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ADVANCED ALGEBRA PROBLEMS

Mr. X helps math students better understand Advanced Algebra. Our sample math problems are designed to provide the necessary practice to know and understand the ideas and principles of advanced algebra. The sample problems reinforce the advanced algebra lessons available to our subscribers. Check out our free samples below, as well as the advanced algebra problem set. Advanced algebra lessons and problems are included with a subscription to Mr. X.

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Advanced Algebra Sample Problem 1

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Advanced Algebra Sample Problem 2

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Advanced Algebra Sample Problem 3

Advanced Algebra Problem Set

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Title Description
Adding and Subtracting Complex Numbers Addition and subtraction of complex numbers of the form: (a + bi) or (c - di). Play_video Printer
Advanced Algebra Problem 301 Exercises of Powers and Roots. Twelve problems; I work the first six, you work the last six. Play_video
Advanced Algebra Problem 302 More exercises of powers and roots. Ten problems; I work five and leave five for you. Play_video
Advanced Algebra Problem 303 More exercises of powers and roots. Eight problems; I work four and leave four for you to do. Play_video
Advanced Algebra Problem 304 We solve an inequality with a fraction of linear binomials by finding Critical Points of the function. Play_video
Advanced Algebra Problem 304a 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. Play_video
Advanced Algebra Problem 305 We graph a linear inequality. Although this is more advanced than "y = mx + b," we still use that familiar linear relation. Play_video
Advanced Algebra Problem 305a These problems with radicals and roots are appropriate for some students in Basic Algebra. I work five and leave five problems to work yourself. Play_video
Advanced Algebra Problem 306 We graph a linear inequality. Play_video
Advanced Algebra Problem 306a These problems can be done by advanced students in Basic Algebra. Ten problems; I work four and leave six for you to work. Play_video
Advanced Algebra Problem 309 We solve an inequality in one variable with AND logic and graph the solution set. Basic Algebra students doing well can do this in a first-year course as well. Play_video
Advanced Algebra Problem 310 We solve an inequality with Absolute Value in one variable. We show a "shortcut," but you need to understand the language of algebra. Play_video
Advanced Algebra Problem 322 We solve (by two different methods) parametric equations that are functions of "t" by expressing them in terms of x and y. Play_video
Advanced Algebra Problem 328 We solve an inequality in one variable with an Absolute Value condition. Play_video
Advanced Algebra Problem 330 We determine the domains of three functions. This problem (particularly part c) is appropriate for Basic Algebra. Play_video
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. Play_video Printer
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. Play_video Printer
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. Play_video Printer
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. Play_video Printer
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. Play_video Printer
Algebraic Fractions Simplified 17 With both addition and subtraction of fractions with binomials in x, we obtain a common denominator. You should know that a² - b² = (a-b)(a+b). Play_video Printer
Analytic Geoemtry - Circles Problem Set 44 Practice with Advanced Algebra and conic sections, namely, circles. 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. Play_video
Analytic Geometry - Ellipses Problem Set 48 Given equations of ellipses, determine center, foci, vertices, eccentricity, and length of axes (major and minor). Play_video Printer
Analytic Geometry - Ellipses, Problem Set 49 Given parameters of an ellipse, determine the equation. Or, given an equation for an ellipse, determine the parameters (foci, center, eccentricity, etc.) Play_video Printer
Analytic Geometry - Hyperbolas, Problem Set 50 Given parameters of a hyperbola (foci, eccentricity, etc.) determine other parameters or the equation. Or, given an equation for a hyperbola, determine various parameters. Play_video Printer
Area of Square 14013 Version E Given vertices of a square in Cartesian Coordinates, find the area of the square. This is Version E (explanatory). Play_video
