About Mathematics Knowledge

Mathematics Knowledge tests your understanding of mathematical concepts beyond word problems. Unlike Arithmetic Reasoning which focuses on applied math, MK tests pure mathematical knowledge including algebra, geometry, and basic number theory. On the CAT-ASVAB, you have approximately 23 minutes for 15 questions. As an AFQT component, your MK score directly impacts your enlistment eligibility. Questions cover topics from basic algebra (solving equations, inequalities) to geometry (area, volume, angles) and some basic probability and statistics. A solid foundation in high school math is essential for this section.

Topics Covered

Algebraic Equations
Inequalities
Exponents & Radicals
Factoring Polynomials
Geometry: Area & Perimeter
Geometry: Volume & Surface Area
Angles & Triangles
The Pythagorean Theorem
Basic Probability
Order of Operations (PEMDAS)

Sample Questions

Sample Question 1
What is 2³ × 2⁴?
  • 2⁷
  • 2¹²
  • 4⁷
  • 8
When multiplying same bases, add exponents: 2³ × 2⁴ = 2^(3+4) = 2⁷.
Sample Question 2
A ladder 10 feet long leans against a wall. If the base is 6 feet from the wall, how high up the wall does the ladder reach?
  • 4 feet
  • 6 feet
  • 8 feet
  • 16 feet
Pythagorean theorem: 10² = 6² + h². 100 = 36 + h². h² = 64. h = 8 feet.
Sample Question 3
What is the derivative of x³?
  • x²
  • 3x²
  • 3x
  • x⁴/4
Using the power rule: d/dx(x³) = 3x².

Study Tips for Mathematics Knowledge

Memorize Key Formulas

Know the formulas for area, perimeter, volume, and the Pythagorean theorem. These appear frequently and are not provided on the test.

Practice Algebra Daily

Solving equations and simplifying expressions are the most common MK question types. Practice these skills until they become automatic.

Review Geometry Basics

Know the properties of common shapes (triangles, circles, rectangles). Understand how to calculate area, perimeter, and volume.