The Ultimate DAT Quantitative Reasoning Course (+FREE Worksheets & Tests)

Welcome to the most complete free DAT Quantitative Reasoning course on the web. The DAT (Dental Admission Test) Quantitative Reasoning section tests your ability to apply mathematical thinking to problem solving, and a strong score is critical for competitive dental school admissions. This online center gathers every math lesson, practice test, and book recommendation that maps to the DAT QR content.

The DAT Quantitative Reasoning section covers algebra, fundamental mathematical operations, conversions, geometry and trigonometry, probability and statistics, and applied mathematics (word problems). You have 45 minutes for 40 questions, speed matters as much as accuracy. Work the lessons below in order and you’ll feel the difference within a few weeks.

Bookmark this page. Every link below opens a focused lesson with worked examples and free practice problems.

Graduate and Professional School Tests

Looking for the best resource to help you succeed on the DAT Quantitative Reasoning test?

A Strong Foundation Book for DAT QR Prep

GRE Math for Beginners 2026 The Ultimate Step by Step Guide to Preparing for the GRE Math Test

Download

$27.99 Original price was: $27.99.$17.99Current price is: $17.99.

DAT Quantitative Reasoning Test Prep Resources

Before you dive into the topic-by-topic lessons, get the lay of the land. These guides cover what’s on the test, how it’s scored, and how to put together a study plan that fits your life.

Understanding Graduate Math Test Content

• How to Ace the GRE Quant Section (similar topics)

DAT Quantitative Reasoning Complete Course

This is the heart of the course. Each section below is a topic family that the test loves to ask about. Work one section at a time and check your understanding with the practice problems before moving on.

Number Sense, Integers, and Order of Operations

• Opposite Integers
• Number Lines for Integers
• Adding and Subtracting Integers
• Multiplying and Dividing Integers
• Order of Operations
• Absolute Value
• Integers and Absolute Value

Fractions, Decimals, and Mixed Numbers

• Simplifying Fractions
• Word Problems: Fractions
• Repeating Decimals
• Convert Between Fractions and Decimals
• Improper Fractions and Mixed Numbers
• Ordering Decimals, Mixed Numbers, and Fractions
• Multiplying Mixed Numbers
• Dividing Mixed Numbers
• Multiplying and Dividing Decimals

Ratios, Proportions, and Percentages

• Writing a Ratio
• Ratio Tables
• Finding Equivalent Ratios
• Equivalent Rates
• Word Problems: Rates and Ratios
• Representing Percentages
• Solving Percentage Word Problems
• Converting Between Percent, Fractions, and Decimals
• Percent Problems
• Simple Interest

Algebraic Expressions and Equations

• Expressions and Equations
• Equivalent Expressions
• Properties to Write Equivalent Expressions
• Exponents in Multiplication
• Prime Factorization with Exponents
• One-Step Equations
• Multi-Step Equations
• Rearranging Multi-Variable Equations
• Factoring Variable Expressions
• Multiplying Rational Expressions
• Adding and Subtracting Rational Expressions
• Writing a Quadratic Function
• Radical Equations

Inequalities and Linear Word Problems

• Writing Inequalities from Number Lines
• Graphing Single-Variable Inequalities
• One-Step Inequalities
• Word Problems: One-Step Inequalities
• Linear Equation and Inequality Word Problems

Geometry: Lines, Angles, and Triangles

• Triangles
• Triangle Inequality
• Sides and Angles of a Triangle
• Area of a Triangle
• Area of a Parallelogram
• Area of a Trapezoid
• Area of Compound Figures
• Word Problems: Area

Solid Figures, Volume, and Coordinate Plane

• Cubes
• Rectangular Prisms
• Word Problems: Volume
• Objects on a Coordinate Plane
• Understanding Quadrants
• Coordinate Planes as Maps

Statistics, Data Analysis, and Probability

• Mean, Median, Mode, and Range
• Mean, Median, Mode from Charts
• Identifying Outliers
• Range, Quartiles, and Interquartile Range
• Pie Graphs
• Line Plots
• Frequency Distribution Tables
• Finding the Probability of an Event

Frequently Asked Questions

What is on the DAT Quantitative Reasoning section?

The DAT Quantitative Reasoning section has 40 questions in 45 minutes, testing algebra, word problems, data interpretation, and probability and statistics. Expect equations, ratios, percents, and reading tables or graphs under time pressure. The official DAT Guide from the American Dental Association lists the current content areas, so check it before planning your review.

Can you use a calculator on the DAT Quantitative Reasoning section?

Yes, but only the basic on-screen calculator that appears during the QR section; you cannot bring your own. It handles simple arithmetic, so practice doing fractions, exponents, and estimation by hand. For example, knowing that 15% of 80 is 12 without typing it saves time across 40 questions.

Is there a DAT Quantitative Reasoning cheat sheet?

No reference sheet is given on test day, but making your own study cheat sheet is a smart move. Put the formulas and shortcuts you forget most on one page, such as percent change, the probability of independent events, and unit conversions like 1 inch = 2.54 cm. Review it daily until you no longer need it.

Where can I find DAT Quantitative Reasoning practice questions?

The ADA offers sample DAT questions, and the free lessons and worksheets in this course give practice on every QR skill. Work topic sets first, such as ratio word problems or probability, then switch to mixed timed sets. Aim for roughly a minute per question, which matches the pace of 40 questions in 45 minutes.

Is there a DAT Quantitative Reasoning practice test?

Yes. Official sample questions are available from the ADA, and many prep resources offer full-length timed QR sections. Take one early to find weak spots, then another after a few weeks of review. Track both your score and how many questions you had to rush, since pacing is often the real problem on DAT QR.

Cover Every Topic with the High School Math Bundle

The Ultimate High School Math Bundle From Algebra I to Pre-Calculus

Download

$109.99 Original price was: $109.99.$54.99Current price is: $54.99.

Have any questions about the DAT Quantitative Reasoning test?

Drop your question in the comments below, about a specific topic, the test format, study planning, anything, and we’ll reply.