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ASVAB Test Prep Topics

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1. Numbers and Relations

1.1

1.2

Comparing and ordering numbers

1.3

Rounding numbers

2. Number Theory

2.1

Divisibility Rules

2.2

Determining Common Factors

2.3

Determining Common Multiples

3. Adding and Subtracting Integers

3.1

Introduction to integer addition

3.2

Adding integers

3.3

Introduction to integer subtraction

3.4

Subtracting integers

3.5

Application of integer operations

4. Multiplying and Dividing Integers

4.1

Understanding integer multiplication

4.2

Multiplying integers

4.3

Understanding integer division

4.4

Dividing integers

4.5

Applications of integer operations

5. Adding and Subtracting Fractions

5.1

Using models to add and subtract fractions

5.2

Adding fractions with like denominators

5.3

Subtracting fractions with like denominators

5.4

Adding and subtracting fractions with unlike denominators

5.5

Adding and subtracting mixed numbers

6. Multiplying and Dividing Fractions

6.1

Multiplying fractions and whole numbers

6.2

Dividing fractions with whole numbers

6.3

Multiplying proper fractions

6.4

Multiplying improper fractions and mixed numbers

6.5

Dividing fractions and mixed numbers

6.6

Applications of fraction operations

7. Number System and Radicals

7.1

Understanding the number systems

7.2

Prime factorization

7.3

Greatest Common Factors (GCF)

7.4

Least Common Multiple (LCM)

7.5

Rational vs. Irrational numbers

7.6

Converting repeating decimals to fractions

8. Fractions, Decimals, and Percents

8.1

Representing percents

8.2

Percent of a number

8.3

Converting among decimals, fractions, and percents

8.4

Adding and multiplying percents

8.5

Applications of percents

8.6

Taxes, discounts, tips and more

8.7

Simple interest

9. Ratios, Rates, and Proportions

9.1

9.2

9.3

10. Introduction to Variables and Expressions

10.1

Evaluating algebraic expressions

11. Introduction to Equations

11.1

Solving one - step equations: x + a = b

12. Solving Linear Equations

12.1

Solving linear equations using multiplication and division

12.2

Solving two-step linear equations: ax + b = c, x/a + b = c

12.3

Solving linear equations using distributive property: a(x + b) = c

12.4

Solving linear equations with variables on both sides

12.5

Solving literal equations

13. Linear Inequalities

13.1

Express linear inequalities graphically and algebraically

13.2

Solving one-step linear inequalities

13.3

Solving multi-step linear inequalities

13.4

Compound inequalities

14. Linear Functions

14.1

Distance formula:

d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

14.2

Midpoint formula:

M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)

14.3

Slope equation:

m = \frac{y_2-y_1}{x_2- x_1}

14.4

Slope intercept form: y = mx + b

14.5

General form: Ax + By + C = 0

14.6

Point-slope form:

y - y_1 = m (x - x_1)

14.7

14.8

Graphing linear functions using table of values

14.9

Graphing linear functions using x- and y-intercepts

14.10

Graphing from slope-intercept form y=mx+b

14.11

Graphing linear functions using a single point and slope

14.12

Word problems of graphing linear functions

14.13

Parallel and perpendicular lines in linear functions

14.14

Applications of linear relations

15. Solving Systems of Linear Equations

15.1

Determining number of solutions to linear equations

15.2

Solving systems of linear equations by graphing

15.3

Using elimination method to solve systems of equations

15.4

Using substitution method to solve systems of equations

15.5

Money related questions in linear equations

15.6

Unknown number related questions in linear equations

15.7

Distance and time related questions in linear equations

15.8

Rectangular shape related questions in linear equations

16. Exponents

16.1

Product rule of exponents

16.2

Quotient rule of exponents

16.3

Power of a product rule

16.4

Power of a quotient rule

16.5

Power of a power rule

16.6

Negative exponent rule

16.7

Combining the exponent rules

16.8

Scientific notation

16.9

Convert between radicals and rational exponents

16.10

Solving for exponents

17. Operations of Polynomials

17.1

What is a polynomial?

