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

Read the last sentence first: what exactly is asked, and in which unit or form (lowest terms, nearest cent, one decimal place)?
Write the numbers in one form: turn mixed numbers into improper fractions, percents into decimals, and hours and minutes into one unit.
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.
Work one step at a time and write each line down; round only at the very end.
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

Write the given quantity with its unit and the unit you want.
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.
Write it as a fraction so that the unwanted unit cancels; for a rate, use one fraction per unit that changes.
Check the direction: a smaller unit gives a bigger number.
Round only the final answer, to the precision the question names.

2Practice problems

1.Pre-nursing math (entrance exam)Medium

A recipe uses 1.5 cups of flour for 3 batches of muffins. At the same rate, how many cups of flour x are needed for 18 batches?

1.5 : 3x : 18

x = cups

2.Pre-nursing math (entrance exam)Hard

A recipe says to bake at 220 °C. What is that temperature T in degrees Fahrenheit?

220 °C

T = °F

3.Nursing math & unit conversionsMedium

Practice exercise (made-up values, not clinical guidance). A drip-rate calculation gives 100.988 gtt/min. The rule in this exercise is that drip rates are rounded to the nearest whole drop. What value x do you record?

100.988 gtt/min

x = gtt/min

4.Nursing math & unit conversionsHard

Practice exercise (made-up values, not clinical guidance). An infusion starts at 17:00 and finishes at 02:45 the next morning (24-hour clock). How many hours t did it run? Give the answer in hours as a decimal, rounded to two decimal places.

17:0002:45

t = h

3Solutions

1.Pre-nursing math (entrance exam)

Answer: x = 9 cups

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.

Proportion

1.5/3 = x/18

Cross-multiply and solve

3·x = 27

x = 27/3 = 9 cups

Answer

x = 9 cups

2.Pre-nursing math (entrance exam)

Answer: T = 428 °F

Temperature scales: °F = °C × 9/5 + 32 and °C = (°F − 32) × 5/9. A temperature change converts without the 32, because the 32 only shifts the zero point: a change of 1 °C is a change of 1.8 °F.

Multiply by 9/5

220 × 9/5 = 396

Add 32

T = 396 + 32 = 428 °F

Answer

T = 428 °F

3.Nursing math & unit conversions

Answer: x = 101 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

100.988 → 0

Only the next digit decides

100.988 → 9

9 is 5 or more, so round 0 up.

The digits after it (88) are ignored: round once, never step by step.

Round

x = 101 gtt/min

Answer

x = 101 gtt/min

4.Nursing math & unit conversions

Answer: t = 9.75 h

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

17:00 → 24:00 = 420 min

After midnight

00:00 → 02:45 = 165 min

Total

420 + 165 = 585 min

t = 585/60 = 9.75 h

Answer

t = 9.75 h

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