Grammar Hero Series - ASVAB Mathematics Knowledge Practice Test

Introduction

• Purpose: Practice test questions for the ASVAB (Armed Services Vocational Aptitude Battery) and PCAT.
• Format: 45 practice questions similar to the ASVAB Mathematics Knowledge Subtest.
• Test Rules:
  • 20 minutes to answer 16 questions.
  • No calculator or reference sheet allowed.
• Advice: Understand basic formulas and practice without additional resources.

Key Points Covered

Basic Concepts

• Area of a Square: Side length squared.
• Volume of a Cylinder: Requires understanding of π and radius.

Practice Questions and Solutions

Rounding Numbers

• Example: Rounding 250.025 to the nearest hundredth results in 250.03.

Absolute Value

• Absolute Value of (-2) is 2 (distance from zero).

Adding Fractions

• Common denominator method.

Time Conversion

• Calculate total minutes in a week by multiplying days, hours, and minutes.

Factorials

• Example: 6! = 720.

Algebraic Simplifications

• Distributive property and combining like terms.

Probability

• Example: Probability of drawing a King after one is removed from a deck.

Converting Improper Fractions

• Convert to mixed numbers using long division.

Order of Operations

• Follow PEMDAS/BODMAS rules.

Geometry

• Volume of a Cube: Side cubed.
• Area of Circle: πr² (given diameter, convert to radius).

Solving Equations

• Subtracting and solving linear equations.
• Solving quadratic equations by factoring.

Prime Numbers and Factors

• Distinct prime factors identification.
• Understanding the concept of prime numbers.

Converting Units

• Metric system conversions (cm to meters).

Pythagorean Theorem

• Calculating hypotenuse: a² + b² = c².

Inequalities

• Solve and represent inequalities on a number line.

Shapes and Areas

• Perimeter and area calculations for polygons (e.g., hexagons, rectangles).

Translating Word Problems to Equations

• Finding numbers from worded math problems.

Simplifying Expressions

• Algebraic expressions simplification.

Slope Calculation

• Using two points to calculate the slope of a line.

Percentages

• Converting word problems into equations involving percentages.

Greatest Common Factor vs Least Common Multiple

• Understanding and finding GCF and LCM.

Verification and Checking Work

• Always verify your solutions to ensure correctness.

Study Tips

• Utilize free resources and practice consistently.
• Understand and memorize key formulas.
• Focus on problem areas and review regularly.

Conclusion

• Focus on basics and practice without relying on external aids to prepare for the ASVAB test effectively.