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Elementary Algebra Test Prep

Chapter Test Prep problems, by Angel & Runde

Introduction and Table of Contents

This video series is entitled, "Elementary Algebra Test Prep," which provides chapter Test Prep problems, by Angel & Runde. The series presents 243 individual examples organized over 10 chapters and span the subject of Algebra 1. These videos have a total playtime duration of 6 hrs 01 min 35 sec.

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. 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 1: Elementary Algebra Test Prep
Chapter 1: Real Numbers

EExample titles for Ch 1: Real NumbersTimeNote
1Word problem, real numbers2:251.2 Problem Solving
2word problem1:411.3 Fractions
3word problem, median value, bar graph1:25
4Natural numbers, number line, whole numbers, integers2:051.4 The Real Number System
5real numbers, number line, greater value, negative numbers0:261.5 Inequalities
6absolute values, greater value, greater magnitude0:30
7number line, addition of negative numbers0:261.6 Addition of Real Numbers
8subtraction of negative numbers0:191.7 Subtraction of Real Numbers
9subtracting larger numbers from smaller numbers0:15
10order of operations0:38
11multiplication with negative numbers0:321.8 Multiplication and Division of Real Numbers
12fractions with negative signs0:48
13multiply & divide rational numbers or fractions with negative signs0:41
14adding and subtracting fractions1:00
15order of operations, negative numbers, division, parentheses0:461.9 Exponents, Parentheses, and the Order of Operations
16exponents, multiplication of fractions with negative signs0:47
17order of operations, exponents, parentheses1:43
18order of operations, negative signs on numbers with exponents1:08
19substitution and evaluating expressions0:42
20substitution and evaluating expressions0:49
21multiple variable substitution and evaluating expressions0:43
22multiple variable substitution and evaluating expressions with exponents0:55
23commutative property0:181.10 Properties of the Real Number System
24distributive property0:27
25associative property, can affect of order of operations0:29
 Total Time of videos in this Chapter = 21:58  
 

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Algebra 1: Elementary Algebra Test Prep
Chapter 2: Solving Linear Equations & Inequalities

EExample titles for Ch 2: Solving Linear Equations & InequalitiesTimeNote
1distributive property in multiplication, parentheses0:432.1 Combining Like Terms
2distributing negative one, negative multiplication0:59
3simplify and collect like terms0:342.2 The Addition Property of Equality
4simplify and collect like terms, commutative property0:48
5simplify and combine like terms0:382.3 The Multiplication Property of Equality
6combine like terms0:39
7order of operations1:15
8solve for x in a linear equation, long division2:072.4 Solving Linear Equations with a Variable on Only One Side of the Equation
9solve for x in a linear equation, distributive property3:192.5 Solving Linear Equations with the Variable on Both Sides of the Equation
10solve for x, linear equation, distributive1:13
11solve for x in a linear equation, recognizing when there is no solution, no intersection0:55never true, not true for all x
12solve for x in a linear equation, true for all x, when x = all real numbers, not "no solution", rather an infinite number of solutions0:59
13solve for x, in a multivariable linear equation1:10
14solve for x, in a multivariable linear equation1:032.6 Formulas
15solve for x, in linear equation, fractions, recognizing when x = 02:25 1) clear parentheses first, 2) clear fractions
16solve for x, linear equation, fractions0:34
17exactly one solution --> conditional solution, no solution --> contradiction no intersection, solution x = all real values --> Identity0:54
18solve and graph an inequality1:302.8 Inequalities in One Variable
19solve and graph an inequality1:27
20solve and graph an inequality when no solution1:02
21solve for x, always true, x = any real number, infinite number of solutions1:18
22proportions, similar triangles1:142.7 Ratios and Proportions
23principle & interest, I=prt1:24
24Circumference of a circle equals 2*Pi*r1:24
25rate problem, r*t = d, travel, speed = rate, distance, time1:48
 Total Time of videos in this Chapter = 31:22  
 

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Algebra 1: Elementary Algebra Test Prep
Chapter 3: Applications of Algebra

