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
d = 26 cm

A circle has a diameter of 26 cm. Using π ≈ 3.14, find its circumference C.

d = 26 cmπ ≈ 3.14
C = cm
2.Pre-nursing math (entrance exam)Hard

During a spring day the outdoor temperature rose by 10 °C. By how many degrees Fahrenheit Δ did it rise?

Δ = 10 °C
Δ = °F
3.Nursing math & unit conversionsMedium
179.015 gtt/min? gtt/minround to 1 gtt/min

Practice exercise (made-up values, not clinical guidance). A drip-rate calculation gives 179.015 gtt/min. The rule in this exercise is that drip rates are rounded to the nearest whole drop. What value x do you record?

179.015 gtt/min
x = gtt/min
4.Nursing math & unit conversionsHard
3 fl oz? mL1½ tsp? mL1½ cups? mL1½ tbsp? mLΣ = ? mL

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

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

3Solutions

1.Pre-nursing math (entrance exam)

Answer: C = 81.64 cm

Perimeter, area and volume: the perimeter is the distance around a shape (rectangle: 2l + 2w). Area is measured in square units: rectangle l × w, triangle ½ × base × height, circle π·r². The circumference of a circle is π·d = 2π·r. Volume is in cubic units: box l × w × h, cylinder π·r²·h. Use the value of π the question gives.

Circumference

C = 3.14 × 26 = 81.64 cm

Answer

C = 81.64 cm
2.Pre-nursing math (entrance exam)

Answer: Δ = 18 °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 = 10 × 9/5 = 18 °F

Answer

Δ = 18 °F
3.Nursing math & unit conversions

Answer: x = 179 gtt/min

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 ones place

179.015 → 9

Only the next digit decides

179.015 → 0
0 is 4 or less, so 9 stays.
The digits after it (15) are ignored: round once, never step by step.

Round

x = 179 gtt/min

Answer

x = 179 gtt/min
4.Nursing math & unit conversions

Answer: V = 480 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

3 fl oz = 3·30 = 90 mL
1½ tsp = 1.5·5 = 7.5 mL
1½ cups = 1.5·240 = 360 mL
1½ tbsp = 1.5·15 = 22.5 mL

Add

V = 90 + 7.5 + 360 + 22.5 = 480 mL

Answer

V = 480 mL

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