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

Two volunteers share $156 in the ratio 7 : 6. How much x does the person with the larger share get, in dollars?

$1567 : 6
x = $
2.Pre-nursing math (entrance exam)Hard

Use the order of operations to find the value of x: x = (−3)² − 9 × (−1) ÷ 3.

x = (−3)² − 9 × (−1) ÷ 3
x =
3.Nursing math & unit conversionsMedium
1234567891011129:40 AM?10:4021:4009:4008:40

Practice exercise (made-up values, not clinical guidance). A dose is charted at 9:40 AM. Which entry is the same time on the 24-hour clock? Click it.

9:40 AM
  1. 110:40
  2. 221:40
  3. 309:40
  4. 408:40
4.Nursing math & unit conversionsHard
3 cups? mL1½ tbsp? mL1½ fl oz? mLΣ = ? mL

Practice exercise (made-up values, not clinical guidance). During a shift a patient takes 3 cups of tea, 1½ tbsp of liquid supplement, 1½ fl oz of juice. 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 mL
V = mL

3Solutions

1.Pre-nursing math (entrance exam)

Answer: x = 84 $

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.

Value of one part

156/(7 + 6) = 12

Larger share

x = 7 × 12 = $84.00

Answer

x = $84.00
2.Pre-nursing math (entrance exam)

Answer: x = 12

Order of operations (PEMDAS/BODMAS): work inside parentheses first, then exponents (powers), then multiplication and division from left to right, and last addition and subtraction from left to right. Multiplication does not come before division, and addition does not come before subtraction: each pair is done in the order it appears. A negative number in parentheses keeps its sign when squared: (−3)² = 9, but −3² = −9.

One operation at a time

(−3)² is positive: a negative times a negative is positive.

x = (−3)² − 9 × (−1) ÷ 3
= 9 − 9 × (−1) ÷ 3
= 9 − (−9) ÷ 3
= 9 − (−3)

Result

x = 12

Answer

x = 12
3.Nursing math & unit conversions

Answer: 09:40

24-hour clock: from 1 PM onwards add 12 to the hour (3:45 PM = 15:45). Midnight to 12:59 AM is 00:00–00:59, and 12:00–12:59 PM stays 12:00–12:59. Going back, subtract 12 from hours 13–23 and add PM; hours 00 become 12 AM. Count time across midnight in two parts: up to 24:00 (00:00), then from 00:00 on.

Convert the hour

9 AM → 09

Answer

09:40

Answer

09:40
4.Nursing math & unit conversions

Answer: V = 787.5 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

3 cups = 3·240 = 720 mL
1½ tbsp = 1.5·15 = 22.5 mL
1½ fl oz = 1.5·30 = 45 mL

Add

V = 720 + 22.5 + 45 = 787.5 mL

Answer

V = 787.5 mL

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