TEAS math formulas to know: percentages, proportions, geometry, and averages

Percentages, proportions, and rates

Most numbers and algebra questions are word problems built on a few relationships. A percentage is part divided by whole, times 100, so part equals percent times whole. Percent change is the new value minus the old value, divided by the old value, times 100. If a question says 18 students is 30% of a class, the class is 18 divided by 0.30, which is 60.

A proportion is two equal ratios, and you solve it by cross-multiplying: if a over b equals c over d, then a times d equals b times c. A rate is an amount per unit of time, so distance equals rate times time, and the same shape works for pay per hour or drops per minute. ATI's topic list also includes solving one-variable equations and turning sentences into expressions, so practise writing the equation before you calculate anything.

Geometry: area, perimeter, circles, and volume

Measurement and data includes calculating geometric quantities. The rectangle is length times width for area and twice length plus twice width for perimeter. A triangle's area is half of base times height. A trapezoid's area is half the height times the sum of the two parallel sides. For a right triangle, the Pythagorean theorem says the squares of the two shorter sides add up to the square of the longest: a squared plus b squared equals c squared.

For a circle, the circumference is pi times the diameter, or two times pi times the radius, and the area is pi times the radius squared. Volume of a rectangular box is length times width times height, and volume of a cylinder is pi times the radius squared times the height. The most common slip is using a diameter where the formula wants a radius, so halve it first.

Averages and reading data

The mean is the sum of the values divided by how many there are. The median is the middle value once they are in order, or the average of the two middle values when the count is even. The mode is the value that appears most often, and the range is the largest minus the smallest.

Data questions often pair these with a table or graph, so the work is reading the right row before you calculate. ATI also lists explaining the relationship between two variables, which in practice means recognising whether one value rises or falls as the other changes.

ATI's own list of sample formulas, taken from its TEAS study manual, includes distance equals rate times time, the Pythagorean theorem, and slope-intercept form for a line. Formulas stick when you use them under time. Our free TEAS math practice questions include an explanation for every answer, so you can see which formula each problem needed.

Sources

ATI: ATI TEAS exam details (sections, question counts, content areas)

ATI Help Center: What formulas do I need to know for the TEAS exam?

ATI TEAS Version 7 sample Individual Performance Profile with topic list (hosted by Hillsborough Community College)

OpenStax Prealgebra 2e, 6.5: Solve proportions and their applications

OpenStax Prealgebra 2e, 9.5: Geometry applications, circles and irregular figures

OpenStax Prealgebra 2e, 9.6: Geometry applications, volume and surface area