Math-ASVAB: Fast-Track Success!

Course Content

Topic 1: Arithmetic Reasoning
This section builds a critical foundation in quantitative thinking, emphasizing accuracy and problem translation. Students develop fluency in operational rules, numeric conversions, and basic computations with integers and rational numbers. Each lesson strengthens a specific arithmetic skill, culminating in solving one- and two-step applied problems in real-world contexts—such as calculating discounts, interpreting ratios, and determining travel time. These are the essential tools for decoding ASVAB-style word problems quickly and effectively.

1.1 Order of Operations (PEMDAS)
1.2 Converting Fractions to Decimals
1.3 Converting Decimals to Percentages
1.4 Converting Percentages to Fractions
1.5 Integer Addition & Subtraction
1.6 Integer Multiplication & Division
1.7 Rational-Number Operations (non-integer fractions)
1.8 Ratio Concepts and Applications
1.9 Proportion Word Problems
1.10 Percent Problems: Discounts
1.11 Percent Problems: Markups and Tax
1.12 Time-Distance-Rate Fundamentals (d = r × t)
1.13 Solving Time-Distance-Rate Word Problems

2. Algebra & Number Theory
This portion of the course sharpens your ability to manipulate algebraic expressions and understand the structure of numbers. Students progress from simplifying equations and inequalities to solving systems using substitution and elimination. Alongside algebra, number theory lessons introduce prime factorization, multiples, and rules of exponents—equipping learners with the analytical skills to handle abstract patterns and relationships. These topics are crucial for success on the ASVAB Math Knowledge section, where precision and strategy are key.

2.1 Combining Like Terms & the Distributive Property
2.2 Simplifying Algebraic Expressions
2.3 Solving Single-Step Linear Equations
2.4 Solving Multi-Step Linear Equations
2.5 Graphing and Solving Inequalities
2.6 Systems of Two Linear Equations by Substitution
2.7 Systems of Two Linear Equations by Elimination
2.8 Identifying Prime vs. Composite Numbers
2.9 Finding Factors and Multiples (GCD & LCM)
2.10 Exponent Rules: Product, Quotient, Power of a Power
2.11 Taking Roots: Square Roots & Cube Roots
2.12 Scientific Notation: Converting to and from Standard Form
2.13 Side Ratios in Similar Figures

3. Geometry & Measurement
Learners develop spatial awareness and formula fluency through the study of two- and three-dimensional figures. Instruction includes identifying properties of triangles, quadrilaterals, and circles; calculating perimeters, areas, volumes, and surface areas; and working with geometric relationships. The emphasis is on recognizing which formula applies, how to organize known and unknown values, and how to apply geometry in time-sensitive test scenarios. By mastering measurement tools and geometry reasoning, students gain confidence in tackling shape-based problems.

3.1 Measuring Angles: Definitions and Notation
3.2 Triangle Classification & Angle Sums
3.3 Quadrilateral Properties and Classifications
3.4 Perimeter Formulas for Polygons
3.5 Area Formulas for Triangles, Rectangles, and Parallelograms
3.6 Circle Basics: Radius, Diameter, Circumference (C = 2πr)
3.7 Circle Area (A = πr²)
3.8 Volume of Rectangular Prisms (V = lwh)
3.9 Volume of Cylinders (V = πr²h)
3.11 Surface Area of Prisms, Cylinders, and Cones
3.12 Composite Figure Perimeter & Area

4. Applied Problem Solving
In this final section, students synthesize skills from arithmetic, algebra, and geometry into complex, multi-step problem environments. Lessons focus on modeling work-rate situations, solving financial applications with interest and markup formulas, and analyzing layered geometry scenarios. The goal is not only accuracy but also efficiency—building stamina and strategic thinking through high-level practice. These applied skills reflect the integrative nature of ASVAB math questions and prepare students to perform under real test pressure.

Course Content

1.1 Order of Operations (PEMDAS)

1.2 Converting Fractions to Decimals

1.3 Converting Decimals to Percentages

1.4 Converting Percentages to Fractions

1.5 Integer Addition & Subtraction

1.6 Integer Multiplication & Division

1.7 Rational-Number Operations (non-integer fractions)

1.8 Ratio Concepts and Applications

1.9 Proportion Word Problems

1.10 Percent Problems: Discounts

1.11 Percent Problems: Markups and Tax

1.12 Time-Distance-Rate Fundamentals (d = r × t)

1.13 Solving Time-Distance-Rate Word Problems

2.1 Combining Like Terms & the Distributive Property

2.2 Simplifying Algebraic Expressions

2.3 Solving Single-Step Linear Equations

2.4 Solving Multi-Step Linear Equations

2.5 Graphing and Solving Inequalities

2.6 Systems of Two Linear Equations by Substitution

2.7 Systems of Two Linear Equations by Elimination

2.8 Identifying Prime vs. Composite Numbers

2.9 Finding Factors and Multiples (GCD & LCM)

2.10 Exponent Rules: Product, Quotient, Power of a Power

2.11 Taking Roots: Square Roots & Cube Roots

2.12 Scientific Notation: Converting to and from Standard Form

2.13 Side Ratios in Similar Figures

3.1 Measuring Angles: Definitions and Notation

3.2 Triangle Classification & Angle Sums

3.3 Quadrilateral Properties and Classifications

3.4 Perimeter Formulas for Polygons

3.5 Area Formulas for Triangles, Rectangles, and Parallelograms

3.6 Circle Basics: Radius, Diameter, Circumference (C = 2πr)

3.7 Circle Area (A = πr²)

3.8 Volume of Rectangular Prisms (V = lwh)

3.9 Volume of Cylinders (V = πr²h)

3.11 Surface Area of Prisms, Cylinders, and Cones

3.12 Composite Figure Perimeter & Area

4.1 Combined Work-Rate Problems (two workers/taps)

4.2 Complex Filling & Emptying Scenarios

4.3 Simple Interest Formula (I = P × r × t)

4.4 Finding Principal, Rate, or Time from Interest Problems

4.5 Multi-Step Discount + Markup + Tax Calculations

4.6 Real-World Geometry Problems: Fence and Flooring

4.7 Composite Shape Area/Perimeter Applications

4.8 Timed, Mixed-Topic Practice Drills

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Derivatives in Action: Curve Analysis, Theorem Insights & Optimization (4)

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