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 ages of the patients seen at a clinic one morning were 19, 28, 19, 24, 22, 6, 24, 19. What is the mode M?

19, 28, 19, 24, 22, 6, 24, 19
M =
2.Pre-nursing math (entrance exam)Hard

In a course, homework counts 25%, the midterm 25% and the final exam 50% of the grade. A student scores 98% on homework, 98% on the midterm and 85% on the final. What is the course grade G? Round to one decimal place.

25% · 9825% · 9850% · 85
G = %
3.Nursing math & unit conversionsMedium
83.078 gtt/min? gtt/minround to 1 gtt/min

Practice exercise (made-up values, not clinical guidance). A drip-rate calculation gives 83.078 gtt/min. The rule in this exercise is that drip rates are rounded to the nearest whole drop. What value x do you record?

83.078 gtt/min
x = gtt/min
4.Nursing math & unit conversionsHard
00:0018:4508:30t = ?

Practice exercise (made-up values, not clinical guidance). An infusion starts at 18:45 and finishes at 08:30 the next morning (24-hour clock). How many minutes t did it run?

18:4508:30
t = min

3Solutions

1.Pre-nursing math (entrance exam)

Answer: M = 19

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.

Count each value

6, 19, 19, 19, 22, 24, 24, 28

Most frequent

M = 19 (3×)

Answer

M = 19
2.Pre-nursing math (entrance exam)

Answer: G = 91.5 %

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

0.25 × 98 = 24.5
0.25 × 98 = 24.5
0.5 × 85 = 42.5

Add

G = 24.5 + 24.5 + 42.5 = 91.5%

Answer

G = 91.5%
3.Nursing math & unit conversions

Answer: x = 83 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

83.078 → 3

Only the next digit decides

83.078 → 0
0 is 4 or less, so 3 stays.
The digits after it (78) are ignored: round once, never step by step.

Round

x = 83 gtt/min

Answer

x = 83 gtt/min
4.Nursing math & unit conversions

Answer: t = 825 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

18:45 → 24:00 = 315 min

After midnight

00:00 → 08:30 = 510 min

Total

t = 315 + 510 = 825 min

Answer

t = 825 min

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