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Intermediate Algebra Test Prep Problems

275 worked math help tutor video examples on Intermediate Algebra examples, well organized by chapter, from textbook: Angel & Runde's "Intermediate Algebra"

Introduction and Table of Contents

This video series is entitled, "Intermediate Algebra Test Prep Problems," which provides 275 worked math help tutor video examples on Intermediate Algebra examples, well organized by chapter, from textbook: Angel & Runde's "Intermediate Algebra". The series presents 275 individual examples organized over 11 chapters and span the subject of Algebra 2. These videos have a total playtime duration of 7 hrs 12 min 27 sec. These videos were based in part on the book entitled, "Intermediate Algebra," written by Angel & Runde.

These worked examples come from the textbook entitled, "Intermediate Algebra," by Allen Angel & Dennis Runde. The particular examples come from the book's chapter test prep sections. These tutor videos address all major topics of the textbook in the proper order. Although these video exorcises were designed specifically for this textbook, they apply equally well to any algebra textbook. This is a fantastic resource for anyone studying algebra or seeking a well organized, systematic and all encompasing quick review, using any Algebra textbook. Note that each video clip is very short about 1 minute and covers one example each. All together, this video series includes 275 worked examples and is about 6.5 hours long. If you don't find the particular math problem you're looking for, try other video sets here. Remember my advice?

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FREE Online Math Video Tutor Lessons & Examples

Algebra 2: Intermediate Algebra Test Prep Problems
Chapter 1: Basic Concepts

EExample titles for Ch 1: Basic ConceptsTimeNote
1Sets, Natural numbers, and Set Notation.0:281.1 Study Skills for Success in Mathematics, and Using a Calculator
2Sets, Rational Numbers, and Real Numbers.0:141.2 Sets and Other Basic Concepts
3Sets, Rational Numbers, and Real Numbers.0:15
4Sets, Real Numbers, and Elements of a Set.0:30
5Sets, Real Numbers, and Elements of a Set.0:25
6Union of Sets and Intersection of Sets.0:38
7Union of Sets and Intersection of Sets.0:321.3 Properties of and Operations with Real Numbers
8Graphing, open set or closed set.0:32
9Graphing, open sets and closed sets.0:38
10Order of Magnitude.0:25
11Associative Property of Addition.0:20
12Commutative Property of Addition.0:18
13Order of operations.1:131.4 Order of Operations
14Simplify and Evaluate Rational Expressions.0:42
15Simplify and evaluate rational expressions.1:15
16Simplify and evaluate rational expressions.1:13
17Evaluating an expression.0:36
18Word problems, story problems, and formulas.1:57
19Simplify and evaluate exponential expressions.0:151.5 Exponents
20Simplifying and evaluating compound exponents.0:40
21Simplifying and evaluating a rational expressions with exponents.1:24
22Simplifying and evaluating a rational expressions with compound exponents1:43
23Scientific Notation.0:341.6 Scientific Notation
24Simplify and express without exponents.0:49
25fraction of a population, percentage and scientific notation.4:01
 Total Time of videos in this Chapter = 21:37  
 

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Algebra 2: Intermediate Algebra Test Prep Problems
Chapter 2: Equations and Inequalities

EExample titles for Ch 2: Equations and InequalitiesTimeNote
1Degree of an expression and Graphs & functions.0:26sum of exponents across variables
2Order of operations and Simplify expressions.0:462.1 Solving Linear Equations
3Order of operations and simplify expressions.1:47
4Solving linear equations.1:07
5Solving linear equations and least common denominator (LCD).1:17
6Solving linear equations, order of operations, brackets, parentheses.2:35
7Solving linear equations, infinite, finite, one, or no solutions.1:12
8Solving linear equations. Identities? Always True?1:18
9Evaluating formulas.2:032.2 Problem Solving and Using Formulas
10Solving multiple variable equations.1:23
11Solving formulas.1:12
12Word problems and story problems.1:022.3 Applications of Algebra
13Solving word problems and story problems.1:14
14Solving multiple rate problems, word problems, and story problems.1:32
15Solving mixing solutions problems, word problems, story problems.2:082.4 Additional Application Problems
16Simple interest, multiple rate problem, word problem, story problem, applications.2:52
17Graphing linear inequalities.1:132.5 Solving Linear Inequalities
18Solving inequality for a variable1:11
19Systems of inequalities. Set builder notation or interval notation.1:33
20Solving inequalities and interval notation.1:27
21Solving absolute value equations.0:522.6 Solving Equations and Inequalities Containing Absolute Values
22Solving double absolute value equations and solution sets.2:08
23Solving absolute value equations.0:28
24Solving absolute value inequalities.1:13
25Solving an absolute value inequality.1:34
 Total Time of videos in this Chapter = 35:33  
 

