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CLEP College Math Topics

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1. Adding and Subtracting Integers

1.1

Introduction to integer addition

1.2

Adding integers

1.3

Introduction to integer subtraction

1.4

Subtracting integers

1.5

Application of integer operations

2. Multiplying and Dividing Integers

2.1

Multiplying integers

2.2

Dividing integers

3. Primes and Common Factors

3.1

Prime factorization

3.2

Least Common Multiple (LCM)

3.3

Greatest Common Factors (GCF)

4. Fractions

4.1

Adding fractions with like denominators

4.2

Subtracting fractions with like denominators

4.3

Adding and subtracting fractions with unlike denominators

4.4

Multiplying proper fractions

4.5

Dividing fractions and mixed numbers

5. Decimals

5.1

Adding and subtracting decimals

5.2

Multiplying decimals

5.3

Dividing decimals

5.4

Order of operations (BEDMAS)

5.5

Scientific notation

5.6

Rational vs. Irrational numbers

6. Expressions and Equations

6.1

Patterns

6.2

Adding and subtracting polynomials

6.3

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

6.4

Multiplying polynomials by monomials

6.5

Solving linear equations using multiplication and division

6.6

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

6.7

Solving one - step equations: x + a = b

6.8

Solving linear equations with variables on both sides

7. Introduction to Equations

7.1

Evaluating algebraic expressions

7.2

Solving literal equations

7.3

Applications of polynomial functions

7.4

8. Absolute Value Equations

8.1

Absolute value functions

8.2

Solving absolute value equations

8.3

Solving absolute value inequalities

9. Graphing Inequalities

9.1

Express linear inequalities graphically and algebraically

9.2

Solving one-step linear inequalities

9.3

Solving multi-step linear inequalities

9.4

Graphing linear inequalities in two variables

10. Linear Equations

10.1

Word problems of graphing linear functions

10.2

Rate of change

10.3

Slope equation:

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

10.4

Graphing linear functions using a single point and slope

10.5

General form: Ax + By + C = 0

10.6

Point-slope form:

y - y_1 = m (x - x_1)

10.7

Parallel and perpendicular lines in linear functions

11. Graphing Functions

11.1

Domain and range of a function

11.2

Identifying functions

11.3

Function notation

11.4

Graphing linear functions using table of values

11.5

Graphing from slope-intercept form y=mx+b

11.6

Graphing linear functions using x- and y-intercepts

11.7

Using elimination method to solve systems of equations

11.8

Using substitution method to solve systems of equations

12. Exponents and Multiplying Polynomials

12.1

Direct variation

12.2

Multiplying binomial by binomial

13. Factoring

13.1

Common factors of polynomials

13.2

Factor by taking out the greatest common factor

13.3

Factoring polynomials:

ax^2 + bx + c

13.4

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

13.5

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

13.6

Introduction to quadratic functions

14. Radical Expressions and Quadratic Equations

14.1

Evaluating and simplifying radicals

14.2

Converting radicals to mixed radicals

14.3

Solving quadratic equations by factoring

14.4

Solving quadratic equations by completing the square

14.5

Using quadratic formula to solve quadratic equations

14.6

Transformations of quadratic functions

15. Introduction to Geometry

15.1

Cartesian plane

15.2

Parallel and perpendicular line segments

15.3

Horizontal and vertical distances

16. Statistics

16.1

Reading and drawing bar graphs

16.2

Reading and drawing line graphs

16.3

Circle graphs

16.4

Reading and drawing histograms

16.5

Box-and-whisker plots and scatter plots

16.6

Median and mode

16.7

Mean

16.8

Application of averages

17. Probability

17.1

Introduction to probability

17.2

Organizing outcomes

17.3

Probability of independent events

17.4

Comparing experimental and theoretical probability

18. Angle Pair, Parallel, and Perpendicular Lines

18.1

Parallel line proofs

18.2

Perpendicular line proofs

18.3

Inscribed Angles and Proofs

18.4

Standard angles

18.5

Coterminal angles

18.6

Reference angles

19. Triangles

19.1

Classifying Triangles

19.2

Congruence and Congruent Triangles

19.3

Triangles Congruent by SSS Proofs

19.4

Triangles Congruent by SAS and HL Proofs

19.5

Triangles Congruent by ASA and AAS Proofs

19.6

Isosceles and Equilateral Triangles

20. Relations in Triangles

20.1

Unit circle

20.2

Law of sines

20.3

Law of cosines

20.4

Applications of the sine law and cosine law

21. Ratio, Proportion, Similarity, & Percent

21.1

Ratios

21.2

Similar polygons

21.3

Percents, fractions, and decimals

21.4

Percent of a number

21.5

Pythagorean theorem

21.6

Applications of pythagorean theorem

21.7

Solving expressions using 30-60-90 special right triangles

21.8

Solving expressions using 45-45-90 special right triangles

22. Right Triangles

22.1

Use sine ratio to calculate angles and side (Sin =

\frac{o}{h}

)

22.2

Use cosine ratio to calculate angles and side (Cos =

\frac{a}{h}

)

22.3

Use tangent ratio to calculate angles and side (Tan =

\frac{o}{a}

)

22.4

Other word problems relating angles in trigonometry

23. Beginning Measurement

23.1

Metric systems

23.2

Imperial systems

23.3

Conversions between metric and imperial systems

23.4

Conversions involve squares and cubic

24. Circles

24.1

Tangent properties

24.2

Circle and circumference

24.3

Arcs of a circle

24.4

Areas and sectors of circles

24.5

Central and inscribed angles in circles

25. Surface Area and Volume

25.1

Surface area and volume of prisms

25.2

Surface area and volume of pyramids

25.3

Surface area and volume of cylinders

25.4

Surface area and volume of cones

25.5

Surface area and volume of spheres

26. Coordinate Geometry

26.1

Distance formula:

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

26.2

Midpoint formula:

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

26.3

Solving second degree trigonometric equations

27. Negative and Rational Exponents

27.1

Exponents: Negative exponents

27.2

Combining the exponent rules

27.3

Rational exponents

27.4

Solving radical equations

27.5

Basic radical functions

28. Composite Functions and Inverses

28.1

Composite functions

28.2

Inverse functions

29. Logarithms and Exponential Functions

29.1

What is a logarithm?

29.2

Evaluating logarithms without a calculator

29.3

Product rule of logarithms

29.4

Quotient rule of logarithms

29.5

Combining product rule and quotient rule in logarithms

29.6

Solving logarithmic equations

29.7

Evaluating logarithms using change-of-base formula

29.8

Exponential growth and decay by a factor

29.9

Exponential decay: Half-life

29.10

Natural log: ln

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