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

The price of a textbook changed from $790 to $1185. What is the percent increase p?

790 → 1185

p = %

2.Pre-nursing math (entrance exam)Hard

In a course, homework counts 20%, the midterm 30% and the final exam 50% of the grade. A student scores 93% on homework, 84% on the midterm and 65% on the final. What is the course grade G? Round to one decimal place.

20% · 9330% · 8450% · 65

G = %

3.Nursing math & unit conversionsMedium

Practice exercise (made-up values, not clinical guidance). A newborn weighs 4 lb 7 oz. Using 1 lb = 16 oz and 1 kg = 2.2 lb, find the weight m in kilograms. Round to two decimal places.

4 lb 7 oz1 lb = 16 oz1 kg = 2.2 lb

m = kg

4.Nursing math & unit conversionsHard

Practice exercise (made-up values, not clinical guidance). A prescription reads 1 tsp of an oral suspension every 6 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?

1 tspevery 6 hours14 days50 mL1 tsp = 5 mL

N =

3Solutions

1.Pre-nursing math (entrance exam)

Answer: p = 50 %

Percent means per hundred: p% of a number is (p/100) × the number. To find what percent A is of B, divide A by B and multiply by 100. A percent change compares the change with the original value: percent change = (new − original)/original × 100.

Change

1185 − 790 = 395

Compare with the original

p = 395/790 × 100 = 50%

Answer

p = 50%

2.Pre-nursing math (entrance exam)

Answer: G = 76.3 %

Weighted average: when parts count for different percentages, multiply each score by its weight (as a decimal) and add. A plain mean of the scores is only right when every part counts equally.

Weight each score

0.2 × 93 = 18.6

0.3 × 84 = 25.2

0.5 × 65 = 32.5

Add

G = 18.6 + 25.2 + 32.5 = 76.3%

Answer

G = 76.3%

3.Nursing math & unit conversions

Answer: m = 2.02 kg

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.

Ounces to pounds

7 oz/16 = 0.4375 lb

4 + 0.4375 = 4.438 lb

Pounds to kilograms

m = 4.438/2.2 = 2.017 ≈ 2.02 kg

Answer

m = 2.02 kg

4.Nursing math & unit conversions

Answer: N = 6

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

5 mL × 4 × 14 = 280 mL

Bottles

280/50 = 5.6 → N = 6

Answer

N = 6

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