DAT (Dental Admission Test) Quantitative Reasoning Syllabus

Quantitative Reasoning syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Quantitative Reasoning in DAT (Dental Admission Test), not a summary of it.

1. 1

   Numerical Calculations

   3 topics

   • Arithmetic Operations
     • Fractions, decimals, percentages
     • Ratios and proportions
   • Number Properties
     • Factors, multiples, primes
     • Exponents and radicals
   • Scientific Notation
     • Operations with powers of ten
2. 2

   Algebra

   3 topics

   • Equations and Inequalities
     • Linear and quadratic equations
     • Systems of equations
   • Expressions and Polynomials
     • Factoring and simplifying
   • Functions and Graphs
     • Slope and intercepts
     • Function evaluation
3. 3

   Geometry and Trigonometry

   3 topics

   • Plane Geometry
     • Area and perimeter of polygons
     • Circles: area, circumference, arcs
   • Solid Geometry
     • Volume and surface area
   • Trigonometry
     • Right triangle ratios
     • Trigonometric identities
4. 4

   Probability and Statistics

   3 topics

   • Descriptive Statistics
     • Mean, median, mode, range
     • Standard deviation basics
   • Probability
     • Independent and dependent events
     • Permutations and combinations
   • Data Interpretation
     • Reading charts and graphs
5. 5

   Applied Mathematics (Word Problems)

   4 topics

   • Rate, Time, and Distance
     • Speed and travel problems
   • Work and Mixture Problems
     • Combined work rates
     • Concentration and mixtures
   • Conversions and Measurement
     • Unit conversions and dimensional analysis
   • Interest and Financial Math
     • Simple and compound interest

Quantitative Reasoning flashcards for DAT (Dental Admission Test)

25 of 51 cards from the Quantitative Reasoning deck — real questions with worked answers.

1. What is the order of operations (PEMDAS) for evaluating arithmetic expressions?

   Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).

2. What is the result of dividing any nonzero number by zero, and zero divided by a nonzero number?

   Dividing by zero is undefined; zero divided by any nonzero number equals 0.

3. How do you add or subtract fractions with different denominators?

   Find a common denominator, convert each fraction to it, then add or subtract the numerators and keep the denominator.

4. What is the definition of an integer's absolute value?

   Its distance from zero on the number line, always nonnegative: |x| = x if x is greater than or equal to 0, and -x if x is less than 0.

5. Define prime number and give the smallest prime.

   A whole number greater than 1 with exactly two factors, 1 and itself. The smallest prime is 2 (the only even prime).

6. What are the divisibility rules for 3 and 9?

   A number is divisible by 3 if its digit sum is divisible by 3; divisible by 9 if its digit sum is divisible by 9.

7. How do you find the greatest common factor (GCF) and least common multiple (LCM) using prime factorization?

   GCF = product of the lowest powers of common primes; LCM = product of the highest powers of all primes appearing in either number.

8. What is the difference between rational and irrational numbers?

   Rational numbers can be written as a ratio of two integers (terminating or repeating decimals); irrational numbers cannot (non-repeating, non-terminating decimals like pi or sqrt(2)).

9. How do you write a number in scientific notation?

   As a x 10^n where 1 is less than or equal to |a| is less than 10 and n is an integer; move the decimal so one nonzero digit is to its left, counting places as the exponent.

10. When multiplying numbers in scientific notation, what happens to the coefficients and exponents?

    Multiply the coefficients and add the exponents: (a x 10^m)(b x 10^n) = (ab) x 10^(m+n), then normalize the coefficient.

11. Express 0.00047 in scientific notation.

    4.7 x 10^-4.

12. What does a negative exponent in scientific notation indicate about the number's magnitude?

    A negative exponent indicates a number less than 1 (a small magnitude); the decimal point moves left |n| places.

13. How do you solve a linear equation such as 3x + 5 = 20?

    Isolate x: subtract 5 (3x = 15), then divide by 3 (x = 5).

14. What happens to an inequality when you multiply or divide both sides by a negative number?

    The inequality sign reverses direction (e.g., -2x is less than 6 becomes x is greater than -3).

15. What is the quadratic formula for ax^2 + bx + c = 0?

    x = [-b plus or minus sqrt(b^2 - 4ac)] / (2a).

16. What does the discriminant b^2 - 4ac tell you about a quadratic's roots?

    Positive = two distinct real roots; zero = one repeated real root; negative = two complex (no real) roots.

17. How do you solve a system of two linear equations by substitution?

    Solve one equation for a variable, substitute that expression into the other equation, solve for the remaining variable, then back-substitute.

18. What are the rules for multiplying and dividing powers with the same base?

    Add exponents when multiplying (x^a · x^b = x^(a+b)); subtract when dividing (x^a / x^b = x^(a-b)).

19. What is the FOIL method for multiplying two binomials?

    Multiply First, Outer, Inner, Last terms, then combine: (a+b)(c+d) = ac + ad + bc + bd.

20. State the difference of squares factoring formula.

    a^2 - b^2 = (a + b)(a - b).

21. Expand the perfect square binomials (a + b)^2 and (a - b)^2.

    (a + b)^2 = a^2 + 2ab + b^2; (a - b)^2 = a^2 - 2ab + b^2.

22. What is the slope-intercept form of a line and what does each variable represent?

    y = mx + b, where m is the slope (rise over run) and b is the y-intercept.

23. How do you calculate the slope between two points (x1, y1) and (x2, y2)?

    m = (y2 - y1) / (x2 - x1).

24. What defines a function in terms of inputs and outputs?

    A relation where each input (x) maps to exactly one output (y); it passes the vertical line test.

25. What is the vertex form of a parabola and what does it reveal?

    y = a(x - h)^2 + k, where (h, k) is the vertex; a greater than 0 opens up, a less than 0 opens down.

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