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

Work out 1 1/4 ÷ 2 1/2. Click the answer in lowest terms.

1 1/4 ÷ 2 1/2

12
23 1/8
31
41/2

2.Pre-nursing math (entrance exam)Hard

The pie chart shows how a hospital’s 400 employees are split between departments A to C. What is the angle θ of the sector for department C, in degrees?

θ = °

3.Nursing math & unit conversionsMedium

Practice exercise (made-up values, not clinical guidance). A dose calculation for an injection gives 7.0231 mL. The rule in this exercise is that volumes of 1 mL or more are rounded to the nearest tenth of a mL. What value x do you record?

7.0231 mL

x = mL

4.Nursing math & unit conversionsHard

Practice exercise (made-up values, not clinical guidance). During a shift a patient takes 1 tbsp of liquid supplement, 2½ tsp of cough syrup, 8 fl oz of juice, 1½ cups of tea. Using the equivalents given, find the total oral intake V in mL.

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

V = mL

3Solutions

1.Pre-nursing math (entrance exam)

Answer: 1/2

Multiplying and dividing fractions: first turn mixed numbers into improper fractions (2 1/3 = 7/3). To multiply, multiply the numerators and the denominators. To divide, keep the first fraction, change ÷ to ×, and flip the second fraction (multiply by its reciprocal). Cancel common factors and write the result in lowest terms as a mixed number.

Improper fractions

1 1/4 = 5/4

2 1/2 = 5/2

Multiply by the reciprocal

5/4 ÷ 5/2 = 5/4 × 2/5 = 10/20

Simplify

10/20 = 1/2

Answer

1/2

2.Pre-nursing math (entrance exam)

Answer: θ = 90 °

Reading charts and tables: read the title, the categories and the scale first. On a bar chart or line graph, follow the top of the bar or the point across to the vertical axis; every gridline is one step of the scale. A pie chart shows parts of a whole: a sector of p% stands for p% of the total and has an angle of p% of 360°.

Share of 360°

θ = 0.25 × 360° = 90°

Answer

θ = 90°

3.Nursing math & unit conversions

Answer: x = 7 mL

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 tenths place

7.0231 → 0

Only the next digit decides

7.0231 → 2

2 is 4 or less, so 0 stays.

The digits after it (31) are ignored: round once, never step by step.

Round

x = 7 mL

Answer

x = 7 mL

4.Nursing math & unit conversions

Answer: V = 627.5 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

1 tbsp = 1·15 = 15 mL

2½ tsp = 2.5·5 = 12.5 mL

8 fl oz = 8·30 = 240 mL

1½ cups = 1.5·240 = 360 mL

Add

V = 15 + 12.5 + 240 + 360 = 627.5 mL

Answer

V = 627.5 mL

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