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

  1. Read the last sentence first: what exactly is asked, and in which unit or form (lowest terms, nearest cent, one decimal place)?
  2. Write the numbers in one form: turn mixed numbers into improper fractions, percents into decimals, and hours and minutes into one unit.
  3. 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.
  4. Work one step at a time and write each line down; round only at the very end.
  5. 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

  1. Write the given quantity with its unit and the unit you want.
  2. 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.
  3. Write it as a fraction so that the unwanted unit cancels; for a rate, use one fraction per unit that changes.
  4. Check the direction: a smaller unit gives a bigger number.
  5. Round only the final answer, to the precision the question names.

2Practice problems

1.Pre-nursing math (entrance exam)Medium

A bookshelf is 2 ft 2 in tall. How many inches x is that?

2 ft 2 in1 ft = 12 in
x = in
2.Pre-nursing math (entrance exam)Hard

A box of 208 gloves is shared between three wards in the ratio 1 : 2 : 5. How many gloves x does the first ward get?

2081 : 2 : 5
x =
3.Nursing math & unit conversionsMedium
94969810010210410635363738394041°F°C99.8 °F? °C

Practice exercise (made-up values, not clinical guidance). A patient’s temperature is 99.8 °F. Convert it to degrees Celsius T with °C = (°F − 32) × 5/9. Round to one decimal place.

99.8 °F
T = °C
4.Nursing math & unit conversionsHard
¾ cup? mL4 fl oz? mL½ tbsp? mLΣ = ? mL

Practice exercise (made-up values, not clinical guidance). During a shift a patient takes ¾ cup of tea, 4 fl oz of juice, ½ tbsp of liquid supplement. Using the equivalents given, find the total oral intake V in mL.

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

3Solutions

1.Pre-nursing math (entrance exam)

Answer: x = 26 in

Unit conversions: multiply by a factor that equals 1, written so that the old unit cancels: 3 ft × 12 in/1 ft = 36 in. Metric length: 1 km = 1000 m, 1 m = 100 cm = 1000 mm, 1 cm = 10 mm. US customary: 1 ft = 12 in, 1 yd = 3 ft, 1 mi = 5280 ft; 1 gal = 4 qt, 1 qt = 2 pt, 1 pt = 2 cups; 1 ton = 2000 lb. Time: 1 h = 60 min, 1 min = 60 s, 1 day = 24 h, 1 week = 7 days. A smaller unit gives a bigger number.

Feet to inches

2 × 12 = 24 in

Add

x = 24 + 2 = 26 in

Answer

x = 26 in
2.Pre-nursing math (entrance exam)

Answer: x = 26

Ratios and proportions: a ratio a : b compares two amounts. In a proportion two ratios are equal, a/b = c/d, and you solve it by cross-multiplying: a·d = b·c. To share an amount in the ratio m : n, divide it into m + n equal parts; one share is m parts, the other n parts.

One part

208/8 = 26

Share

x = 1 × 26 = 26

Answer

x = 26
3.Nursing math & unit conversions

Answer: T = 37.7 °C

Temperature: °C = (°F − 32) × 5/9 and °F = °C × 9/5 + 32. Subtract 32 before you multiply when going from °F, and add 32 after you multiply when going from °C. A quick check: 37 °C is 98.6 °F, and every 1 °C is 1.8 °F.

Subtract 32

99.8 − 32 = 67.8

Multiply by 5/9

T = 67.8·5/9 = 37.67 ≈ 37.7 °C

Answer

T = 37.7 °C
4.Nursing math & unit conversions

Answer: V = 307.5 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

¾ cup = 0.75·240 = 180 mL
4 fl oz = 4·30 = 120 mL
½ tbsp = 0.5·15 = 7.5 mL

Add

V = 180 + 120 + 7.5 = 307.5 mL

Answer

V = 307.5 mL

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