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.

New problems Back to the course

In the print window, choose “Save as PDF” to keep a copy on your device.

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

Solve for x: 3x − 16 = −40.

3x − 16 = −40

x =

2.Pre-nursing math (entrance exam)Hard

A recipe needs 1 2/3 cups of flour. You make 1 1/3 times the recipe. How much do you need? Click the answer in lowest terms.

1 2/3× 1 1/3

11 1/4
23
32 2/9
41 1/3

3.Nursing math & unit conversionsMedium

Practice exercise (made-up values, not clinical guidance). A weight conversion gives 49.3058 kg. The rule in this exercise is that weights are rounded to the nearest tenth of a kilogram. What value x do you record?

49.3058 kg

x = kg

4.Nursing math & unit conversionsHard

Practice exercise (made-up values, not clinical guidance). During a shift a patient takes 1½ tsp of cough syrup, 2 tbsp of liquid supplement, 1½ fl oz of juice, 2 cups of tea. Using the equivalents given, find the total oral intake V in mL.

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

V = mL

3Solutions

1.Pre-nursing math (entrance exam)

Answer: x = −8

Solving equations: do the same thing to both sides until x stands alone. Undo operations in reverse order: first undo addition or subtraction, then multiplication or division. Clear parentheses with the distributive property, a(x + b) = ax + ab, and collect the x terms on one side. Check the answer by substituting it back.

Add 16 to both sides.

3x = −24

Divide both sides by 3.

x = −8

Check

3·(−8) − 16 = −40

Answer

x = −8

2.Pre-nursing math (entrance exam)

Answer: 2 2/9

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 2/3 = 5/3

1 1/3 = 4/3

Multiply

5/3 × 4/3 = 20/9 = 2 2/9

Answer

2 2/9

3.Nursing math & unit conversions

Answer: x = 49.3 kg

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

49.3058 → 3

Only the next digit decides

49.3058 → 0

0 is 4 or less, so 3 stays.

The digits after it (58) are ignored: round once, never step by step.

Round

x = 49.3 kg

Answer

x = 49.3 kg

4.Nursing math & unit conversions

Answer: V = 562.5 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

1½ tsp = 1.5·5 = 7.5 mL

2 tbsp = 2·15 = 30 mL

1½ fl oz = 1.5·30 = 45 mL

2 cups = 2·240 = 480 mL

Add

V = 7.5 + 30 + 45 + 480 = 562.5 mL

Answer

V = 562.5 mL

This is independent practice material. ExamProblems is not affiliated with or endorsed by the organisation that runs this exam, and the exam name is used only to describe the content. ATI TEAS is a trademark of Assessment Technologies Institute, LLC (ATI), which is not affiliated with ExamProblems and does not endorse it or vouch for its accuracy.

ExamProblems · examproblems.com/courses/teas-math-practice