EExample titles for Ch 3: Applications of AlgebraTimeNote
1story problem, word problem, money1:073.1 Changing Application Problems into Equations
2story problem0:433.2 Solving Application Problems
3story problem, interest change, cost, price0:22
4story problem, interest change, cost, price1:09
5story problem, word problem, problem formulation1:25 simple translation
6story problem, word problem, problem formulation0:36simple translation
7story problem, riddle problem, problem formulation1:20simple translation
8story problem, word problem, problem formulation0:47simple translation
9story problem, word problem, problem formulation, percent, ratio, proportion1:36simple translation
10story problem, word problem, problem formulation2:02solve
11consecutive odd numbers, integers2:27
12word problem, problem formulation, "the word is"1:49 3.4 Motion, Money, and Mixture Problems
13percent solution problem, mixing acid solutions2:05
14percent solution problem, mixing salt solutions2:04
15mixing candy bags for price, mixing problem3:09
16multiple rate problem, r1*t1=d1, r2*t2=d2, When does r1=r2?, or t1=t2?, or when does d1=d2?1:36multiple rates problem
17when does d1 + d2= given constant total distance?3:13note: t1=t2
18word problem, geometry refresher, Isosceles Trapezoid, symmetry problem, story problem. Note: in Euclidean space, every triangle has 180 degrees & every trapezoid has 360 degrees2:333.3 Geometric Problems
 Total Time of videos in this Chapter = 30:03  
 

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Algebra 1: Elementary Algebra Test Prep
Chapter 4: Exponents and Polynomials

EExample titles for Ch 4: Exponents and PolynomialsTimeNote
1exponent product rule0:474.1 Exponents
2simplify expression with exponents inside and outside of parentheses0:50
3simplify rational expressions involving exponents, exponent quotient rule0:38
4rational expressions, with exponents, parentheses and order of operations1:12
5simplify expression with negative exponents, parentheses0:544.2 Negative Exponents
6zero exponents and order of operations0:39
7simplify multivariable exponential rational expressions1:20
8scientific notation2:104.3 Scientific Notation
9using scientific notation to simplify expressions1:34
10polynomials include singular nomials AKA monomial, but does not include 4x-11:24
11polynomials, binomials like 4x + 51:02
12polynomials dont include negative exponents of the highest degree (convention)0:25
13descending order, degree of each term of a polynomial0:52
14simplify sum of polynomials1:004.4 Addition and Subtraction of Polynomials
15subtracting polynomials0:53
16subtracting polynomials0:46
17multiply a monomial times a binomial polynomial0:294.5 Multiplication of Polynomials
18FOIL, multiplying polynomials0:57
19FOIL, multiplying polynomials, binomial times a binomial0:54
20multiply a binomial times a trinomial polynomial1:39
21divide a polynomial0:534.6 Division of Polynomials
22divide a trinomial polynomial by a monomial1:10
23polynomial division, divide a trinomial by a binomial1:57
24long division of polynomials2:05
25compare half-lifes, dividing monomials with exponents2:24
 Total Time of videos in this Chapter = 28:54  
 

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Algebra 1: Elementary Algebra Test Prep
Chapter 5: Factoring

EExample titles for Ch 5: FactoringTimeNote
1What's the difference between: Greatest common factor (GCF), Lowest common denominator (LCD), and Lowest Common Multiple (LCM)1:55
2Identify the GCF given various expressions1:26
3factor binomial like 5x2y3 - 15x5y21:555.1 Factoring a Monomial from a Polynomial
4factoring trinomials1:25
5factor by grouping1:295.2 Factoring by Grouping
6factor by grouping, good example1:51
7factor a trinomial using FOIL into a pair of binomials1:575.3 Factoring Trinomials of the Form ax2 + bx + c, when a = 1
8factor a trinomial using FOIL into binomial factors3:30 AKA "trial and error"
9factor trinomial first by common factor then FOIL0:585.4 Factoring Trinomials of the Form ax2 + bx + c, a ∋ 1
10factor trinomial first by common factor then FOIL1:38
11factor multivariable trinomial by FOIL2:28
12factor a Difference of Squares by "Similar Results"1:215.5 Special Factoring Formulas and a General Review of Factoring
13factor a Difference of Cubes by "Similar Results"1:21 remember to plug back in & test
14solve an equation by factoring to find zeros1:07
15solve an equation by factoring to find zeros0:37
16solve by factoring a Difference of Cubes to find zeros1:11
17solve by factoring trinomial with FOIL to find zeros1:005.6 Solving Quadratic Equations Using Factoring
18solve trinomial by factoring with FOIL to find zeros0:52
19solve by setting equal to zero and factoring with FOIL to find zeros1:24remember to test results
20solving right triangles with Pythagorean Theorem, Difference of Squares, and discarding non-physical solutions2:095.7 Applications of Quadratic Equations
21solving right triangle with Pythagorean Theorem, complicated example, discarding non-physical results, and making sure you answer the actual question4:20
22mystery integers problem, word problem, story problem, solution by factoring, finding zeros4:39
23mystery integers problem, word problem, story problem, solution by factoring, finding zeros1:25
24word problem, story problem, problem formulation, solution by factoring, finding zeros, discarding non-physical solutions1:56
25given formula, apply correctly to solve, discarding non-physical solutions0:57
 Total Time of videos in this Chapter = 44:51  
 

