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Outline: ASVAB Arithmetic Reasoning and ASVAB Mathematics Knowledge Study “Cheat” Sheet

ASVAB Math Practice: Arithmetic Reasoning and Mathematics KnowledgeThe Arithmetic Reasoning section is one out of the two major math sections that is on the Armed Services Vocational Aptitude Battery (ASVAB) military entrance test. Below is a “cheat sheet”, or outline of information, that will be tested on during the Arithmetic Reasoning section of the ASVAB:


  1. Divide, Multiply, Add or Subtract the following:
    • Whole Numbers (positive and negative)
    • Decimals (positive and negative)
    • Fractions (positive and negative)
    • Exponents
  2. Factorization
  3. Least Common Multiple
  4. Order of Operations
    • PEMDAS (Parenthesis, Exponents, Multiply, Divide, Add, Subtract)
  5. Scientific Notation
  6. Change a Fraction to Decimal
  7. Change a Decimal to Fraction
  8. Square Root
  9. Simplify Radicals
  10. Factorials
  11. Ratios
  12. Proportions
  13. Rate = Distance ÷ Time
  14. Average
    • Mean
    • Median
    • Mode
  15. Probability

Here is the outline of topics that will be tested on during the Mathematics Knowledge section of the ASVAB:

  1. Algebra
    • Expressions
    • Equations
      • Quadratic Equation
        • FOIL (First, Outside, Inner, Last)
    • Substitute variables
    • Inequalities
      • Greater than
      • Less than
  2. Geometry
    • Line Segments
      • Perpendicular
      • Parallel
    • Angles
      • Adjacent
      • Right
      • Obtuse
      • Acute
    • Triangles
      • Sub of Interior Angles (180°)
      • Perimeter
      • Area
      • Types
        • Equilateral
        • Isosceles
        • Right
      • Pythagorean Theorem
    • Quadrilaterals
      • Perimeter
      • Area
      • Types
        • Rectangle
        • Square
        • Parallelogram
        • Trapezoid
      • Circles
        • Radius
        • Chord
        • Diameter
        • Circumference
        • Area
      • Rectangular Solids
        • Volume


The ASVAB Arithmetic Reasoning section consists of 30 questions you must answer in 36 minutes. The ASVAB Mathematics Knowledge section contains 25 questions that must be answered in 24 minutes. This may not seem like a lot of time to answer all the questions, but most people do finish in time if they have taken ASVAB math practice tests to get familiar with the pace that must be maintained to answer all the questions in time. If you’ve used a course for ASVAB math practice then you can use the above list as a checklist to make sure you study each topic that will be tested on during the Arithmetic Reasoning and Mathematics Knowledge sections of the ASVAB.