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

Solve for x: 9x + 11 = 101.

9x + 11 = 101

x =

2.Pre-nursing math (entrance exam)Hard

Which fraction or mixed number in lowest terms equals the decimal 3.59? Click it.

3.59

11 41/59
28 9/10
33 59/1000
43 59/100

3.Nursing math & unit conversionsMedium

Practice exercise (made-up values, not clinical guidance). A patient is 6 ft 0 in tall. Using 1 ft = 12 in and 1 in = 2.54 cm, find the height h in centimetres, to the nearest whole centimetre.

6 ft 0 in1 ft = 12 in1 in = 2.54 cm

h = cm

4.Nursing math & unit conversionsHard

Practice exercise (made-up values, not clinical guidance). During a shift a patient takes 2 tbsp of liquid supplement, 4 fl oz of juice, 3 tsp of cough syrup, 1½ cups of tea. Using the equivalents given, find the total oral intake V in mL.

1 tbsp = 15 mL1 fl oz = 30 mL1 tsp = 5 mL1 cup = 8 fl oz = 240 mL

V = mL

3Solutions

1.Pre-nursing math (entrance exam)

Answer: x = 10

Solving equations: do the same thing to both sides until x stands alone. Undo operations in reverse order: first undo addition or subtraction, then multiplication or division. Clear parentheses with the distributive property, a(x + b) = ax + ab, and collect the x terms on one side. Check the answer by substituting it back.

Subtract 11 from both sides.

9x = 90

Divide both sides by 9.

x = 10

Check

9·10 + 11 = 101

Answer

x = 10

2.Pre-nursing math (entrance exam)

Answer: 3 59/100

Fractions, decimals and percents are three ways to write the same number. Fraction → decimal: divide the numerator by the denominator. Decimal → percent: multiply by 100 (move the point two places right). Percent → decimal: divide by 100. Decimal → fraction: write the digits over 10, 100 or 1000 (one zero per decimal place) and simplify.

Over a power of ten

0.59 = 59/100

Simplify

59/100

3.59 = 3 59/100

Answer

3 59/100

3.Nursing math & unit conversions

Answer: h = 183 cm

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.

Height in inches

6·12 + 0 = 72 in

Inches to centimetres

h = 72·2.54 = 182.9 ≈ 183 cm

Answer

h = 183 cm

4.Nursing math & unit conversions

Answer: V = 525 mL

Each item in mL

2 tbsp = 2·15 = 30 mL

4 fl oz = 4·30 = 120 mL

3 tsp = 3·5 = 15 mL

1½ cups = 1.5·240 = 360 mL

Add

V = 30 + 120 + 15 + 360 = 525 mL

Answer

V = 525 mL

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