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

Work out 1 3/10 + 1/2. Click the answer in lowest terms.

1 3/10 + 1/2

11 1/6
27/10
31 2/5
41 4/5

2.Pre-nursing math (entrance exam)Hard

A mother is 4 years older than 4 times her son’s age. Together their ages add up to 24 years. How old x is the son?

Σ = 24

x = years

3.Nursing math & unit conversionsMedium

Practice exercise (made-up values, not clinical guidance). A dose is charted at 10:25 PM. Which entry is the same time on the 24-hour clock? Click it.

10:25 PM

121:25
210:25
323:25
422:25

4.Nursing math & unit conversionsHard

Practice exercise (made-up values, not clinical guidance). During a shift a patient takes 1 tbsp of liquid supplement, 3 tsp of cough syrup, 2 cups of tea. Using the equivalents given, find the total oral intake V in mL.

1 tbsp = 15 mL1 tsp = 5 mL1 cup = 8 fl oz = 240 mL

V = mL

3Solutions

1.Pre-nursing math (entrance exam)

Answer: 1 4/5

Adding and subtracting fractions: the denominators must be the same. Find the least common denominator (LCD), rewrite each fraction with it by multiplying top and bottom by the same number, then add or subtract the numerators only. Simplify by dividing top and bottom by their greatest common factor, and write an improper fraction as a mixed number.

Improper fractions

1 3/10 = 13/10

1/2 = 1/2

Common denominator

The least common multiple of 10 and 2 is 10.

13/10 = 13/10

1/2 = 5/10

Add the numerators

13/10 + 5/10 = 18/10

Simplify

18/10 = 1 4/5

Answer

1 4/5

2.Pre-nursing math (entrance exam)

Answer: x = 4 years

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

x + (4x + 4) = 24

Solve

5x = 20

x = 4

Answer

x = 4 years

3.Nursing math & unit conversions

Answer: 22:25

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

10 PM → 10 + 12 = 22

Answer

22:25

Answer

22:25

4.Nursing math & unit conversions

Answer: V = 510 mL

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.

Each item in mL

1 tbsp = 1·15 = 15 mL

3 tsp = 3·5 = 15 mL

2 cups = 2·240 = 480 mL

Add

V = 15 + 15 + 480 = 510 mL

Answer

V = 510 mL

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