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

Read the last sentence first: what exactly is asked, and in which unit or form (lowest terms, nearest cent, one decimal place)?
Write the numbers in one form: turn mixed numbers into improper fractions, percents into decimals, and hours and minutes into one unit.
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.
Work one step at a time and write each line down; round only at the very end.
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

Write the given quantity with its unit and the unit you want.
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.
Write it as a fraction so that the unwanted unit cancels; for a rate, use one fraction per unit that changes.
Check the direction: a smaller unit gives a bigger number.
Round only the final answer, to the precision the question names.

2Practice problems

1.Pre-nursing math (entrance exam)Medium

How many minutes x are there in 3 days?

3 days1 day = 24 h1 h = 60 min

x = min

2.Pre-nursing math (entrance exam)Hard

Use the order of operations to find the value of x: x = 5 × (32 − 9 × 3) − 3².

x = 5 × (32 − 9 × 3) − 3²

x =

3.Nursing math & unit conversionsMedium

Practice exercise (made-up values, not clinical guidance). A patient is 163 cm tall. Using 1 in = 2.54 cm, find the height h in inches. Round to one decimal place.

163 cm1 in = 2.54 cm

h = in

4.Nursing math & unit conversionsHard

Practice exercise (made-up values, not clinical guidance). A blood glucose result is 341 mg/dL. Using 1 mmol/L = 18 mg/dL for glucose, find c in mmol/L. Round to one decimal place.

341 mg/dL1 mmol/L = 18 mg/dL

c = mmol/L

3Solutions

1.Pre-nursing math (entrance exam)

Answer: x = 4320 min

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.

Days to hours

3 × 24 = 72 h

Hours to minutes

x = 72 × 60 = 4320 min

Answer

x = 4320 min

2.Pre-nursing math (entrance exam)

Answer: x = 16

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

Inside the parentheses, multiply 9 × 3 before subtracting.

x = 5 × (32 − 9 × 3) − 3²

= 5 × (32 − 27) − 3²

= 5 × 5 − 3²

= 5 × 5 − 9

= 25 − 9

Result

x = 16

Answer

x = 16

3.Nursing math & unit conversions

Answer: h = 64.2 in

Household measures and weight: nursing exams use rounded equivalents: 1 teaspoon (tsp) = 5 mL, 1 tablespoon (tbsp) = 15 mL = 3 tsp, 1 fluid ounce (fl oz) = 30 mL = 2 tbsp, and 1 cup = 8 fl oz = 240 mL. For weight, 1 kg = 2.2 lb and 1 lb = 16 oz; for length, 1 inch = 2.54 cm. Set the conversion up so that the unit you do not want cancels out.

Centimetres to inches

h = 163/2.54 = 64.17 ≈ 64.2 in

Answer

h = 64.2 in

4.Nursing math & unit conversions

Answer: c = 18.9 mmol/L

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.

Convert

c = 341/18 = 18.94 ≈ 18.9 mmol/L

Answer

c = 18.9 mmol/L

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