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Algebra 2: Intermediate Algebra Test Prep Problems
Chapter 3: Graphs and Functions

EExample titles for Ch 3: Graphs and FunctionsTimeNote
1Graphing equations of a straight line in 2 variables.1:163.1 Graphs
2Graphing equations with table of sample values.0:56
3Graphing nonlinear equations.1:23
4Graphing absolute value equations with a table of test values.0:58
5What is a function?0:423.2 Functions
6Sets of ordered pairs and testing if a function.0:34
7Vertical Line Test, graphs representing functions. Domain & range of a function.0:433.3 Linear Functions: Graphs and Applications
8Vertical line test and domain & range of a function.0:57
9Evaluating functions given a test value.0:50
10Graphing equations using x and y intercepts.0:58
11Graphing equations using y and x intercepts.1:02
12Graphing functions of a line parallel to an axis.0:36
13Graphing functions of a line parallel to an axis.0:34
14Graphing profit as function of units sold and the break even point.1:18
15Slope and y-intercept of a given equation.0:573.4 The Slope-Intercept Form of a Linear Equation
16Equation of a line through given points and calculating slope.1:283.5 The Point-Slope Form of a Linear Equation
17Equation of a line through a given point and perpendicular to a given line.1:07
18Reading ordered pairs from a graph. Satisfying given points. word problems.2:20
19Given lines parallel, perpendicular or neither.1:16
20Reading ordered pairs from a graph. Making an estimate. story problem.3:17
21Combining functions.0:493.6 The Algebra of Functions
22Evaluating combined functions.1:04
23Evaluating given functions.0:18
24Solving word problems and story problems.1:10
25Graphing linear inequalities.1:293.7 Graphing Linear Inequalities
 Total Time of videos in this Chapter = 28:02  
 

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Algebra 2: Intermediate Algebra Test Prep Problems
Chapter 4: Systems of Equations and Inequalities

EExample titles for Ch 4: Systems of Equations and InequalitiesTimeNote
1Consistent systems, dependent systems, and inconsistent systems of equations.0:49solution exists, infinite number of solutions, no solutions
2Do equations have a solution, no solution or an infinite number of solutions.1:214.1 Solving Systems of Linear Equations in Two Variables
3Systems of equations are consistent, dependent, or inconsistent.1:20
4Systems of equations are consistent, dependent, or inconsistent.1:35
5Solving systems of equations by graphed intercepts.1:01
6Solving systems of equations graphically with intercepts.1:01
7Solving linear systems of equations by substitution1:03
8Solving systems of linear equations by substitution.1:30
9Solving linear systems of equations by addition.1:29
10Solving systems of linear equations by addition.1:42
11Solving linear systems of 2 equations by addition.2:35
12Solving systems of 3 linear equations by addition.3:124.2 Solving Systems of Linear Equations in Three Variables
13Augmented matricies.0:244.4 Solving Systems of Equations Using Matrices
14Row reduction on a augmented matrix. Matrix row operations.1:02
15Writing and reducing an augmented matrix and equivalent equations.3:27
16Write and reducing an augmented matrix and extract equivalent equations.8:20
17Calculating a 2x2 determinate0:18
18Evaluating a 3x3 determinate.1:37
19Solving systems of equations using determinates and Cramer's Rule.1:534.5 Solving Systems of Equations Using Determinants and Cramer's Rule
20Solving systems of linear equations with Cramer's Rule.9:10
21Solving mixture problems, mixing problems, application problem.3:224.3 Systems of Linear Equations: Applications and Problem Solving
22Solving mixture problems. application problem3:53
23Find numbers satisfying given relationships. word problems.2:34
24Find a solution set to a system of inequalities by graphing.2:054.6 Solving Systems of Linear Inequalities
25Find a solution set by graphing a system of absolute value inequalities.2:52IMPORTANT EXAMPLE
 Total Time of videos in this Chapter = 59:35  
 

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Algebra 2: Intermediate Algebra Test Prep Problems
Chapter 5: Polynomials and Polynomial Functions