Area of Square 14013 Version F Given vertices of a square in Cartesian Coordinates, find the area of the square. This is Version F (fast and fleeting). Play_video
Area of Square 14013 Version G Given vertices of a square in Cartesian Coordinates, find the area of the square. This is Version G (good and general). Play_video
Area of Square 14014 Version E Given only two vertices of a square in Cartesian Coordinates, find the area of the square. This is Version E (explanatory). Play_video
Area of Square 14014 Version F Given only two vertices of a square in Cartesian Coordinates, find the area of the square. This is Version F (fast). Play_video
Area of Square 14014 Version G Given two vertices of a square in Cartesian Coordinates, find the area of the square. This is Version G (general). Play_video
Biquadratic Equations These fourth-order polynomial problems resemble quadratics. We solve with a basic substitution for x². Play_video Printer
Conic Sections: Circles 12 Four problems (I work two of them); we graph circles from equations. Play_video Printer
Conic Sections: 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. Play_video Printer
Cubic Inequality in One Variable Consider 2x^3 + 5x^2 is less than or equal to 12x. We solve for the values of x that make the statement true. Play_video
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. Play_video
Dividing "complex" fraction 303 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. Play_video
Evaluate (1.04) to 3rd power Version E We use the binomial theorem (expansion) to calculate (1.04) cubed. This is version E, the elaborate, expansive, explanatory version. Play_video
Evaluate (1.04) to 3rd power Version F We use the binomial theorem (expansion) to calculate (1.04) cubed. This is version F, the fast, furious, and fun version. Play_video
Evaluate (1.04) to 3rd power Version G We use the binomial theorem (expansion) to calculate (1.04) cubed. This is version G, the generally good, grade-level version. Play_video
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. Play_video Printer
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. Play_video Printer
Geometric Progression 14012 Version E We are to find three (consecutive) numbers in a Geometric Progression whose product is 216 and whose sum is 19. This is version E, the explanatory version. Play_video
Geometric Progression 14012 Version F We are to find three (consecutive) numbers in a Geometric Progression whose product is 216 and whose sum is 19. This is version F, the fast and fun version. Play_video
Geometric Progression 14012 Version G We are to find three (consecutive) numbers in a Geometric Progression whose product is 216 and whose sum is 19. This is version G, the general, grade-level version. Play_video
Graph Inequalities in 2 Variables Graph linear inequalities in two variables. I like to picture equalities and equations of lines. Play_video Printer
Graph Inequalities in Two Variables Here we graph solutions to linear inequalities. Play_video Printer
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. Play_video Printer
Inequalities in Two Variables 07 We use equalities to graph these inequalities. These problems use linear relationships. Play_video Printer
Inequality in One Variable with Absolute Value This simple problem is appropriate toward the end of a course in Basic Algebra. Play_video
Inverses of Functions Six little problems, you get three to do on your own. We look at inverses of functions of x, as y=f(x) and the inverse is the mirror image about the x=y line. Play_video Printer
Logarithmic Exercises We solve basic log problems in these exercises. Play_video
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. Play_video Printer
Multiply and Divide Complex Numbers Division of complex numbers involves multiplication that employs the complex conjugate of the divisor. Play_video Printer
Non-linear Equations Here we solve non-linear systems of equations. We have variables raised to powers other than one; we have x² and y² terms. Play_video Printer
Polynomial Division Quotients and remainders result from these division problems where both dividend and divisor are polynomials in one variable. Play_video Printer
Polynomial Division 09 Division of polynomials can be done with a process that looks just like "long division." Play_video Printer
Problem 261 - Domain of Quotient Function With a quotient of f(x)/g(x) we can easily find the domain of the new function. Note that at one point Mr. X mistakenly calls "the square root of x" function "x-squared." You'll see. Play_video
Problem 262 - Graph a Simple Parabola We walk through a simple sketch of a graph of y = x² - 5. The parabola is a conic section. Play_video
