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ASVAB Test Prep Topics

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Numbers and Relations
Place value
Comparing and ordering numbers
Rounding numbers
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Number Theory
Divisibility Rules
Determining Common Factors
Determining Common Multiples
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Adding and Subtracting Integers
Introduction to integer addition
Adding integers
Introduction to integer subtraction
Subtracting integers
Application of integer operations
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Multiplying and Dividing Integers
Understanding integer multiplication
Multiplying integers
Understanding integer division
Dividing integers
Applications of integer operations
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Adding and Subtracting Fractions
Using models to add and subtract fractions
Adding fractions with like denominators
Subtracting fractions with like denominators
Adding and subtracting fractions with unlike denominators
Adding and subtracting mixed numbers
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Multiplying and Dividing Fractions
Multiplying fractions and whole numbers
Dividing fractions with whole numbers
Multiplying proper fractions
Multiplying improper fractions and mixed numbers
Dividing fractions and mixed numbers
Applications of fraction operations
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Number System and Radicals
Understanding the number systems
Prime factorization
Greatest Common Factors (GCF)
Least Common Multiple (LCM)
Rational vs. Irrational numbers
Converting repeating decimals to fractions
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Fractions, Decimals, and Percents
Representing percents
Percent of a number
Converting among decimals, fractions, and percents
Adding and multiplying percents
Applications of percents
Taxes, discounts, tips and more
Simple interest
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Ratios, Rates, and Proportions
Ratios
Rates
Proportions
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Introduction to Variables and Expressions
Evaluating algebraic expressions
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Introduction to Equations
Solving one - step equations: x + a = b
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Solving Linear Equations
Solving linear equations using multiplication and division
Solving two-step linear equations: ax + b = c, x/a + b = c
Solving linear equations using distributive property: a(x + b) = c
Solving linear equations with variables on both sides
Solving literal equations
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Linear Inequalities
Express linear inequalities graphically and algebraically
Solving one-step linear inequalities
Solving multi-step linear inequalities
Compound inequalities
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Linear Functions
Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}d=(x2​−x1​)2+(y2​−y1​)2​
Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)M=(2x1​+x2​​,2y1​+y2​​)
Slope equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}m=x2​−x1​y2​−y1​​
Slope intercept form: y = mx + b
General form: Ax + By + C = 0
Point-slope form: y−y1=m(x−x1)y - y_1 = m (x - x_1)y−y1​=m(x−x1​)
Rate of change
Graphing linear functions using table of values
Graphing linear functions using x- and y-intercepts
Graphing from slope-intercept form y=mx+b
Graphing linear functions using a single point and slope
Word problems of graphing linear functions
Parallel and perpendicular lines in linear functions
Applications of linear relations
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Solving Systems of Linear Equations
Determining number of solutions to linear equations
Solving systems of linear equations by graphing
Using elimination method to solve systems of equations
Using substitution method to solve systems of equations
Money related questions in linear equations
Unknown number related questions in linear equations
Distance and time related questions in linear equations
Rectangular shape related questions in linear equations
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Exponents
Product rule of exponents
Quotient rule of exponents
Power of a product rule
Power of a quotient rule
Power of a power rule
Negative exponent rule
Combining the exponent rules
Scientific notation
Convert between radicals and rational exponents
Solving for exponents
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Operations of Polynomials
What is a polynomial?
Polynomial components
Multiplying monomial by monomial
Multiplying monomial by binomial
Multiplying binomial by binomial
Multiplying polynomial by polynomial
Applications of polynomials
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Factoring Polynomial Expressions
Common factors of polynomials
Factoring polynomials by grouping
Solving polynomials with the unknown "b" from x^2 + bx + c
Solving polynomials with the unknown "c" from x^2 + bx + c
Factoring polynomials: x^2 + bx + c
Applications of polynomials: x^2 + bx + c
Solving polynomials with the unknown "b" from ax2+bx+cax^2 + bx + cax2+bx+c
Factoring polynomials: ax2+bx+cax^2 + bx + cax2+bx+c
Factoring perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2
Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)
Evaluating polynomials
Using algebra tiles to factor polynomials
Solving polynomial equations
Word problems of polynomials
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Factoring Trinomials
Factor by taking out the greatest common factor
Factor by grouping
Factoring difference of squares: x^2 - y^2
Factoring trinomials
Factoring difference of cubes
Factoring sum of cubes
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Radicals
Operations with radicals
Conversion between entire radicals and mixed radicals
Adding and subtracting radicals
Multiplying radicals
Solving radical equations
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Rational Expressions
Simplifying rational expressions and restrictions
Adding and subtracting rational expressions
Multiplying rational expressions
Dividing rational expressions
Solving rational equations
Applications of rational equations
Simplifying complex fractions
Partial fraction decomposition
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Reciprocal Functions
Graphing reciprocals of linear functions
Graphing reciprocals of quadratic functions
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Angles, Lines, and Transversals
Pairs of lines and angles
Parallel lines and transversals
Parallel line proofs
Perpendicular line proofs
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Scale Factors and Similarity
Enlargements and reductions with scale factors
Scale diagrams
Similar triangles
Similar polygons
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Measuring Systems
Metric systems
Imperial systems
Conversions between metric and imperial systems
Conversions involve squares and cubic
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Surface Area and Perimeter of Polygons
Classifying triangles
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Circles
Circles and circumference
Arcs of a circle
Areas and sectors of circles
Angles in a circle
Chord properties in circles
Tangent properties in circles
Central and inscribed angles in circles
Equation of a circle
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Surface Area and Volume of 3-Dimensional Shapes
Surface area and volume of prisms
Surface area and volume of pyramids
Surface area and volume of cylinders
Surface area and volume of cones
Surface area and volume of spheres
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Statistics
Median and mode
Mean
Range and outliers
Application of averages
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Probability
Determining probabilities using tree diagrams and tables
Probability of independent events
Probability with Venn diagrams
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Exponential Functions
Exponents: Product rule (a^x)(a^y) = a^(x+y)
Exponents: Division rule (a^x / a^y) = a^(x-y)
Exponents: Power rule (a^x)^y = a^(x * y)
Exponents: Negative exponents
Exponents: Zero exponent: a^0 = 1
Exponents: Rational exponents
Solving exponential equations using exponent rules
Graphing exponential functions
Graphing transformations of exponential functions
Finding an exponential function given its graph
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Inequalities in Two Variables
Graphing linear inequalities in two variables
Graphing systems of linear inequalities
Graphing quadratic inequalities in two variables
Graphing systems of quadratic inequalities
Applications of inequalities
What is linear programming?
Linear programming word problems
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Permutations and Combinations
Fundamental counting principle
Factorial notation
Path counting problems
Permutation vs. Combination
Permutations
Combinations
Problems involving both permutations and combinations
Pascal's triangle
Binomial theorem

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