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# Math Training

## ADVANCED ALGEBRA PROBLEMS

❶Algebraic Fractions Simplified 12 With both multiplication and division of fractions with binomials in x, we can simplify by cancelling factors from both numerator and denominator.

## Information   Check out our free samples below, as well as the advanced algebra problem set. Twelve problems; I work the first six, you work the last six. Advanced Algebra Problem More exercises of powers and roots. Ten problems; I work five and leave five for you.

Eight problems; I work four and leave four for you to do. Advanced Algebra Problem We solve an inequality with a fraction of linear binomials by finding Critical Points of the function. Advanced Algebra Problem a Ten problems with powers and roots; I work three and leave seven problems for you to work on your own. This lesson is appropriate for good students in Basic Algebra. Advanced Algebra Problem We graph a linear inequality.

Advanced Algebra Problem a These problems with radicals and roots are appropriate for some students in Basic Algebra. I work five and leave five problems to work yourself. Ten problems; I work four and leave six for you to work. Basic Algebra students doing well can do this in a first-year course as well. We show a "shortcut," but you need to understand the language of algebra.

Advanced Algebra Problem We solve by two different methods parametric equations that are functions of "t" by expressing them in terms of x and y. Advanced Algebra Problem We solve an inequality in one variable with an Absolute Value condition. Advanced Algebra Problem We determine the domains of three functions. This problem particularly part c is appropriate for Basic Algebra. Algebraic Fractions Simplified 12 With both multiplication and division of fractions with binomials in x, we can simplify by cancelling factors from both numerator and denominator.

Algebraic Fractions Simplified 13 With both multiplication and division of fractions with binomials in x, we can simplify by cancelling factors from both numerator and denominator. Algebraic Fractions Simplified 14 With both multiplication and division of fractions with binomials in x, we can simplify by cancelling factors from both numerator and denominator.

Algebraic Fractions Simplified 15 With both addition and subtraction of fractions with binomials in x, we can sum or take a difference by obtaining a common denominator. Algebraic Fractions Simplified 16 With both addition and subtraction of fractions with binomials in x, we can sum or take a difference by obtaining a common denominator.

Algebraic Fractions Simplified 17 With both addition and subtraction of fractions with binomials in x, we obtain a common denominator. Given an equation, find the equation of a line tangent to the circle at a given point. Or, given a radius and center, determine the equation of the circle.

Analytic Geometry - Ellipses Problem Set 48 Given equations of ellipses, determine center, foci, vertices, eccentricity, and length of axes major and minor. Or, given an equation for an ellipse, determine the parameters foci, center, eccentricity, etc. Analytic Geometry - Hyperbolas, Problem Set 50 Given parameters of a hyperbola foci, eccentricity, etc. Or, given an equation for a hyperbola, determine various parameters. This is Version E explanatory.

This is Version F fast and fleeting. This is Version G good and general. Area of Square Version E Given only two vertices of a square in Cartesian Coordinates, find the area of the square.

Area of Square Version F Given only two vertices of a square in Cartesian Coordinates, find the area of the square. This is Version F fast. This is Version G general. Biquadratic Equations These fourth-order polynomial problems resemble quadratics. Circles 12 Four problems I work two of them ; we graph circles from equations. Circles 13 We look for tangent lines to a circle in problem 1,; in problem 3 we calculate center, radius, and equation of a circle.

We solve for the values of x that make the statement true. Divide binomials in fractions for Advanced Algebra You need to understand the division of binomials top-and-bottom in fractional expressions to venture future into the language of mathematics. Dividing "complex" fraction We walk through division of a "complex" fraction with a fraction divided by another fraction, with numerator and denominator each a polynomial in two variables.

This is version E, the elaborate, expansive, explanatory version. This is version F, the fast, furious, and fun version. This is version G, the generally good, grade-level version. Exercises of Equations 21 We solve for x or y or x using a variety of techniques. In this problem set we have lots of binomials and linear factors. Function Domains 05 To stay in the real numbers we cannot take an even root of a negative value, nor can we divide by zero. Geometric Progression Version E We are to find three consecutive numbers in a Geometric Progression whose product is and whose sum is This is version E, the explanatory version.

