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Precalculus Help and Problems

Topics in precalculus will serve as a transition between algebra and calculus, containing material covered in advanced algebra and trigonometry courses. Precalculus consists of insights needed to understand calculus.

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Sets

A brief overview of sets, one of the fundamental principles of mathematics. The topic of sets introduces grouping of objects and number classifications.

Exponential Functions

An extension of exponents in terms of functions, as well as introducing the constant e. Topics include exponential growth and decay, solving with logs, compound and continuously compounded interest, and the exponential function of e.

Logarithmic Functions

A more in depth look at logarithms and logarithmic functions, as well as how they relate to exponents. Topics include the standard and natural log, solving for x and the inverse properities of logarithms.

Radical Functions

An introduction to functions with square roots and radicals and how they relate to conic sections. Topics include functions finding zeros of radical functions, functions with square roots and higher roots, and functions with no solution.

Series and Sequences

Sequences and Series always go hand in hand and they introduce the concept of Mathematical Patterns and how to deal with them. This section deals with the different types of Series and Sequences as well as the methods of finding the next term in a sequence or the sum of a series.

The major types of series and sequences include:

Arithmetic Progression

Geometric Progression

Factorials, Permutations and Combinations

Introduction to the factorial notation. The concept of combinations and permutations is introduced and explained.

Binomial Theorem

Statement of the Binomial Theorem. Pascals' Triangle and its relation to Binomial Theorem. Expanding polynomials using the Binomial Theorem.

Parametric Equations

An overview of the use of parametric equations, including parametrizing functions and finding a function for a set of parametric equations. Topics include parametrizing lines, segments, circles and ellipses, and peicewise functions.

Polar Coordinates

An introduction to the polar coordinate system. Topics include graphing points, converting from rectangular to polar and polar to rectangular coordinates, converting degrees and radians, and polar equations.

Matrices

Introduction to the concept of matrices. Different types of matrices discussed. Matrix algebra including addition, subtraction and multiplication. Matrix inverses and determinants.

Subpages include:

Matrix Equality

Matrix Addition and Subtraction

Matrix Multiplication

Special Matrices

Inverse Matrix

Reduction to Row Echelon Form

Systems of Equations

Many times we come cross systems of equations and we're usually at odds with how to solve them. Most times we deal with two-variable or three-variable systems of equations but the methods explained in this section can be used to solve any number variable system of equations. The trick is picking which one would work better and faster for you.

The methods explained include:

Substitution Method

Elimination Method

Matrix Method

Consistent and Inconsistent Systems

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