Armed Services Vocational Aptitude Battery (ASVAB) Mathematics Knowledge (MK) Syllabus

Mathematics Knowledge (MK) syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematics Knowledge (MK) in Armed Services Vocational Aptitude Battery (ASVAB), not a summary of it.

1. 1

   Algebra Fundamentals

   4 topics

   • Expressions and Variables
     • Evaluating algebraic expressions
     • Combining like terms
     • Distributive property
   • Linear Equations and Inequalities
     • Solving one- and two-step equations
     • Solving and graphing inequalities
     • Solving for a variable in a formula
   • Exponents and Radicals
     • Laws of exponents
     • Square roots and simplifying radicals
     • Scientific notation
   • Polynomials and Factoring
     • Adding, subtracting, multiplying polynomials
     • Factoring and FOIL
     • Solving quadratic equations
2. 2

   Geometry

   4 topics

   • Lines, Angles, and Triangles
     • Angle relationships and parallel lines
     • Triangle types and angle sums
     • Pythagorean theorem
   • Polygons and Circles
     • Properties of quadrilaterals
     • Circle radius, diameter, circumference
     • Interior angles of polygons
   • Perimeter, Area, and Volume
     • Area and perimeter of plane figures
     • Surface area and volume of solids
     • Area of circles
   • Coordinate Geometry
     • Plotting points and the coordinate plane
     • Slope and intercepts
     • Distance and midpoint
3. 3

   Numbers and Quantitative Concepts

   3 topics

   • Number Properties
     • Rational and irrational numbers
     • Reciprocals and number classifications
   • Sequences and Patterns
     • Arithmetic and geometric sequences
     • Recognizing numerical patterns
   • Probability and Basic Statistics
     • Simple probability
     • Mean, median, mode, and range

Mathematics Knowledge (MK) flashcards for Armed Services Vocational Aptitude Battery (ASVAB)

21 of 51 cards from the Mathematics Knowledge (MK) deck — real questions with worked answers.

1. What is a variable in algebra?

   A symbol (usually a letter) that represents an unknown or changeable numerical value.

2. What is a coefficient in an algebraic term?

   The numerical factor that multiplies a variable. In 7x, the coefficient is 7.

3. What is a constant in an algebraic expression?

   A term whose value does not change because it contains no variable, such as the 5 in 3x + 5.

4. What are like terms, and what can you do with them?

   Terms with the same variable raised to the same power; they can be combined (added or subtracted), e.g. 3x + 5x = 8x.

5. State the order of operations (PEMDAS).

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

6. What does the distributive property state?

   a(b + c) = ab + ac; multiply the outside factor by each term inside the parentheses.

7. How do you evaluate an algebraic expression?

   Substitute the given numerical values for the variables, then simplify using the order of operations.

8. What is the goal when solving a linear equation in one variable?

   To isolate the variable on one side using inverse operations, keeping both sides equal.

9. How does multiplying or dividing an inequality by a negative number affect it?

   It reverses (flips) the direction of the inequality sign.

10. What is the slope-intercept form of a linear equation?

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

11. What does the slope (m) of a line represent, and how is it calculated?

    The rate of change, rise over run: m = (y2 - y1) / (x2 - x1).

12. How do you check the solution to an equation?

    Substitute the solution back into the original equation and verify both sides are equal.

13. What is the product rule for exponents?

    When multiplying like bases, add the exponents: a^m * a^n = a^(m+n).

14. What is the quotient rule for exponents?

    When dividing like bases, subtract the exponents: a^m / a^n = a^(m-n).

15. What is the power rule for exponents?

    To raise a power to a power, multiply the exponents: (a^m)^n = a^(mn).

16. What does any nonzero number raised to the power of zero equal?

    1. For any a ≠ 0, a^0 = 1.

17. What does a negative exponent mean?

    The reciprocal of the base raised to the positive exponent: a^(-n) = 1 / a^n.

18. What does a fractional exponent represent, e.g. a^(1/2)?

    A root. a^(1/2) is the square root of a; a^(m/n) is the nth root of a^m.

19. What is a radical, and what is the index of a square root?

    A radical (√) indicates a root of a number; the square root has an implied index of 2.

20. How do you simplify a radical such as √12?

    Factor out the largest perfect square: √12 = √(4·3) = 2√3.

21. What is a monomial, binomial, and trinomial?

    A polynomial with one term (monomial), two terms (binomial), or three terms (trinomial).

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