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OAT (Optometry Admission Test) Quantitative Reasoning Syllabus

The Quantitative Reasoning syllabus for OAT (Optometry Admission Test) in full: 4 chapters, 13 topics and 31 sub-topics, every one listed below, plus 67 Quantitative Reasoning flashcards with answers.

4Chapters
13Topics
31Sub-topics
67Flashcards

Quantitative Reasoning syllabus: all 4 chapters

Expand any chapter to see its topics and sub-topics.

  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. 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. 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. 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

OAT (Optometry Admission Test) Quantitative Reasoning flashcards — 67 questions with 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.

Show the other 47 Quantitative Reasoning flashcards

  1. 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.

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

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

  3. What is the definition of a function?

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

  4. What is the vertical line test?

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

  5. 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.

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

    m = (y2 − y1) / (x2 − x1) (rise over run).

  7. What is the relationship between the slopes of perpendicular lines?

    Their slopes are negative reciprocals; the product of the slopes is −1.

  8. For the parabola y = ax² + bx + c, what is the x-coordinate of the vertex?

    x = −b / (2a).

  9. What is the domain of a function, versus its range?

    Domain is the set of all allowable inputs (x-values); range is the set of all resulting outputs (y-values).

  10. What is the area of a circle and the circumference, given radius r?

    Area = πr²; Circumference = 2πr (or πd).

  11. What is the sum of the interior angles of a polygon with n sides?

    (n − 2) × 180°.

  12. What is the area of a triangle with base b and height h?

    Area = (1/2) × b × h.

  13. What is the volume of a rectangular box (rectangular prism)?

    Volume = length × width × height.

  14. What are the formulas for the volume and surface area of a sphere with radius r?

    Volume = (4/3)πr³; Surface area = 4πr².

  15. What is the volume of a cylinder with radius r and height h?

    Volume = πr²h.

  16. What is the Pythagorean theorem?

    In a right triangle, a² + b² = c², where c is the hypotenuse (the side opposite the right angle).

  17. What is the side-length ratio of a 45-45-90 right triangle?

    1 : 1 : √2 (the two legs are equal; the hypotenuse is leg × √2).

  18. What is the side-length ratio of a 30-60-90 right triangle?

    1 : √3 : 2 (opposite 30°, 60°, and 90° respectively).

  19. Name two common Pythagorean triples.

    3-4-5 and 5-12-13 (also 8-15-17 and 7-24-25).

  20. What does it mean for two triangles to be similar, and what follows about their sides?

    They have equal corresponding angles; their corresponding sides are proportional.

  21. What are the definitions of sine, cosine, and tangent in a right triangle (SOH-CAH-TOA)?

    sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent.

  22. What is the fundamental Pythagorean trigonometric identity?

    sin²θ + cos²θ = 1.

  23. How is tangent expressed in terms of sine and cosine?

    tan θ = sin θ / cos θ.

  24. What are the sine and cosine values for 0°, 30°, 45°, 60°, and 90°?

    sin: 0, 1/2, √2/2, √3/2, 1; cos: 1, √3/2, √2/2, 1/2, 0.

  25. What is the relationship between degrees and radians?

    180° = π radians; multiply degrees by π/180 to get radians.

  26. What is the difference between the mean, median, and mode?

    Mean is the arithmetic average; median is the middle value when ordered; mode is the most frequently occurring value.

  27. What is the range of a data set, and how is it calculated?

    The range is the spread of the data: maximum value minus minimum value.

  28. What is standard deviation a measure of?

    The average amount that data values deviate (spread) from the mean; larger SD means more dispersion.

  29. In a normal distribution, what percentage of data falls within one standard deviation of the mean (68-95-99.7 rule)?

    About 68% within ±1 SD, 95% within ±2 SD, and 99.7% within ±3 SD.

  30. What is the basic formula for the probability of an event?

    P(event) = (number of favorable outcomes) / (total number of equally likely outcomes).

  31. What is the probability rule for two independent events both occurring?

    P(A and B) = P(A) × P(B).

  32. What is the addition rule for the probability of A or B (mutually exclusive events)?

    P(A or B) = P(A) + P(B); if not mutually exclusive, subtract P(A and B).

  33. What is the formula for the number of permutations of n items taken r at a time?

    nPr = n! / (n − r)! (order matters).

  34. What is the formula for the number of combinations of n items taken r at a time?

    nCr = n! / [r!(n − r)!] (order does not matter).

  35. How do you read the value of a slice in a pie chart relative to the whole?

    Each slice's percentage of the total = (slice's central angle / 360°), or read the labeled percent; multiply by the total to get the count.

  36. When interpreting a line graph, what does the slope between two points represent?

    The rate of change of the y-variable per unit change in the x-variable over that interval.

  37. How do you set up and solve a proportion a/b = c/d for an unknown?

    Cross-multiply (ad = bc), then solve the resulting equation for the unknown variable.

  38. What is the formula relating distance, rate, and time?

    Distance = rate × time (d = rt).

  39. In a work-rate problem, how do you combine two workers' rates?

    Add their individual rates (jobs per unit time); combined time = 1 / (sum of rates).

  40. How many centimeters are in 1 meter, and millimeters in 1 centimeter?

    1 meter = 100 cm; 1 cm = 10 mm.

  41. How do you convert a quantity using dimensional analysis (unit factors)?

    Multiply by conversion fractions equal to 1, arranged so unwanted units cancel and the desired unit remains.

  42. How many milliliters are in 1 liter, and grams in 1 kilogram?

    1 liter = 1000 mL; 1 kilogram = 1000 g.

  43. What is the conversion between Celsius and Fahrenheit?

    F = (9/5)C + 32; C = (5/9)(F − 32).

  44. A good general strategy when a word problem seems complex: what should you do first?

    Identify what is asked and what is given, define variables, then translate the words into equations before solving.

  45. What estimation strategy helps eliminate wrong multiple-choice answers quickly?

    Round numbers to convenient values to approximate the answer, then discard choices that are far off.

  46. How can you check whether an algebraic answer is reasonable?

    Substitute it back into the original equation/problem and verify the units and order of magnitude make sense.

  47. What is the strategy of 'plugging in answer choices' (backsolving)?

    Test the given answer choices in the problem's conditions—often starting with the middle value—until one satisfies all constraints.

OAT (Optometry Admission Test) Quantitative Reasoning FAQ

What is in the OAT (Optometry Admission Test) Quantitative Reasoning syllabus?

OAT (Optometry Admission Test) Quantitative Reasoning is split into 4 chapters: Algebra and Numerical Skills, Geometry and Trigonometry, Data Analysis, Probability, and Statistics and Applied and Word Problems. Together they contain 13 topics and 31 sub-topics.

How many chapters are in OAT (Optometry Admission Test) Quantitative Reasoning?

4 chapters, containing 13 topics and 31 sub-topics. The largest chapter is Algebra and Numerical Skills, with 4 topics.

Are there flashcards for OAT (Optometry Admission Test) Quantitative Reasoning?

Yes — a 67-card Quantitative Reasoning deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.