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 numbers of call-light requests on a unit over 6 nights were 31, 22, 27, 3, 20, 5. What is the median m?

31, 22, 27, 3, 20, 5
m =
2.Pre-nursing math (entrance exam)Hard

On a map, 1 cm represents 5 km. Two towns are 6 cm apart on the map. What is the real distance x in kilometres?

1 cm : 5 km6 cm
x = km
3.Nursing math & unit conversionsMedium
12345678910111221:45?11:45 PM9:45 AM9:45 PM8:45 PM

Practice exercise (made-up values, not clinical guidance). A dose is charted at 21:45 (24-hour clock). Which entry is the same time on the 12-hour clock? Click it.

21:45
  1. 111:45 PM
  2. 29:45 AM
  3. 39:45 PM
  4. 48:45 PM
4.Nursing math & unit conversionsHard
1 tsp · 2/day · 14 d? × 100 mL1 tsp = 5 mL

Practice exercise (made-up values, not clinical guidance). A prescription reads 1 tsp of an oral suspension twice a day for 14 days. The suspension comes in 100 mL bottles. Using 1 tsp = 5 mL, how many whole bottles N must be supplied so the course is complete?

1 tsptwice a day14 days100 mL1 tsp = 5 mL
N =

3Solutions

1.Pre-nursing math (entrance exam)

Answer: m = 21

Mean, median, mode and range: the mean (average) is the sum divided by the number of values. The median is the middle value once the values are in order; with an even number of values it is the mean of the two middle ones. The mode is the value that occurs most often. The range is the largest value minus the smallest.

Order the values

3, 5, 20, 22, 27, 31

Middle

m = (20 + 22)/2 = 21

Answer

m = 21
2.Pre-nursing math (entrance exam)

Answer: x = 30 km

Rates and scales: speed = distance ÷ time, with the time in the unit of the answer (2 h 15 min = 2.25 h, because 15 min = 15/60 h). A map scale is a proportion: 1 cm on the map stands for a fixed distance on the ground, so multiply the map distance by it.

Multiply by the scale

x = 6 × 5 = 30 km

Answer

x = 30 km
3.Nursing math & unit conversions

Answer: 9:45 PM

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

21 − 12 = 9 → PM

Answer

9:45 PM

Answer

9:45 PM
4.Nursing math & unit conversions

Answer: N = 2

Dimensional analysis: write the given quantity, then multiply by conversion factors written as fractions (for example 60 min/1 h or 1 mg/1000 mcg) so that each unwanted unit appears once on top and once underneath and cancels. When only the wanted unit is left, calculate. Use the equivalents the question gives and round only the final answer.

Total volume

5 mL × 2 × 14 = 140 mL

Bottles

140/100 = 1.4 → N = 2

Answer

N = 2

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