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

The Mathematics Knowledge (MK) syllabus for Armed Services Vocational Aptitude Battery (ASVAB) in full: 3 chapters, 11 topics and 30 sub-topics, every one listed below, plus 51 Mathematics Knowledge (MK) flashcards with answers.

3Chapters

11Topics

30Sub-topics

51Flashcards

Mathematics Knowledge (MK) syllabus: all 3 chapters

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

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
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
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

Armed Services Vocational Aptitude Battery (ASVAB) Mathematics Knowledge (MK) flashcards — 51 questions with answers

What is a variable in algebra?
A symbol (usually a letter) that represents an unknown or changeable numerical value.
What is a coefficient in an algebraic term?
The numerical factor that multiplies a variable. In 7x, the coefficient is 7.
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.
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.
State the order of operations (PEMDAS).
Parentheses, Exponents, Multiplication and Division (left to right), then Addition and Subtraction (left to right).
What does the distributive property state?
a(b + c) = ab + ac; multiply the outside factor by each term inside the parentheses.
How do you evaluate an algebraic expression?
Substitute the given numerical values for the variables, then simplify using the order of operations.
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.
How does multiplying or dividing an inequality by a negative number affect it?
It reverses (flips) the direction of the inequality sign.
What is the slope-intercept form of a linear equation?
y = mx + b, where m is the slope and b is the y-intercept.
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).
How do you check the solution to an equation?
Substitute the solution back into the original equation and verify both sides are equal.
What is the product rule for exponents?
When multiplying like bases, add the exponents: a^m * a^n = a^(m+n).
What is the quotient rule for exponents?
When dividing like bases, subtract the exponents: a^m / a^n = a^(m-n).
What is the power rule for exponents?
To raise a power to a power, multiply the exponents: (a^m)^n = a^(mn).
What does any nonzero number raised to the power of zero equal?
1. For any a ≠ 0, a^0 = 1.
What does a negative exponent mean?
The reciprocal of the base raised to the positive exponent: a^(-n) = 1 / a^n.
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.
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.
How do you simplify a radical such as √12?
Factor out the largest perfect square: √12 = √(4·3) = 2√3.

Show the other 31 Mathematics Knowledge (MK) flashcards

What is a monomial, binomial, and trinomial?
A polynomial with one term (monomial), two terms (binomial), or three terms (trinomial).
What is the degree of a polynomial?
The highest exponent of the variable in the polynomial.
State the FOIL method for multiplying two binomials.
Multiply the First, Outer, Inner, and Last terms, then combine like terms.
What is the factored form of a difference of squares, a² - b²?
(a + b)(a - b).
What is the expansion of (a + b)²?
a² + 2ab + b².
What does it mean to factor a polynomial?
To write it as a product of simpler polynomials or factors; the reverse of multiplying.
What is the sum of the interior angles of any triangle?
180 degrees.
What is a right angle, an acute angle, and an obtuse angle?
Right = exactly 90 degrees; acute = less than 90 degrees; obtuse = between 90 and 180 degrees.
What are complementary and supplementary angles?
Complementary angles sum to 90 degrees; supplementary angles sum to 180 degrees.
State the Pythagorean theorem.
In a right triangle, a² + b² = c², where c is the hypotenuse (side opposite the right angle).
What defines an equilateral, isosceles, and scalene triangle?
Equilateral = all three sides equal; isosceles = two sides equal; scalene = no sides equal.
What are vertical angles, and how are they related?
The opposite angles formed when two lines intersect; they are always equal (congruent).
What is the sum of the interior angles of any quadrilateral?
360 degrees.
What is the formula for the sum of interior angles of a polygon with n sides?
(n - 2) × 180 degrees.
What is the difference between the radius and diameter of a circle?
The diameter passes through the center and equals twice the radius: d = 2r.
What is the formula for the circumference of a circle?
C = 2πr (or C = πd).
What is the formula for the area of a circle?
A = πr².
What is the formula for the area of a rectangle and of a triangle?
Rectangle: A = length × width; Triangle: A = (1/2) × base × height.
What is the formula for the perimeter of a rectangle?
P = 2(length + width).
What is the formula for the volume of a rectangular box (cube/prism)?
V = length × width × height (for a cube, V = s³).
What is the formula for the volume of a cylinder?
V = πr²h (base area times height).
In the coordinate plane, what are the x- and y-coordinates in an ordered pair (x, y)?
x is the horizontal position (abscissa); y is the vertical position (ordinate).
State the distance formula between two points.
d = √[(x2 - x1)² + (y2 - y1)²].
State the midpoint formula between two points.
Midpoint = ((x1 + x2)/2, (y1 + y2)/2).
What distinguishes a prime number from a composite number?
A prime has exactly two factors (1 and itself); a composite has more than two factors.
What is the difference between a factor and a multiple of a number?
A factor divides the number evenly; a multiple is the product of the number and an integer.
What is the difference between the GCF and the LCM?
GCF is the greatest factor shared by numbers; LCM is the smallest multiple they share.
What is an arithmetic sequence, and how do you find the next term?
A sequence with a constant difference between terms; add the common difference to the previous term.
What is a geometric sequence, and how do you find the next term?
A sequence with a constant ratio between terms; multiply the previous term by the common ratio.
How is the probability of a single event calculated?
Probability = (number of favorable outcomes) / (total number of possible outcomes).
How do you find the mean, median, and mode of a data set?
Mean = sum of values ÷ count; median = middle value when ordered; mode = most frequent value.

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

What is in the Armed Services Vocational Aptitude Battery (ASVAB) Mathematics Knowledge (MK) syllabus?

Armed Services Vocational Aptitude Battery (ASVAB) Mathematics Knowledge (MK) is split into 3 chapters: Algebra Fundamentals, Geometry and Numbers and Quantitative Concepts. Together they contain 11 topics and 30 sub-topics.

How many chapters are in Armed Services Vocational Aptitude Battery (ASVAB) Mathematics Knowledge (MK)?

3 chapters, containing 11 topics and 30 sub-topics. The largest chapter is Algebra Fundamentals, with 4 topics.

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

Yes — a 51-card Mathematics Knowledge (MK) 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.