CLEP College Mathematics Exam - Numbers, Algebra & Functions

This course covers the essential concepts from the Numbers and Algebra & Functions categories of the College Mathematics CLEP exam. Together, these two topics account for approximately 30% of the exam content, based on guidance from the College Board.

Whether you're brushing up on math fundamentals or preparing to earn college credit by exam, this course will help you build a strong foundation in:

• Core number concepts (≈10% of the exam)

• Algebraic reasoning and functions (≈20% of the exam)

The College Mathematics CLEP exam is accepted for credit at many colleges and universities. Credit policies vary by institution, so please check with your school to confirm how CLEP credit may apply to your degree program.

By mastering these two content areas, you'll be well on your way to confidently tackling nearly one-third of the College Mathematics CLEP exam.

The following lectures are included:

1. Real numbers - definition, properties of real numbers, order of operations, components of real numbers

2. Fractions and number rules - proper and improper fractions, rules of odd and even numbers, factors and multiples, prime numbers and composite numbers

3. Exponents - negative exponents, exponent of zero, fractional exponents, negative fractional exponents, the laws of exponents

4. Inequalities and absolute value - definition, order property of real numbers, transitive property of inequalities, addition property of inequality, graphing inequalities, intervals on a number line, absolute value definition, how to solve expressions with absolute values, the rules of absolute values

5. Imaginary and complex numbers - define imaginary numbers, define complex numbers, adding complex numbers, subtracting complex numbers, multiplying complex numbers, dividing complex numbers

6. Scientific notation - definition/form of scientific notation, how to convert to standard notation, how to convert from standard notation to scientific notation, multiplication of numbers in scientific notation, division of numbers in scientific notation

7. Systems of measurement - imperial system and metric system units of length, weight and volume; units of time; how to convert units

8. Equations - how to solve for unknown variable in equations, how to solve equations in fractional form, and how to solve exponential equations

9. Logarithms - how to find logarithms, common logarithm, and logarithm rules

10. Linear equations - define linear equation, solve linear equations with one unknown, general format for linear equations with two unknowns, slope-intercept form, and how to graph linear equations

11. Modeling real-world problems - modeling linear functions and using tabular form to write an equation for a linear function

12. Point-Slope and Intercept Form - point-slope form, how to find linear equation given two points using point-slope form, intercept form, how to find linear equation given the x and y intercepts using intercept form, horizontal lines, and vertical lines

13. Simultaneous linear equations - how to solve simultaneous linear equations using substitution, addition or subtraction, and graphing

14. Other systems of equations - dependent equations, consistent vs inconsistent system of linear equations, parallel lines and perpendicular lines

15. Inequality and absolute value equations - how to solve inequalities, graphing linear inequalities, and solving absolute value equations

16. Quadratic equations - define quadratic equations, quadratic equations with one unknown, quadratic equations with two unknowns, and solving quadratic equations with one unknown using factoring, difference of two squares, and quadratic formula

17. Quadratic formula - quadratic formula examples, discriminant definition, and impact of the discriminant on the nature of the roots of a quadratic equation

18. Relations - ordered pairs, relations, and domain and range of a relation

19. Functions - function definition, the three ways that functions can be represented, numerical representation of functions,  how to identify relations that are functions, graphical representation of functions, the vertical line test, symbolic representation of functions, evaluating functions to find y with a given x value, and piecewise functions

20. Domain of functions - 5 options for specifying domain of a function, domain of function rules, and domain of function examples

21. Other functions- inverses of a function and exponential functions

22. Combining functions - Composition of functions and combining functions algebraically

23. Transformation of graphs - common graph transformations and their impact on the function in functional notation