EExample titles for Ch 5: Polynomials and Polynomial FunctionsTimeNote
1Trinomials, ordering trinomials, and degree of a polynomial?0:51
2Subtract polynomials.0:595.1 Addition and Subtraction of Polynomials
3Multipling polynomials and the distributive property.0:405.2 Multiplication of Polynomials
4Multiply binomials using FOIL method.0:43
5Vertical multiplication of polynomials.1:20
6Divide a polynomial by a monomial.1:145.3 Division of Polynomials and Synthetic Division
7Long division of polynomials.1:44
8Synthetic division of polynomials.1:26
9Remainder Theorem for polynomials.1:22
10Factoring trinomials and the greatest common factor, GCF.1:015.4 Factoring a Monomial from a Polynomial and Factoring by Grouping
11Greatest common factor. Factoring by trial and error.0:52
12Factor a 4 term polynomial by grouping.0:54
13Factor a trinomial using substitution1:215.5 Factoring Trinomials
14Factor by substitution.1:035.6 Special Factoring Formulas
15Factor using substitution.1:03
16Factoring by difference of cubes.1:125.7 A General Review of Factoring
17Product of functions1:315.8 Polynomial Equations
18Simplifying a factored expression, geometry.1:27
19Simplify a factored expression, word problem, geometry.1:37
20Factor given trinomial by trial and error.1:05
21Factor a trinomial.0:54
22Factoring to find x-intercepts.1:35
23Find an equation with given x-intercepts. Reverse of factoring, FOIL.0:55
24Story problem, geometry, triangle, area2:53
25Solve for x-intercepts, story problem, projectile problem.2:05
 Total Time of videos in this Chapter = 31:47  
 

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Algebra 2: Intermediate Algebra Test Prep Problems
Chapter 6: Rational Expressions and Equations

EExample titles for Ch 6: Rational Expressions and EquationsTimeNote
1Domains of rational expressions.1:006.1 The Domains of Rational Functions and Multiplication and Division of Rational Expressions
2Determining the domain, by zeros in the denominator.1:20
3Simplify by factoring.1:18
4Simplify a given expression by factoring.0:44
5Fractions with exponential expressions.1:306.2 Addition and Subtraction of Rational Expressions
6Factoring and multiplying rational expressions.0:59
7Dividing rational expressions.1:34
8Dividing, simplifying and factoring rational expressions.1:19
9Adding rational expressions using the least common denominator.1:146.3 Complex Fractions
10Least common denominator LCD for two expressions.2:39
11Adding rational expressions using the least common denominator LCD.3:25
12Adding rational expressions with the least common denominator LCD.2:35
13Simplify division of rational expressions by factoring.1:35
14Adding functions using the least common denominator LCD.3:146.4 Solving Rational Equations
15Dividing complicated rational expressions.1:51
16Addition, subtraction, and division of rational expressions.1:05
17Simplify a complex fraction.1:23complex imply complex numbers and imaginary numbers
18Complex fractions in rational expressions.0:45
19Subtracting to solve a linear equation.0:42
20Adding to solve quadratic equation by factoring.2:41
21Solving a multivariable formula for a particular variable1:166.5 Rational Equations: Applications and Problem Solving
22Solving proportion problems of directly related values.2:196.6 Proportional Variation
23Solving proportion problems of inversely related proportions2:09
24Solving multiple rate problems for time1:48
25Solving multiple rate problems for distance.1:55
 Total Time of videos in this Chapter = 42:20  
 

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Algebra 2: Intermediate Algebra Test Prep Problems
Chapter 7: Roots, Radicals, and Complex Numbers

EExample titles for Ch 7: Roots, Radicals, and Complex NumbersTimeNote
1Always write the absolute value of terms extracted from an even radical.0:297.1 Roots and Radicals, Any negative direction must be specified outside the even root radical. Ex: -21/2 = -(21/2) = -(square root of 2), not square root of (-2).
2Simplify expressions with rational exponents and negative exponents.1:347.2 Rational Exponents
3Factor exponential polynomial.1:04
4Graph a radical function using a t-chart (sample points).1:17
5Simplify radicals by re-writing internal factors as perfect and non-perfect squares.1:137.3 Simplifying Radicals
6Simplifying products of radical expressions.1:537.4 Adding, Subtracting, and Multiplying Radicals
7Simplifying expressions and removing radicals from the denominator.2:44
8Simplifying rational expressions with radicals in the denominator.0:47
9Simplifying expressions with a radical or binomial in the denominator.2:14
10Simplifying polynomial expressions with radical terms.1:22
11Simplifying radical expressions by rewriting factors as products of perfect and non-perfect cubes.1:36
12Simplifying products of binomials with radical terms.1:337.5 Dividing Radicals
13Simplifying compound radical expressions, a radical within a radical.0:53
14Simplifying rational radical expressions containing binomial expressions with exponents.1:26
15Solving radical equations and checking for extraneous solutions.1:26
16Solving radical equations and testing for extraneous solutions.2:16
17Solving radical equations and extraneous solutions.2:227.6 Solving Radical Equations
18Finding intersection amoung functions and check for extraneous solutions.2:53
19Solving radical equations and a physics formula.1:17
20Applying a radical formula, story problem.0:57
21Use pythagorean theorem to solve right triangle problems, word problem.1:18
22Apply a formula, word problem, calculate a result.1:12
23Simplifying expressions with complex binomials in denominator and complex conjugate.1:197.7 Complex Numbers
24Complex rational expressions with complex binomial in denominator and complex conjugate.2:09
25Simplify by substituting a variable out for a complex binomial constant.1:31
 Total Time of videos in this Chapter = 38:45  
 