Geometric Progression Version F We are to find three consecutive numbers in a Geometric Progression whose product is and whose sum is This is version F, the fast and fun version. Geometric Progression Version G We are to find three consecutive numbers in a Geometric Progression whose product is and whose sum is This is version G, the general, grade-level version.

Graph Inequalities in 2 Variables Graph linear inequalities in two variables. I like to picture equalities and equations of lines.

Graph Inequalities in Two Variables Here we graph solutions to linear inequalities. Inequalities in Two Variables Six little problems in rectangular or Cartesian coordinates. These are linear functions with x and y raised to the first power. Inequalities in Two Variables 07 We use equalities to graph these inequalities. These problems use linear relationships. Inverses of Functions Six little problems, you get three to do on your own. Logarithmic Exercises We solve basic log problems in these exercises.

Multiplication and Division of Complex Numbers Multiplication and division of complex numbers uses much of "regular" arithmetic and algebra. Division employs the "complex conjugate" of the denominator. Multiply and Divide Complex Numbers Division of complex numbers involves multiplication that employs the complex conjugate of the divisor.

Non-linear Equations Here we solve non-linear systems of equations. Polynomial Division Quotients and remainders result from these division problems where both dividend and divisor are polynomials in one variable. Polynomial Division 09 Division of polynomials can be done with a process that looks just like "long division. Note that at one point Mr. X mistakenly calls "the square root of x" function "x-squared.

The parabola is a conic section. Problem - Graph Circles from Equations We look at two circles in Cartesian coordinates from their equations in x and y. Problem - Graph Ellipse We complete the square to build the equation of an ellipse prior to graphing it. Problem Fora conic section ellipse with a given center and vertices, and a relation between a and c, sketch the graph and find the equation of the ellipse. Quiz, Algebra Version E A customer can buy one shirt for x dollars, and additional shirts cost four dollars less than the first.

Find the expression that describes the function for the cost of n shirts purchased. This is Version E. Quiz, Algebra Version F A customer can buy one shirt for x dollars, and additional shirts cost four dollars less than the first. This is Version F shortest. Quiz, Algebra Version G A customer can buy one shirt for x dollars, and additional shirts cost four dollars less than the first.

Simplify Algebraic Fractions Twelve problems, six of them "worked. This is also a Problem Set in Basic Algebra. Simplify Algebraic Fractions 17 We simplify algebraic factors by canceling common factors top and bottom. We also divide by multiplying by the reciprocal of the divisor. We employ augmented matrices. We factor second-order polynomials into linear factors.

Solving Basic Quadratic Equations 30 Factoring quadratics with coefficients with many factors gives us reason to scratch our heads just a little. Solving Basic Quadratic Equations 31 A variety of techniques are used to factor quadratics.

Solving Basic Quadratic Equations 32 More factoring of quadratics. Practice and knowing facts of arithmetic are key. We look briefly at a graph from Wolfram Alpha. Solving Basic Quadratic Equations 33 Not every quadratic equation factors into neat binomials or linear factors.

In such cases we use the Quadratic Formula. Solving Basic Quadratic Equations 34 Factor, if possible. Build experience to see factorizations when they're possible.

Help your child conquer algebra by printing this free algebra worksheet for middle school. Want to give your child some extra practice in algebra? Print this fun worksheet today! Make algebra easier for your little scholar by downloading this free printable algebra worksheet.

The internet is a valuable resource for both homeschooling parents as well as teachers. You can find a wide array of algebra problems online for all grades. From simple, easy algebra problems to tougher, more complex ones, you can find it all online. Most online resources mention the age and grade for which the algebra problems are suited. Get the kids started on pre algebra problems and monitor their progress. With regular practice, kids will soon be able comfortable solving any kind of algebraic equation!

Algebra Problems Looking for algebra problems to give kids to solve? ## Main Topics

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Sample problems are under the links in the "Sample Problems" column and the corresponding review material is under the "Concepts" column. New problems are given each time the problem links are followed. Free math problem solver answers your algebra homework questions with step-by-step explanations.