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 line graph shows the outdoor temperature every 2 hours, from hour 0 to hour 10. What was the largest increase Δ between two neighbouring readings (2 hours apart)?

Δ = °C

2.Pre-nursing math (entrance exam)Hard

During a spring day the outdoor temperature rose by 4 °C. By how many degrees Fahrenheit Δ did it rise?

Δ = 4 °C

Δ = °F

3.Nursing math & unit conversionsMedium

Practice exercise (made-up values, not clinical guidance). A patient is 184 cm tall. Using 1 in = 2.54 cm, find the height h in inches. Round to one decimal place.

184 cm1 in = 2.54 cm

h = in

4.Nursing math & unit conversionsHard

Practice exercise (made-up values, not clinical guidance). An order reads 10 mcg/kg/min for a patient who weighs 45 kg. Express the dose rate D in mg/h. Round to two decimal places.

10 mcg/kg/min45 kg

D = mg/h

3Solutions

1.Pre-nursing math (entrance exam)

Answer: Δ = 4 °C

Reading charts and tables: read the title, the categories and the scale first. On a bar chart or line graph, follow the top of the bar or the point across to the vertical axis; every gridline is one step of the scale. A pie chart shows parts of a whole: a sector of p% stands for p% of the total and has an angle of p% of 360°.

Changes between neighbours

0→2: +4, 2→4: −2, 4→6: +2, 6→8: +2, 8→10: 0

Largest increase

Δ = 4 °C

Answer

Δ = 4 °C

2.Pre-nursing math (entrance exam)

Answer: Δ = 7.2 °F

Temperature scales: °F = °C × 9/5 + 32 and °C = (°F − 32) × 5/9. A temperature change converts without the 32, because the 32 only shifts the zero point: a change of 1 °C is a change of 1.8 °F.

Change only: no 32

Δ = 4 × 9/5 = 7.2 °F

Answer

Δ = 7.2 °F

3.Nursing math & unit conversions

Answer: h = 72.4 in

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.

Centimetres to inches

h = 184/2.54 = 72.44 ≈ 72.4 in

Answer

h = 72.4 in

4.Nursing math & unit conversions

Answer: D = 27 mg/h

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.

Set up the chain

D = 10 mcg/kg/min × 45 kg × (60 min/1 h) × (1 mg/1000 mcg)

Calculate

D = 10·45·60/1000 = 27 mg/h

Answer

D = 27 mg/h

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