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

A clinic saw 40 patients in March and 36 in April. What is the percent decrease p?

40 → 36

p = %

2.Pre-nursing math (entrance exam)Hard

A hospital fundraiser has 54 raffle tickets. 1/3 of them are sold on the first day, and 1/3 of the remaining tickets are sold on the second day. How many tickets x are still unsold?

541/31/3

x =

3.Nursing math & unit conversionsMedium

Practice exercise (made-up values, not clinical guidance). A dose is charted at 7:15 AM. Which entry is the same time on the 24-hour clock? Click it.

7:15 AM

107:15
208:15
319:15
406:15

4.Nursing math & unit conversionsHard

Practice exercise (made-up values, not clinical guidance). A prescription reads 1 tbsp of an oral suspension three times a day for 10 days. Using 1 tbsp = 15 mL, how many mL V are needed for the whole course?

1 tbspthree times a day10 days1 tbsp = 15 mL

V = mL

3Solutions

1.Pre-nursing math (entrance exam)

Answer: p = 10 %

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

36 − 40 = −4

Compare with the original

p = 4/40 × 100 = 10%

Answer

p = 10%

2.Pre-nursing math (entrance exam)

Answer: x = 24

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.

After the first day

54 − 1/3·54 = 54 − 18 = 36

After the second day

36 − 1/3·36 = 36 − 12 = 24

Answer

x = 24

3.Nursing math & unit conversions

Answer: 07:15

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

7 AM → 07

Answer

07:15

Answer

07:15

4.Nursing math & unit conversions

Answer: V = 450 mL

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.

Volume per dose

1 tbsp = 1·15 = 15 mL

Whole course

V = 15 mL × 3/day × 10 = 450 mL

Answer

V = 450 mL

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