TEAS ExamStudy Topic
TEAS Mathematics and Quantitative Reasoning Study Guide
Review fractions, percentages, ratios, algebra, measurement, geometry, probability, and data with self-contained worked practice.
Topic Overview
Name the quantity and unit
Before calculating, identify what the question requests: a remainder, a rate, a percent change, a length, an area, or a volume. Write its unit beside the unknown. This simple step catches answers that compute a discount instead of a sale price or an amount removed instead of the amount remaining.
Use equivalent forms deliberately
Fractions need a common denominator for addition and subtraction. Decimals and percentages can be converted to a shared form for comparison. In a ratio mixture, add the parts before dividing the total into equal units. For percent change, divide the change by the original quantity, not the new one.
Translate words into a model
A one-time fee plus a per-item charge gives a fixed term plus a variable term. Solve equations by performing the same operation on both sides. Preserve the inequality direction when dividing by a positive number; a negative multiplier or divisor requires special attention because it reverses the direction. Check a solution by substituting it into the original relation.
Keep measurement dimensions distinct
Perimeter adds boundary lengths. Area measures a surface, and volume measures space. A rectangle uses length times width for area, while a rectangular prism adds the third dimension through multiplication. In unit conversions, write the conversion factor so that the original unit cancels and the requested unit remains.
Interpret data rather than only calculating
Mean is the sum divided by the number of equally weighted observations. Median is the middle of an ordered set. Range measures the distance between the largest and smallest values. Probability compares favorable outcomes with all equally likely outcomes under the stated model. Always check that the denominator represents the relevant whole.
Review with an estimate
A 25% discount leaves most of the original price, so a tiny remaining price deserves another look. A conversion from kilometers to meters should produce a larger numerical value. An approximate check can reveal an operation error even before exact arithmetic is repeated.
- Subtracting fraction denominators directly.
- Using the new value as the denominator for percent increase.
- Confusing perimeter, area, and volume.
- Reporting a total when the question asks for a mean.
- Dropping units or reversing a conversion factor.
Checkpoint Quiz
Test your understanding of TEAS Mathematics and Quantitative Reasoning
These questions are for study practice only and are not official exam questions.
1. A club charges a $12 registration fee plus $8 for each workshop. If total cost is C for n workshops, which equation models the cost?
2. A rectangular poster is 18 inches long and 12 inches wide. What is its perimeter?
3. A triangle has a base of 10 centimeters and a perpendicular height of 7 centimeters. What is its area?
4. The values 4, 7, 7, 10, and 12 describe five observations. What is the median?
5. Solve the inequality 3x − 2 > 10.
6. A chart lists 18 attendees on Tuesday, 27 on Wednesday, and 15 on Thursday. What fraction of the three-day attendance occurred Wednesday?
7. A sample has mass 54 grams and volume 6 cubic centimeters. Density is defined as mass divided by volume. What is its density?
8. A storage room was at −4°C. Its temperature rose by 9°C. What is the new temperature?
9. Solve the equation 4x + 7 = 31.
10. A paint mixture uses blue and white paint in a ratio of 2:5. If the mixture contains 14 liters total, how many liters are blue?
Frequently asked questions
How should I begin a word problem?
State the unknown and its unit, identify the given quantities, and choose an operation or model before doing arithmetic.
What is the denominator for percent change?
Use the original quantity: percent change equals change divided by original amount, multiplied by 100.
How do mean and median differ?
Mean averages all values arithmetically. Median is the middle value after ordering the data, or the average of the two middle values when there are an even number.
How can I check a unit conversion?
Write the factor with units so the original unit cancels. Then check whether the numerical size should increase or decrease when changing to the requested unit.