Problem 265 - Graph Circles from Equations We look at two circles in Cartesian coordinates from their equations in x and y. We employ desmos.com to see the graphs. Play_video
Problem 266 - Graph a Parabola As y = f(x), we have a simple quadratic that graphs to a parabola. We employ y = a(x-h)² + k. Play_video
Problem 267 - Parabola as x = f(y) We look at a "sideways" function with the relation x = f(y) instead of our usual y = f(x). Play_video
Problem 268 - Sketch graph of Ellipse We look at the conic section Ellipse with an equation in x² and y². Play_video
Problem 269 - Sketch an Ellipse For an ellipse centered at (h,k) we have equations in x² and y². We look at a² and b² to determine whether the major axis is horizontal or vertical. Play_video
Problem 270 - Graph Ellipse We complete the square to build the equation of an ellipse prior to graphing it. Play_video
Problem 271 - Graph Ellipse From an equation in x² and y² we complete squares of binomials and build the equation for the ellipse before graphing it. Play_video
Problem 272 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. Play_video
Quiz, Algebra 14015 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. Play_video
Quiz, Algebra 14015 Version F 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 F (shortest). Play_video
Quiz, Algebra 14015 Version G 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 G (general). Play_video
Simplify Algebraic Fractions Twelve problems, six of them "worked." We factor out from numerator and denominator common factors, most often linear factors. This is also a Problem Set in Basic Algebra. Play_video Printer
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. Play_video Printer
Solve a cubic polynomial for zeroes (roots) Set y = x^3 + x^2 - 6x = 0 and solve. Play_video
Solve a cubic polynomial in one variable for zeroes Solve y = 5x^3 - 6x^2 - 8x = 0. Play_video
Solve a fourth-order polynomial for zeroes (roots) Solve y = x^4 - 4x^3 - 5x^2 =0 Play_video
Solve Two Eqns. in 3 Unknowns Solve two equations in three unknowns: x, y and z. We employ augmented matrices. Play_video
Solving Basic Quadratic Equations 27 This is generally considered Basic Algebra, but it begins the foundation for a journey into Advanced Algebra. Play_video Printer
Solving Basic Quadratic Equations 28 Factor quadratics of the form ax² - bx + c = 0. Play_video Printer
Solving Basic Quadratic Equations 29 While this is still Basic Algebra, it underlies our work in Advanced Algebra. We factor second-order polynomials into linear factors. Play_video Printer
Solving Basic Quadratic Equations 30 Factoring quadratics with coefficients with many factors gives us reason to scratch our heads just a little. Of course, you may always use the Quadratic Formula to solve ax² + bx + c = 0. Play_video Printer
Solving Basic Quadratic Equations 31 A variety of techniques are used to factor quadratics. Play_video Printer
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. Play_video Printer
Solving Basic Quadratic Equations 33 Not every quadratic equation factors into neat binomials or linear factors. In such cases we use the Quadratic Formula. Play_video Printer
Solving Basic Quadratic Equations 34 Factor, if possible. Build experience to see factorizations when they're possible. The Quadratic Formula will always work on a quadratic equation. Play_video Printer
Solving Basic Quadratic Equations 35 We now emphasize the Quadratic Formula, which always serves to solve for the roots of an equation of the form ax² + bx + c = 0. Play_video Printer
Solving Basic Quadratic Equations 36 The Quadratic Formula, which always serves to solve for the roots of an equation of the form ax² + bx + c = 0, should be practiced repeatedly. Play_video Printer
Solving Basic Quadratic Equations 37 A final problem set before embarking on genuine Advanced Algebra with complex answers. This problem set is still entirely "real." Play_video Printer
Solving Basic Quadratic Equations 38 With a negative discriminant we obtain complex roots for the quadratic. Those complex roots always come in pairs. Play_video Printer
Solving Basic Quadratic Equations 39 Twenty-five problems, all solved visually without explanation. You should work these problems before watching the video. Play_video Printer
Solving Basic Quadratic Equations 40 You never know when the discriminant of a quadratic will be negative. Be prepared for complex roots. Play_video Printer
Solving Basic Quadratic Equations 41 Factor when you can, but reliance on the Quadratic Formula is best, particularly with negative discriminants and complex roots. Play_video
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