OAT (Optometry 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 OAT (Optometry Admission Test), not a summary of it.

1. 1

   Algebra and Numerical Skills

   4 topics

   • Fundamental Arithmetic
     • Fractions, decimals, and percentages
     • Ratios and proportions
     • Order of operations
   • Algebraic Equations
     • Linear equations and inequalities
     • Quadratic equations
     • Systems of equations
   • Exponents and Radicals
     • Laws of exponents
     • Roots and scientific notation
   • Functions and Graphs
     • Interpreting and graphing functions
     • Slope and intercepts
2. 2

   Geometry and Trigonometry

   3 topics

   • Plane and Solid Geometry
     • Area and perimeter of polygons
     • Circles and arcs
     • Surface area and volume of solids
   • Triangles and the Pythagorean Theorem
     • Triangle properties and similarity
     • Right triangle relationships
   • Trigonometry
     • Trigonometric ratios
     • Trigonometric identities
     • Unit circle and angles
3. 3

   Data Analysis, Probability, and Statistics

   3 topics

   • Descriptive Statistics
     • Mean, median, mode, and range
     • Standard deviation
   • Probability
     • Basic probability rules
     • Permutations and combinations
   • Data Interpretation
     • Reading charts and graphs
     • Drawing conclusions from data sets
4. 4

   Applied and Word Problems

   3 topics

   • Quantitative Reasoning Problems
     • Rate, distance, and time problems
     • Work and mixture problems
     • Interest and finance problems
   • Conversions and Measurement
     • Unit conversions
     • Estimation and approximation
   • Problem-Solving Strategies
     • Translating words into equations
     • Using the on-screen calculator efficiently

Quantitative Reasoning flashcards for OAT (Optometry Admission Test)

25 of 67 cards from the Quantitative Reasoning deck — real questions with worked answers.

1. What is the order of operations used to evaluate arithmetic expressions?

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

2. How do you find the least common multiple (LCM) of two numbers using their prime factorizations?

   Take each prime factor to its highest power appearing in either number, then multiply those together.

3. How do you find the greatest common divisor (GCD) of two numbers using prime factorizations?

   Take each common prime factor to its lowest power present in both numbers, then multiply them together.

4. What is a prime number, and what is the only even prime?

   A prime has exactly two distinct positive divisors: 1 and itself. The only even prime is 2.

5. To convert a percent to a decimal, what operation do you perform?

   Divide the percent by 100 (move the decimal point two places left); e.g., 45% = 0.45.

6. What is the formula for percent change between an old value and a new value?

   Percent change = ((new value − old value) / old value) × 100%.

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

   Convert both to a common denominator (the LCM), then add or subtract the numerators and keep the denominator.

8. What is the rule for dividing one fraction by another?

   Multiply by the reciprocal of the divisor: (a/b) ÷ (c/d) = (a/b) × (d/c) = ad/bc.

9. What does the distributive property state?

   a(b + c) = ab + ac (multiplication distributes over addition/subtraction).

10. What is the quadratic formula for solving ax² + bx + c = 0?

    x = (−b ± √(b² − 4ac)) / (2a).

11. What does the discriminant b² − 4ac tell you about a quadratic's roots?

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

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

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

13. What is the difference of squares factoring pattern?

    a² − b² = (a + b)(a − b).

14. What are the factored forms of a perfect square trinomial?

    a² + 2ab + b² = (a + b)² and a² − 2ab + b² = (a − b)².

15. When solving an inequality, when must you reverse the inequality sign?

    When you multiply or divide both sides by a negative number.

16. What is the product rule for exponents?

    x^a · x^b = x^(a+b) (same base: add exponents).

17. What is the quotient rule for exponents?

    x^a / x^b = x^(a−b) (same base: subtract exponents).

18. What is the power rule for exponents?

    (x^a)^b = x^(ab) (multiply the exponents).

19. What does a negative exponent mean?

    x^(−n) = 1 / x^n (the reciprocal raised to the positive power).

20. What does a zero exponent equal (for x ≠ 0)?

    x^0 = 1.

21. How is a fractional exponent x^(m/n) expressed as a radical?

    x^(m/n) = the n-th root of x^m = (ⁿ√x)^m.

22. How do you rationalize a denominator of the form 1/√a?

    Multiply numerator and denominator by √a, giving √a / a.

23. What is the definition of a function?

    A relation that assigns exactly one output (y) to each input (x) in its domain.

24. What is the vertical line test?

    A graph represents a function if and only if no vertical line intersects it more than once.

25. What is the slope-intercept form of a line, and what do its constants mean?

    y = mx + b, where m is the slope and b is the y-intercept.

See more Quantitative Reasoning flashcards →

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