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

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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

How long does it take to prepare for the DAT Quantitative Reasoning section?

Most pre-dental students benefit from 6–10 weeks of focused math prep alongside the rest of their DAT studies. If your math foundations are strong, 4 weeks may be enough. If algebra and geometry are rusty, plan for 12 weeks. The fastest gains come from working topic-by-topic and taking timed practice sets.

What math topics are on the DAT QR section?

DAT Quantitative Reasoning covers algebra (linear and quadratic equations, inequalities, exponential functions), basic operations and conversions, geometry (perimeter, area, volume of common shapes), trigonometry basics, probability and statistics, and applied/word problems. Algebra carries the most weight.

Can I use a calculator on the DAT QR section?

Yes — the DAT provides a basic on-screen calculator for the QR section. It’s a four-function calculator (no graphing, no scientific functions). Practice mental math for problems where the calculator would actually slow you down.

What’s a good DAT QR score?

DAT scaled scores range from 1 to 30. The national average QR score is roughly 19. Competitive dental school programs look for 20+, with top programs preferring 22+. The QR score is a key part of your overall DAT Academic Average.

Are these math lessons really free?

Yes — every lesson, worksheet, and practice problem linked above is free. The prep books on this page are the most-relevant resources we offer for the math topics the DAT QR tests.

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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.