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
71/20003 11/202 58/7171/200

Which fraction or mixed number in lowest terms equals the decimal 0.355? Click it.

0.355
  1. 171/2000
  2. 23 11/20
  3. 32 58/71
  4. 471/200
2.Pre-nursing math (entrance exam)Hard

In a course, homework counts 15%, the midterm 35% and the final exam 50% of the grade. A student scores 76% on homework, 78% on the midterm and 72% on the final. What is the course grade G? Round to one decimal place.

15% · 7635% · 7850% · 72
G = %
3.Nursing math & unit conversionsMedium
141 cm1 in = 2.54 cmh = ? in

Practice exercise (made-up values, not clinical guidance). A patient is 141 cm tall. Using 1 in = 2.54 cm, find the height h in inches. Round to one decimal place.

141 cm1 in = 2.54 cm
h = in
4.Nursing math & unit conversionsHard
00:0023:4506:50t = ?

Practice exercise (made-up values, not clinical guidance). An infusion starts at 23:45 and finishes at 06:50 the next morning (24-hour clock). How many minutes t did it run?

23:4506:50
t = min

3Solutions

1.Pre-nursing math (entrance exam)

Answer: 71/200

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

0.355 = 355/1000

Simplify

355/1000 = 71/200
0.355 = 71/200

Answer

71/200
2.Pre-nursing math (entrance exam)

Answer: G = 74.7 %

Weighted average: when parts count for different percentages, multiply each score by its weight (as a decimal) and add. A plain mean of the scores is only right when every part counts equally.

Weight each score

0.15 × 76 = 11.4
0.35 × 78 = 27.3
0.5 × 72 = 36

Add

G = 11.4 + 27.3 + 36 = 74.7%

Answer

G = 74.7%
3.Nursing math & unit conversions

Answer: h = 55.5 in

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.

Centimetres to inches

h = 141/2.54 = 55.51 ≈ 55.5 in

Answer

h = 55.5 in
4.Nursing math & unit conversions

Answer: t = 425 min

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.

Before midnight

23:45 → 24:00 = 15 min

After midnight

00:00 → 06:50 = 410 min

Total

t = 15 + 410 = 425 min

Answer

t = 425 min

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