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

The price of a textbook changed from $625 to $700. What is the percent increase p?

625 → 700
p = %
2.Pre-nursing math (entrance exam)Hard

A box of 60 gloves is shared between three wards in the ratio 5 : 3 : 4. How many gloves x does the second ward get?

605 : 3 : 4
x =
3.Nursing math & unit conversionsMedium
5 lb 1 oz? kg1 lb = 16 oz1 kg = 2.2 lb

Practice exercise (made-up values, not clinical guidance). A newborn weighs 5 lb 1 oz. Using 1 lb = 16 oz and 1 kg = 2.2 lb, find the weight m in kilograms. Round to two decimal places.

5 lb 1 oz1 lb = 16 oz1 kg = 2.2 lb
m = kg
4.Nursing math & unit conversionsHard
6 fl oz? mL2 cups? mL3 tsp? mL4 tbsp? mLΣ = ? mL

Practice exercise (made-up values, not clinical guidance). During a shift a patient takes 6 fl oz of juice, 2 cups of tea, 3 tsp of cough syrup, 4 tbsp of liquid supplement. Using the equivalents given, find the total oral intake V in mL.

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

3Solutions

1.Pre-nursing math (entrance exam)

Answer: p = 12 %

Percent means per hundred: p% of a number is (p/100) × the number. To find what percent A is of B, divide A by B and multiply by 100. A percent change compares the change with the original value: percent change = (new − original)/original × 100.

Change

700 − 625 = 75

Compare with the original

p = 75/625 × 100 = 12%

Answer

p = 12%
2.Pre-nursing math (entrance exam)

Answer: x = 15

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

60/12 = 5

Share

x = 3 × 5 = 15

Answer

x = 15
3.Nursing math & unit conversions

Answer: m = 2.3 kg

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.

Ounces to pounds

1 oz/16 = 0.0625 lb
5 + 0.0625 = 5.063 lb

Pounds to kilograms

m = 5.063/2.2 = 2.301 ≈ 2.3 kg

Answer

m = 2.3 kg
4.Nursing math & unit conversions

Answer: V = 735 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

6 fl oz = 6·30 = 180 mL
2 cups = 2·240 = 480 mL
3 tsp = 3·5 = 15 mL
4 tbsp = 4·15 = 60 mL

Add

V = 180 + 480 + 15 + 60 = 735 mL

Answer

V = 735 mL

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