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 ages of the patients seen at a clinic one morning were 37, 18, 37, 7, 27, 37. What is the mode M?

37, 18, 37, 7, 27, 37

M =

2.Pre-nursing math (entrance exam)Hard

In a 30% off sale, a stethoscope costs $56. What was the original price x, in dollars?

$56−30%

x = $

3.Nursing math & unit conversionsMedium

Practice exercise (made-up values, not clinical guidance). A patient is 6 ft 10 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 10 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 ½ cup of tea, 3 tbsp of liquid supplement, 6 fl oz of juice, ½ tsp of cough syrup. Using the equivalents given, find the total oral intake V in mL.

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

V = mL

3Solutions

1.Pre-nursing math (entrance exam)

Answer: M = 37

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.

Count each value

7, 18, 27, 37, 37, 37

Most frequent

M = 37 (3×)

Answer

M = 37

2.Pre-nursing math (entrance exam)

Answer: x = 80 $

Reverse percentages: when a value has already been increased or decreased by a percent, the new value is a percent of the original, not the other way round. After a 20% discount the price is 80% of the original, so original = new price ÷ 0.80. Never add the 20% back on to the new price.

Set up the equation

0.7 · x = 56

Solve

x = 56/0.7 = $80.00

Answer

x = $80.00

3.Nursing math & unit conversions

Answer: h = 208 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 + 10 = 82 in

Inches to centimetres

h = 82·2.54 = 208.3 ≈ 208 cm

Answer

h = 208 cm

4.Nursing math & unit conversions

Answer: V = 347.5 mL

Each item in mL

½ cup = 0.5·240 = 120 mL

3 tbsp = 3·15 = 45 mL

6 fl oz = 6·30 = 180 mL

½ tsp = 0.5·5 = 2.5 mL

Add

V = 120 + 45 + 180 + 2.5 = 347.5 mL

Answer

V = 347.5 mL

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