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ASVAB Mathematics Test Preparation Guide

May 4, 2025

Lecture Notes: Grammar Hero Series - ASVAB Mathematics Practice Test

Introduction

  • Focus: Mathematics Knowledge subtest of ASVAB and PiCAT
  • Format: 45 practice test questions
  • Test Conditions:
    • 20 minutes to answer 16 questions
    • No calculator or reference sheet allowed
  • Goal: Answer questions quickly and accurately
  • Advice: Basic formulas are essential
  • Link to free reference sheet in video description

Test-Taking Strategy

  • Pause video after each question to attempt solving
  • Resume video to check solutions
  • Do not spend money on tutoring or online boot camps
  • Most can pass with a few weeks of self-study

Sample Questions and Solutions

Rounding

  • Question: Round 250.025 to the nearest hundredth
  • Solution: 250.025 becomes 250.03 (because the thousandth digit is 5)

Absolute Value

  • Question: Absolute value of 13 - 15
  • Solution: |13 - 15| = 2

Adding Fractions

  • Question: 1/2 + 1/3 + 1/4
  • Solution: Common denominator is 12; Result = 1 1/12

Time Calculation

  • Question: How many minutes in a week?
  • Solution: 168 hours in a week x 60 = 10,080 minutes

Factorial

  • Question: 6!
  • Solution: 6! = 720

Algebraic Expressions

  • Question: Simplify 7a - ab + 8b subtracted from 3a - 9ab + b
  • Solution: Result = -4a + 8ab - 7b

Probability

  • Question: Probability of drawing another king after drawing a king (not replaced)
  • Solution: 1/17

Mixed Numbers

  • Question: Simplify 32/7
  • Solution: 4 4/7

Order of Operations

  • Question: Simplify 3 - 1 * 7 - 2 / 2
  • Solution: Result = 8*

Geometry

  • Volume of a Cube: Side length = 7 cm, volume = 343 cm³
  • Volume of a Cylinder: Height = radius, volume = Ï€r³

Algebra

  • Simplifying Expressions: Example: 2(a-b) + 4(a+3b) = 6a + 10b
  • Solving Equations: Example x^2 - x - 6 = 0, solutions x = 3, x = -2

Prime Numbers

  • Identify Prime: 57 and 87 are not prime, reasons for divisibility

Circle Measurements

  • Diameter to Meters: 57.3 cm = 0.573 meters

Word Problems

  • Example: Seven more than three times a number equals 70; n = 21

Area Calculations

  • Square: Side = 5T, Area = 25T²
  • Rectangle: Length = 8, Width = 2.5, Area = 20

Practice Problem Review

  • Emphasis on memorizing basic math formulas and operations
  • Key topics include geometry, algebra, and arithmetic

Conclusion

  • Stick with free resources and practice
  • Most students can prepare for the test in less than a month
  • More practice videos available on the channel for various ASVAB topics

These notes summarize essential points from the video for effective ASVAB test preparation. Ensure to focus on understanding basic math concepts and practicing without additional aids like calculators.

Full transcript