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 + 3/5. Click the answer in lowest terms.

1/3 + 3/5

14/15
21/2
314/15
48/15

2.Pre-nursing math (entrance exam)Hard

A recipe needs 1 3/4 cups of oats. You make 1 1/2 times the recipe. How much do you need? Click the answer in lowest terms.

1 3/4× 1 1/2

12 5/8
23 1/4
31 1/2
41 1/6

3.Nursing math & unit conversionsMedium

Practice exercise (made-up values, not clinical guidance). A dose calculation for a small injection gives 0.67595 mL. The rule in this exercise is that volumes below 1 mL are rounded to the nearest hundredth of a mL. What value x do you record?

0.67595 mL

x = mL

4.Nursing math & unit conversionsHard

Practice exercise (made-up values, not clinical guidance). A prescription reads 1½ tsp of an oral suspension every 12 hours for 14 days. The suspension comes in 50 mL bottles. Using 1 tsp = 5 mL, how many whole bottles N must be supplied so the course is complete?

1½ tspevery 12 hours14 days50 mL1 tsp = 5 mL

N =

3Solutions

1.Pre-nursing math (entrance exam)

Answer: 14/15

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.

Common denominator

The least common multiple of 3 and 5 is 15.

1/3 = 5/15

3/5 = 9/15

Add the numerators

5/15 + 9/15 = 14/15

Answer

14/15

2.Pre-nursing math (entrance exam)

Answer: 2 5/8

Multiplying and dividing fractions: first turn mixed numbers into improper fractions (2 1/3 = 7/3). To multiply, multiply the numerators and the denominators. To divide, keep the first fraction, change ÷ to ×, and flip the second fraction (multiply by its reciprocal). Cancel common factors and write the result in lowest terms as a mixed number.

Improper fractions

1 3/4 = 7/4

1 1/2 = 3/2

Multiply

7/4 × 3/2 = 21/8 = 2 5/8

Answer

2 5/8

3.Nursing math & unit conversions

Answer: x = 0.68 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 hundredths place

0.67595 → 7

Only the next digit decides

0.67595 → 5

5 is 5 or more, so round 7 up.

The digits after it (95) are ignored: round once, never step by step.

Round

x = 0.68 mL

Answer

x = 0.68 mL

4.Nursing math & unit conversions

Answer: N = 5

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.

Total volume

7.5 mL × 2 × 14 = 210 mL

Bottles

210/50 = 4.2 → N = 5

Answer

N = 5

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