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CLEP College Algebra Topics

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

General form: Ax + By + C = 0

Point-slope form:

y - y_1 = m (x - x_1)

Parallel and perpendicular lines in linear functions

Graphing Functions

Domain and range of a function

Identifying functions

Function notation

Graphing linear functions using x- and y-intercepts

Determining number of solutions to linear equations

Using elimination method to solve systems of equations

Using substitution method to solve systems of equations

Solving systems of linear equations by graphing

Exponents and Multiplying Polynomials

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

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

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

Combining the exponent rules

Exponents: Zero exponent: a^0 = 1

Multiplying binomial by binomial

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

Factoring

Common factors of polynomials

Factor by taking out the greatest common factor

Factoring polynomials:

ax^2 + bx + c

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

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

Introduction to quadratic functions

Factoring polynomials by grouping

Factoring polynomials: x^2 + bx + c

Evaluating polynomials

Word problems of polynomials

Radical Expressions and Quadratic Equations

Evaluating and simplifying radicals

Converting radicals to mixed radicals

Imaginary and Complex Numbers

Introduction to imaginary numbers

Adding and subtracting complex numbers

Multiplying and dividing complex numbers

Complex conjugates

Solving Quadratic Equations

Solving quadratic equations by factoring

Solving quadratic equations by completing the square

Solving quadratic equations using the quadratic formula

Nature of roots of quadratic equations: The discriminant

Applications of quadratic equations

Ratio, Proportion, Area, and Perimeter

Ratios

Similar polygons

Surface Area and Volume

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

Probability and Statistics

Median and mode

Mean

Application of averages

Introduction to probability

Organizing outcomes

Probability of independent events

Fundamental counting principle

Combinations

Permutations

Coordinate Geometry

Distance formula:

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

Midpoint formula:

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

Solving second degree trigonometric equations

Negative and Rational Exponents

Rational exponents

Solving radical equations

Basic radical functions

Composite Functions and Inverses

Composite functions

Inverse functions

Logarithms and Exponential Functions

What is a logarithm?

Evaluating logarithms without a calculator

Product rule of logarithms

Quotient rule of logarithms

Combining product rule and quotient rule in logarithms

Solving logarithmic equations

Evaluating logarithms using change-of-base formula

Exponential growth and decay by a factor

Exponential decay: Half-life

Natural log: ln

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