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
b = 22 fth = 16 ft

A triangle has a base of 22 ft and a height of 16 ft. What is its area A?

b = 22 fth = 16 ft
A = ft²
2.Pre-nursing math (entrance exam)Hard

In a course, homework counts 10%, the midterm 40% and the final exam 50% of the grade. A student scores 86% on homework, 87% on the midterm and 68% on the final. What is the course grade G? Round to one decimal place.

10% · 8640% · 8750% · 68
G = %
3.Nursing math & unit conversionsMedium
4 ft 10 in1 ft = 12 in1 in = 2.54 cmh = ? cm

Practice exercise (made-up values, not clinical guidance). A patient is 4 ft 10 in tall. Using 1 ft = 12 in and 1 in = 2.54 cm, find the height h in centimetres, to the nearest whole centimetre.

4 ft 10 in1 ft = 12 in1 in = 2.54 cm
h = cm
4.Nursing math & unit conversionsHard
00:0022:2501:00t = ?

Practice exercise (made-up values, not clinical guidance). An infusion starts at 22:25 and finishes at 01:00 the next morning (24-hour clock). How many minutes t did it run?

22:2501:00
t = min

3Solutions

1.Pre-nursing math (entrance exam)

Answer: A = 176 ft²

Perimeter, area and volume: the perimeter is the distance around a shape (rectangle: 2l + 2w). Area is measured in square units: rectangle l × w, triangle ½ × base × height, circle π·r². The circumference of a circle is π·d = 2π·r. Volume is in cubic units: box l × w × h, cylinder π·r²·h. Use the value of π the question gives.

Area

A = ½ × 22 × 16 = 176 ft²

Answer

A = 176 ft²
2.Pre-nursing math (entrance exam)

Answer: G = 77.4 %

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

0.1 × 86 = 8.6
0.4 × 87 = 34.8
0.5 × 68 = 34

Add

G = 8.6 + 34.8 + 34 = 77.4%

Answer

G = 77.4%
3.Nursing math & unit conversions

Answer: h = 147 cm

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.

Height in inches

4·12 + 10 = 58 in

Inches to centimetres

h = 58·2.54 = 147.3 ≈ 147 cm

Answer

h = 147 cm
4.Nursing math & unit conversions

Answer: t = 155 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

22:25 → 24:00 = 95 min

After midnight

00:00 → 01:00 = 60 min

Total

t = 95 + 60 = 155 min

Answer

t = 155 min

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