 37 °C is 98.6 °F, and every 1 °C is 1.8 °F.

Multiply by 9/5

37.6·9/5 = 67.68

Add 32

T = 67.68 + 32 = 99.68 ≈ 99.7 °F

Answer

T = 99.7 °F
4.Nursing math & unit conversions

Answer: t = 520 min

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

22:55 → 24:00 = 65 min

After midnight

00:00 → 07:35 = 455 min

Total

t = 65 + 455 = 520 min

Answer

t = 520 min

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