What's on TEAS 7 Math
You will see 38 math questions in 57 minutes. Four are unscored pretest items mixed in; you will not know which four, so work every question carefully.
The scored questions come from two areas:
- Numbers and Algebra (18): fractions, decimals, percents, ratios, proportions, rates, and one-variable equations
- Measurement and Data (16): unit conversions, basic geometry, and reading tables, charts, and graphs, including mean, median, mode, and range
The exam includes a basic on-screen calculator that you can use in all four sections. You cannot bring your own.
Fractions, decimals, and percents
You will switch among these three forms often.
- Fraction to decimal: divide the numerator by the denominator
- Decimal to percent: multiply by 100
- Percent to decimal: divide by 100
- A percent of a number: (percent ÷ 100) × the number
- "What percent is A of B?": (A ÷ B) × 100
Example: What is 35% of 80? Change 35% to 0.35, then multiply: 0.35 × 80 = 28. The same idea works in reverse: 15 is 25% of 60, because 15 ÷ 60 = 0.25. And 3/4, 0.75, and 75% are the same number.
Ratios and proportions
A ratio compares two quantities, like 3:4 or 3/4. A proportion says two ratios are equal. To solve one, cross-multiply, then isolate the missing value.
Example: A mix uses 3 scoops of powder for every 6 ounces of water. How many ounces of water do you need for 5 scoops? Set up 3/6 = 5/x. Cross-multiply: 3x = 30, so x = 10 ounces. Keep the units in the same place on both sides.
Percent change
Percent change tells you how much a value went up or down, compared with the starting amount.
- Percent change = (new − original) ÷ original × 100
A positive result is an increase; a negative result is a decrease. Always divide by the original value.
Example: A dose changes from 40 mg to 50 mg. The percent increase is (50 − 40) ÷ 40 × 100 = 25%.
Order of operations
Work in this order: parentheses first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right.
Example: Simplify 6 + 4 × 2². First square the 2, which is 4. Then multiply: 4 × 4 = 16. Then add: 6 + 16 = 22. The answer is not 40, which is what you would get if you added 6 and 4 first.
Solving equations
For a one-variable equation, do the inverse operation to both sides until the variable is alone. If a number is added, subtract it. If a number is multiplied, divide by it.
Example: Solve 3x + 5 = 26. Subtract 5 from both sides: 3x = 21. Divide both sides by 3: x = 7. A simple inequality, such as 2x > 10, is solved the same way. If you multiply or divide both sides by a negative number, flip the inequality sign.
Unit conversions
You will convert within the metric system, within U.S. customary units, and sometimes between the two. If the question gives a conversion factor, use that factor, even if you memorized a slightly different rounding.
Metric units scale by powers of 10. Kilo- means 1,000, centi- means 1/100, milli- means 1/1,000, and micro- (mcg) means 1/1,000,000, so 1 mg = 1,000 mcg.
- 1 km = 1,000 m
- 1 m = 100 cm = 1,000 mm
- 1 L = 1,000 mL
- 1 kg = 1,000 g
- 1 g = 1,000 mg
- 1 mg = 1,000 mcg
Common U.S. customary units:
- 1 ft = 12 in
- 1 yd = 3 ft
- 1 mi = 5,280 ft
- 1 lb = 16 oz
- 1 gal = 4 qt
- 1 qt = 2 pt
- 1 pt = 2 cups
- 1 cup = 8 fl oz
Common conversions between systems, including nursing-relevant ones:
- 1 in = 2.54 cm
- 1 kg = 2.2 lb (use 2.2 unless the question gives another factor)
- 1 fl oz ≈ 30 mL (the exact value is about 29.57 mL; many problems use 30 mL)
- 1 tsp = 5 mL
- 1 tbsp = 15 mL
- °F = (°C × 9/5) + 32
- °C = (°F − 32) × 5/9
Example: Convert 165 lb to kilograms: 165 ÷ 2.2 = 75 kg. A length of 20 inches is 20 × 2.54 = 50.8 cm. Convert 38°C: (38 × 9/5) + 32 = 100.4°F.
Area, perimeter, and volume
These are the geometry formulas worth memorizing. You do not need trigonometry.
- Perimeter of a rectangle: P = 2(l + w)
- Area of a rectangle: A = l × w
- Area of a triangle: A = (1/2) × b × h
- Pythagorean theorem: a² + b² = c², where c is the longest side (hypotenuse) of a right triangle
- Circumference of a circle: C = 2πr, or C = πd
- Area of a circle: A = πr²
- Volume of a rectangular box: V = l × w × h
- Volume of a cube: V = s³
- Volume of a cylinder: V = πr²h
Use the value of π given in the question, or 3.14 if none is given. Radius is half the diameter, so divide a diameter by 2 before you square it.
Example: A circular pad has a diameter of 8 cm, so the radius is 4 cm. Area = π × 4² = 16π cm², or about 50.24 cm² if π = 3.14. A bin that is 2 ft by 3 ft by 4 ft has a volume of 2 × 3 × 4 = 24 cubic feet.
Example: A right triangle has legs 3 and 4, so 3² + 4² = 9 + 16 = 25 and c = √25 = 5. It only works for right triangles.
Mean, median, mode, and range
These four measures show up with lists, tables, and graphs. Put the numbers in order first.
- Mean: add the values, then divide by how many there are
- Median: the middle value in an ordered list (average the two middle values if needed)
- Mode: the value that appears most often (there can be more than one, or none)
- Range: the largest value minus the smallest value
Example: For the data set 4, 7, 7, 10, 12, the mean is 40 ÷ 5 = 8, the median is 7, the mode is 7, and the range is 12 − 4 = 8.
Reading graphs and tables
Look first at the title, labels, and units, then find the exact bar, point, row, or slice the question asks about. Answer from the data in front of you, not from what you would expect.
- On a bar graph or table, match the category to the correct value
- On a line graph, notice whether a value is rising, falling, or staying flat
- If two variables are shown together, notice whether they rise together, move in opposite directions, or do not follow a clear pattern
Example: A table lists 12, 15, and 18 students in three lab groups. The mean group size is (12 + 15 + 18) ÷ 3 = 15. If the question only asks which group is largest, read the table and choose 18.
For more practice on all four sections, see the TEAS 7 prep course.