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Algebra 2: Intermediate Algebra Test Prep Problems
Chapter 8: Quadratic Functions

EExample titles for Ch 8: Quadratic FunctionsTimeNote
1Solving quadratic equations by completing the square.1:438.1 Solving Quadratic Equations by Completing the Square
2Solve a quadratic equations by completing the square.1:29
3Solving quadratic equations using the Quadratic Formula.1:578.2 Solving Quadratic Equations by the Quadratic Formula
4Solve a quadratic equation using the Quadratic Formula.2:07
5Solving quadratic equations using the Quadratic Formula.2:01
6Solve a quadratic equation with the Quadratic Formula.1:31
7Writing functions with x-intercepts at given predetermined points1:28
8Solve a physics formula for one particular variable using the square root.0:55
9Estimate using the quadratic formula.4:368.3 Quadratic Equations: Applications and Problem Solving
10Multiple rate problems, using the Quadratic Formula. Non-physical solutions.5:45
11Solving polynomials of degree 4 with the Quadratic Formula.3:238.4 Writing Equations in Quadratic Form
12Solving polynomials with the Quadratic Formula.2:44
13Finding x-intercepts & writing polynomials of degree 1 in quadratic form1:068.5 Graphing Quadratic Functions
14Graphing parabolas.1:32
15Finding verticies, intercepts, an axis of symmetry and graphing a parabola.2:30
16Number of real solutions of a quadratic equation with the Quadratic Formula.1:12
17Graphing quadratic equations in standard form, intercepts, verticies3:31
18Find a quadratic equation with given x-intercepts with the Zero factor property1:31
19Solving quadratic inequalities, zero factor property & test intervals3:348.6 Quadratic and Other Inequalities in One Variable
20Solving rational inequalities, using test intervals and the domain.3:28
21Rational inequalities in Interval Notation & Set Builder Notation3:37
22Solve an area problem using the Quadratic Formula and non-physical solutions.3:36
23Quadratic equations, position as a function of time and non-physical solutions.2:38
24Solve quadratic equations, find maximum value, vertex & maximize profit1:33
25Solve a quadratic equation, find maximum value, vertex, & maximize profit3:10
 Total Time of videos in this Chapter = 1:02:37  
 

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Algebra 2: Intermediate Algebra Test Prep Problems
Chapter 9: Exponential and Logarithmic Functions

EExample titles for Ch 9: Exponential and Logarithmic FunctionsTimeNote
1Determine if a set of ordered pairs are one-to-one and find the inverse of a function.0:449.1 Composite and Inverse Functions
2Find a function of a function.1:34
3Find a function of another function.1:35
4Find and graph the inverse function. Find the axis of symmetry between a function and it's inverse.2:57
5Find and graph the inverse of a function, determine domain and axis of symmetry.2:19
6Find a domain of a logarithmic function.0:269.2 Exponential Functions
7Re-write and evaluate a logarithmic expression as an exponential expression. Solve for the variable.1:009.3 Logarithmic Functions
8Graph an exponential function with a t-chart, test chart or sample points.1:17
9Re-write a logarithmic function as an exponential and graph. Determine domain.1:26
10Re-write an exponential equation in logarithmic form.0:229.4 Properties of Logarithms
11Re-write a logarithmic equation in exponential form.0:16
12Re-write a logarithmic equation with a binomial or polynomial into exponential form.0:25
13Solve a logarithmic equation.0:47
14Expand a logarithmic expression based on factors and terms.1:109.5 Common Logarithms
15Combine logarithmic terms using the exponent, product, and quotient rule.1:29
16Re-write and evaluate logarithmic expressions by setting equal to variable.1:01
17Use a calculator to evaluate a logarithmic expressions.0:36
18Solve an exponential equation using the natural logarithm.0:529.6 Exponential and Logarithmic Equations
19Solve logarithmic equations with multiple logarithmic terms.0:51
20Solve a logarithmic equation with multiple logarithmic terms.1:18
21Solve a natural logarithmic equation.0:379.7 Natural Exponential and Natural Logarithmic Functions
22Evaluate logarithmic expressions with a given base.0:38
23Solving exponential equations with the natural logarithms.1:36
24Solving a story problem with exponents.0:58
25Solving story problems with the natural logarithm.2:05
 Total Time of videos in this Chapter = 28:19  
 

