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Algebra and Functions Review

One of the best online teaching resources for mathematics, physics and computer science is Educator.com. All of their instructors are university professors and most of them have doctorate degrees. The Educator.com Algebra I instructor is Professor of Mathematics UCLA educated Dr. Grant Fraser while the Algebra II instructor is Dr. Carleen Eaton.

This website was designed mostly for high school students, college students and home school students.

The main topics of these Algebra I lectures are:

I. Basic Concepts
Variables and expressions, order of operations, the distributive property, the real number system, the real number system, the real number system, functions and graphs.

II. Solving Linear Equations
From sentences to equations, addition and subtraction techniques, multiplication and division techniques, techniques for multi-step equations, ratios and proportions, applications of percents, multiple variables.

III. Functions
Relations, functions, linear functions.

IV. Linear Functions and their Graphs
Slope and rate of change, direct variation, slope intercept form of an equation, point slope form of an equation, parallel and perpendicular lines.

V. Systems of Equations
Graphing Systems of Equations, Number of solutions, solving by substitution, solving by addition and subtraction, solving by multiplication, applications: systems of equations.

VI. Inequalities
Inequalities: addition and subtraction techniques, inequalities: multiplication and division techniques, techniques for multi-step inequalities, compound inequalities, equations with absolute values, inequalities with absolute values, graphing inequalities with two variables, graphing systems of inequalities.

VII. Polynomials
Multiplying monomials, dividing monomials, polynomials, adding and subtracting polynomials, multiplying polynomials by monomials, multiplying polynomials.

VIII. Factoring
Factoring monomials, factoring using greatest common factor (GCF), factoring trinomials with leading coefficient, factoring general trinomials, factoring the difference of two squares, factoring perfect squares.

IX. Quadratic Functions
Graphing quadratic functions, solving equations by graphing, solving equations by completing the square, solving equations using the quadratic formula.

X. Radical Expressions and Equations
Simplifying radical expressions, operations with radical expressions, solving radical equations, Pythagorean pheorem, distance formula.

XI. Rational Expressions and Equations
Inverse variation, rational expressions, multiplying rational expressions, dividing rational expressions, dividing polynomials, adding and subtracting rational expressions with like denominators, adding and subtracting rational expressions with unlike denominators, complex fractions, rational equations.

The main topics of these Algebra II lectures are:

I. Equations and Inequalities
Expressions and formulas, monomials, polynomials, properties of real numbers, solving eSolving absolute value equations, solving inequalities, solving compound and absolute value inequalities.

II. Linear Relations and Functions
Relations and functions, linear equations, slope, writing linear functions, special functions, graphing inequalities.

III. Systems of Equations and Inequalities
Solving systems of equations by graphing, solving systems of equations algebraically, solving systems of inequalities by graphing, solving systems of equations in three variables.

IV. Matrices
Basic matrix concepts, matrix operations, matrix multiplication, determinants, Cramer’s rule, identity and inverse matrices, solving systems of equations using matrices.

V. Quadratic Functions and Inequalities
Graphing quadratic functions, solving quadratic equations by graphing, solving quadratic equations by factoring, imaginary and complex numbers, completing the square, quadratic formula and the discriminant, analyzing the graphs of quadratic functions, graphing and solving quadratic inequalities.

VI. Polynomial Functions
Properties of exponents, operations on polynomials, dividing polynomials, polynomial functions, analyzing graphs of polynomial functions , solving polynomial functions, roots and zeros, rational zero theorem.

VII. Radical Expressions and Inequalities
Operations on functions, inverse functions and relations, square Root functions and inequalities, nth roots, operations with radical expressions, rational exponents, solving radical equations and inequalities.

VIII. Rational Equations and Inequalities
Multiplying and dRational Expressions, Adding and subtracting rational expressions, graphing rational functions, direct, joint, and inverse variation, solving rational equations and inequalities.

IX. Exponential and Logarithmic Relations
Exponential functions, logarithms and logarithmic functions, properties of logarithms, common logarithms, base e and natural logarithms, exponential growth and decay.

X. Conic Sections
Midpoint and distance formulas, parabolas, circles, ellipses, hyperbolas, conic Sections, solving quadratic systems.

XI. Sequences and Series
Arithmetic sequences, arithmetic series, geometric sequences, geometric series, infinite geometric series, recursion and special sequences, binomial theorem.

You may review free sample lectures on expressions and formulas, solving equations and parabolas of the Algebra II course.

The cost of a Educator.com monthly subscription plan is $35 and the annual subscription plan is $240, which is less than the cost of traditional tutoring. One nice thing is that this website does not auto-renew your subscription, so you don’t have to worry about canceling. You can pay either through credit card or PayPal. Another advantage is that all Educator.com instructors are university professors, while the experience of local math and science tutors can vary greatly.

One of the main advantages of this website is that you receive unlimited access to all their videos and examples, not just the subject you were interested in when you subscribed. You also get access to other student comments and questions and to the messaging system. The comments sections are visible only after you subscribe and are closely moderated by professors.





 

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