17.2

Polynomial components

17.3

Multiplying monomial by monomial

17.4

Multiplying monomial by binomial

17.5

Multiplying binomial by binomial

17.6

Multiplying polynomial by polynomial

17.7

Applications of polynomials

18. Factoring Polynomial Expressions

18.1

Common factors of polynomials

18.2

Factoring polynomials by grouping

18.3

Solving polynomials with the unknown "b" from x^2 + bx + c

18.4

Solving polynomials with the unknown "c" from x^2 + bx + c

18.5

Factoring polynomials: x^2 + bx + c

18.6

Applications of polynomials: x^2 + bx + c

18.7

Solving polynomials with the unknown "b" from

ax^2 + bx + c

18.8

Factoring polynomials:

ax^2 + bx + c

18.9

Factoring perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2

18.10

Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)

18.11

Evaluating polynomials

18.12

Using algebra tiles to factor polynomials

18.13

Solving polynomial equations

18.14

Word problems of polynomials

19. Factoring Trinomials

19.1

Factor by taking out the greatest common factor

19.2

Factor by grouping

19.3

Factoring difference of squares: x^2 - y^2

19.4

Factoring trinomials

19.5

Factoring difference of cubes

19.6

Factoring sum of cubes

20. Radicals

20.1

Operations with radicals

20.2

Conversion between entire radicals and mixed radicals

20.3

Adding and subtracting radicals

20.4

Multiplying radicals

20.5

Solving radical equations

21. Rational Expressions

21.1

Simplifying rational expressions and restrictions

21.2

Adding and subtracting rational expressions

21.3

Multiplying rational expressions

21.4

Dividing rational expressions

21.5

Solving rational equations

21.6

Applications of rational equations

21.7

Simplifying complex fractions

21.8

Partial fraction decomposition

22. Reciprocal Functions

22.1

Graphing reciprocals of linear functions

22.2

Graphing reciprocals of quadratic functions

23. Angles, Lines, and Transversals

23.1

Pairs of lines and angles

23.2

Parallel lines and transversals

23.3

Parallel line proofs

23.4

Perpendicular line proofs

24. Scale Factors and Similarity

24.1

Enlargements and reductions with scale factors

24.2

24.3

Similar triangles

24.4

Similar polygons

25. Measuring Systems

25.1

25.2

Imperial systems

25.3

Conversions between metric and imperial systems

25.4

Conversions involve squares and cubic

26. Surface Area and Perimeter of Polygons

26.1

Classifying triangles

27. Circles

27.1

Circles and circumference

27.2

Arcs of a circle

27.3

Areas and sectors of circles

27.4

Angles in a circle

27.5

Chord properties in circles

27.6

Tangent properties in circles

27.7

Central and inscribed angles in circles

27.8

Equation of a circle

28. Surface Area and Volume of 3-Dimensional Shapes

28.1

Surface area and volume of prisms

28.2

Surface area and volume of pyramids

28.3

Surface area and volume of cylinders

28.4

Surface area and volume of cones

28.5

Surface area and volume of spheres

29. Statistics

29.1

Median and mode

29.2

29.3

Range and outliers

29.4

Application of averages

30. Probability

30.1

Determining probabilities using tree diagrams and tables

30.2

Probability of independent events

30.3

Probability with Venn diagrams

31. Exponential Functions

31.1

Exponents: Product rule (a^x)(a^y) = a^(x+y)

31.2

Exponents: Division rule (a^x / a^y) = a^(x-y)

31.3

Exponents: Power rule (a^x)^y = a^(x * y)

31.4

Exponents: Negative exponents

31.5

Exponents: Zero exponent: a^0 = 1

31.6

Exponents: Rational exponents

31.7

Solving exponential equations using exponent rules

31.8

Graphing exponential functions

31.9

Graphing transformations of exponential functions

31.10

Finding an exponential function given its graph

32. Inequalities in Two Variables

32.1

Graphing linear inequalities in two variables

32.2

Graphing systems of linear inequalities

32.3

Graphing quadratic inequalities in two variables

32.4

Graphing systems of quadratic inequalities

32.5

Applications of inequalities

32.6

What is linear programming?

32.7

Linear programming word problems

33. Permutations and Combinations

33.1

Fundamental counting principle

33.2

Factorial notation

33.3

Path counting problems

33.4

Permutation vs. Combination

33.5

33.6

33.7

Problems involving both permutations and combinations

33.8

Pascal's triangle

33.9

Binomial theorem

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