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Algebra 2: Intermediate Algebra Test Prep Problems
Chapter 10: Conic Sections

EExample titles for Ch 10: Conic SectionsTimeNote
1Making conic sections.0:1310.1 The Parabola and the Circle
2Finding length of line segments with the Distance Formula.1:17
3Finding midpoints using the Midpoint Formula.0:59
4Graphing parabolas, finding verticies, and intercepts.2:03
5Graphing parabolas, finding verticies, opening, intercepts, and test values.2:52
6Re-write non-standard form equations into standard form parabola.3:14
7Graphing circles with standard form formula, center coordinates & radius1:1410.2 The Ellipse
8Find area of circles given the equation of a circle in standard form.0:42
9Write equations for a circle given center coordinates and radius in standard form.1:00
10Graphing the bottom half of a circle in a radical equation.0:51
11Graphing non-standard form and standard form equations of a circle.2:06
12Obtaining intercepts and graphing an ellipse in non-standard form and standard form.1:32
13Determine if a graph of an ellipse matches given equation of an ellipse.0:49
14Determine if a given equation represents an ellipse. Graphing an ellipse.1:30
15Re-write non-standard form equation of an ellipse into standard form, find center.1:12
16Determine direction and location of the transverse axis for a given hyperbola.0:2410.3 The Hyperbola
17Find the asymptotes of a hyperbola equation in standard form.0:45
18Graph a hyperbola, find the axis of symmetry, intercepts and asymptotes.2:16
19Determine how a hyperbola opens, asymptotes and graph a hyperbola.2:05
20Write equation in standard form, identify conic sections0:53
21Re-write an equation in standard form, determine which conic section it represents.0:33
22Solve for where equations intersect.3:1010.4 Nonlinear Systems of Equations and Their Applications
23Solve for where two equations intersect. Determine if a real solution.2:53
24Solve a word problem to find dimensions of a rectangle given the perimeter.5:49
25Find dimensions of a rectangle given, re-write polynomial of degree 4 into quadratic form7:37
 Total Time of videos in this Chapter = 47:59  
 

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Algebra 2: Intermediate Algebra Test Prep Problems
Chapter 11: Sequences, Series, and the Binomial Theorem

EExample titles for Ch 11: Sequences, Series, and the Binomial TheoremTimeNote
1What is a series? What is a sequence?0:1311.1 Sequences and Series
2What is an Arithmetic Sequence? What is a Geometric Sequence?0:15
3Determine the first 5 terms in a sequence given a formula?1:34
4Determine a partial sum of a sequence given a formula?2:15
5Find the first five terms in a sequence given a formula?1:34
6Evaluate the summation of a sequence given term values of the sequence?0:57
7Find a general equation describing a sequence given the first few terms?1:20
8Determine the kind of sequence. Find equation for a geometric sequence.0:56
9Given equation describing a sequence, determine the first 4 terms.1:41
10Determine if sequence is geometric or arithmetic? Evaluate first four terms.2:1111.2 Arithmetic Sequences and Series
11Evaluate a particular term of a sequence given the equation describing terms.0:53
12Find particular partial sum given sequence formula & 2 non-sequential terms.0:49
13Find the type of a sequence, the general formula, and how many terms are in it.1:55
14Evaluate the value of a term in a geometric sequence given the general formula.1:0311.3 Geometric Sequences and Series
15Find a particular partial sum given an equation for a geometric sequence.1:55
16Given values, find common ratio or constant multiple, for a geometric sequence.1:00
17Find the sum of an infinite geometric sequence.1:27
18Determine if an infinite geometric series and it's sum formula?1:58
19Determine a binomial coefficient? What is the Binomial Formula?1:4811.4 The Binomial Theorem
20Multiply binomials with large exponents using the Binomial Theorem2:47
21Find the Arithmetic Mean. What is the Arithmetic Mean Formula?1:11
22Use an arithmetic sequence to solve a word problem?1:28
23Use arithmetic sequence to solve a word problem with constant repetitive change1:38
24Solve a word problem with a constant percent change using a geometric sequence.1:37
25Use a geometric sequence to estimate growth by both constant multiples and rate.1:28
 Total Time of videos in this Chapter = 35:53  
 

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