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CLEP College Math Topics

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

Graphing linear functions using a single point and slope

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 table of values

Graphing from slope-intercept form y=mx+b

Graphing linear functions using x- and y-intercepts

Using elimination method to solve systems of equations

Using substitution method to solve systems of equations

Exponents and Multiplying Polynomials

Direct variation

Multiplying binomial by binomial

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

Radical Expressions and Quadratic Equations

Evaluating and simplifying radicals

Converting radicals to mixed radicals

Solving quadratic equations by factoring

Solving quadratic equations by completing the square

Using quadratic formula to solve quadratic equations

Transformations of quadratic functions

Introduction to Geometry

Cartesian plane

Parallel and perpendicular line segments

Horizontal and vertical distances

Statistics

Reading and drawing bar graphs

Reading and drawing line graphs

Circle graphs

Reading and drawing histograms

Box-and-whisker plots and scatter plots

Median and mode

Mean

Application of averages

Probability

Introduction to probability

Organizing outcomes

Probability of independent events

Comparing experimental and theoretical probability

Angle Pair, Parallel, and Perpendicular Lines

Parallel line proofs

Perpendicular line proofs

Inscribed Angles and Proofs

Standard angles

Coterminal angles

Reference angles

Triangles

Classifying Triangles

Congruence and Congruent Triangles

Triangles Congruent by SSS Proofs

Triangles Congruent by SAS and HL Proofs

Triangles Congruent by ASA and AAS Proofs

Isosceles and Equilateral Triangles

Relations in Triangles

Unit circle

Law of sines

Law of cosines

Applications of the sine law and cosine law

Ratio, Proportion, Similarity, & Percent

Ratios

Similar polygons

Percents, fractions, and decimals

Percent of a number

Pythagorean theorem

Applications of pythagorean theorem

Solving expressions using 30-60-90 special right triangles

Solving expressions using 45-45-90 special right triangles

Right Triangles

Use sine ratio to calculate angles and side (Sin =

\frac{o}{h}

)

Use cosine ratio to calculate angles and side (Cos =

\frac{a}{h}

)

Use tangent ratio to calculate angles and side (Tan =

\frac{o}{a}

)

Other word problems relating angles in trigonometry

Beginning Measurement

Metric systems

Imperial systems

Conversions between metric and imperial systems

Conversions involve squares and cubic

Circles

Tangent properties

Circle and circumference

Arcs of a circle

Areas and sectors of circles

Central and inscribed angles in circles

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

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

Exponents: Negative exponents

Combining the exponent rules

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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