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 numbers of call-light requests on a unit over 8 nights were 39, 17, 23, 6, 33, 38, 27, 10. What is the median m?

39, 17, 23, 6, 33, 38, 27, 10

m =

2.Pre-nursing math (entrance exam)Hard

A hospital fundraiser has 48 raffle tickets. 1/2 of them are sold on the first day, and 1/2 of the remaining tickets are sold on the second day. How many tickets x are still unsold?

481/21/2

x =

3.Nursing math & unit conversionsMedium

Practice exercise (made-up values, not clinical guidance). A weight conversion gives 147.1779 kg. The rule in this exercise is that weights are rounded to the nearest tenth of a kilogram. What value x do you record?

147.1779 kg

x = kg

4.Nursing math & unit conversionsHard

Practice exercise (made-up values, not clinical guidance). During a shift a patient takes 1½ cups of tea, 3 tsp of cough syrup, 2 fl oz of juice. Using the equivalents given, find the total oral intake V in mL.

1 cup = 8 fl oz = 240 mL1 tsp = 5 mL1 fl oz = 30 mL

V = mL

3Solutions

1.Pre-nursing math (entrance exam)

Answer: m = 25

Mean, median, mode and range: the mean (average) is the sum divided by the number of values. The median is the middle value once the values are in order; with an even number of values it is the mean of the two middle ones. The mode is the value that occurs most often. The range is the largest value minus the smallest.

Order the values

6, 10, 17, 23, 27, 33, 38, 39

Middle

m = (23 + 27)/2 = 25

Answer

m = 25

2.Pre-nursing math (entrance exam)

Answer: x = 12

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

48 − 1/2·48 = 48 − 24 = 24

After the second day

24 − 1/2·24 = 24 − 12 = 12

Answer

x = 12

3.Nursing math & unit conversions

Answer: x = 147.2 kg

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 tenths place

147.1779 → 1

Only the next digit decides

147.1779 → 7

7 is 5 or more, so round 1 up.

The digits after it (79) are ignored: round once, never step by step.

Round

x = 147.2 kg

Answer

x = 147.2 kg

4.Nursing math & unit conversions

Answer: V = 435 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

1½ cups = 1.5·240 = 360 mL

3 tsp = 3·5 = 15 mL

2 fl oz = 2·30 = 60 mL

Add

V = 360 + 15 + 60 = 435 mL

Answer

V = 435 mL

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