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Algebra 1: Elementary Algebra Test Prep
Chapter 6: Rational Expressions and Equations

EExample titles for Ch 6: Rational Expressions and EquationsTimeNote
1simplify rational expressions, divide out common factors0:486.1 Simplifying Rational Expressions
2simplify rational expressions, divide out common factors0:47
3simplify rational expressions with exponents1:36
4simplify rational unfactored expressions, factor, divide out common factors1:22
5[unavailable]0:00
6multiplication of rational expressions, factor, divide out common factors1:346.2 Multiplication and Division of Rational Expressions
7Division of rational expressions, factor, divide out common factors1:33
8Division of rational expressions, factor, divide out common factors1:26
9Division of rational expressions, factor, divide out common factors1:53
10adding rational expressions, Least Common Denominator1:046.3 Addition and Subtraction of Rational Expressions with a Common Denominator and Finding the Least Common Denominator
11subtract rational expressions, Least Common Denominator1:096.4 Addition and Subtraction of Rational Expressions
12subtract rational expressions, Least Common Denominator1:32
13subtract rational expressions, Least Common Denominator2:01
14subtract rational expressions, Least Common Denominator4:22
15simplify complicated fraction, eliminate simpler fractions from numerator and denominator1:346.5 Complex Fractions
16simplify complicated fraction, eliminate simpler fractions from numerator and denominator1:30
17simplify complicated fraction, eliminate simpler fractions from numerator and denominator1:19
18[unavailable]0:00
19[unavailable]0:00
20solve equation with rational expressions, Least Common Denominator, factor, common factor to add fractions, divide out common factors, simplify, convert to linear equation, set to zero, factor, find zeros3:366.6 Solving Rational Equations
21story problem, word problem, r × t = d, translate problem, formulate problem, rate problem, When does r1=r2?, or t1=t2?, or when does d1 = d2?2:396.7 Rational Equations: Applications and Problem Solving; farming
22mystery number problem, word problem, story problem, translate problem, formulate problem, solve2:366.8 Variation
23story problem, word problem, triangle problem, translate problem, formulate, solve, discard non-physical solutions2:44triangles
24story problem, word problem, r × t = d, translate problem, problem formulation, rate problem4:05exorcise
25story problem, word problem, formula, wavelength2:18
 Total Time of videos in this Chapter = 43:28  
 

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Algebra 1: Elementary Algebra Test Prep
Chapter 7: Graphing Linear Equations

EExample titles for Ch 7: Graphing Linear EquationsTimeNote
1What is a Graph?0:177.1 The Cartesian Coordinate System and Linear Equations in Two Variables
2Cartesian coordinate system0:32
3standard form of a linear equation (of a line in 2D), point-slope form of equation of a line (2D), point-slope formula0:387.2 Graphing Linear Equations
4determine what point satisfies an equation of a line, i.e. test each of the possible given solutions2:27
5find slope of a line intersecting two given points0:587.3 Slope of a Line
6find slope and y-intercept of an equation of a line, given standard form1:227.4 Slope-Intercept and Point-Slope Forms of a Linear Equation
7given slope, and y-intercept, determine the equation of a line through that point with that slope0:30
8Graph the line given by the equation x = - 4; What values of y allow for x to equal -4 ?0:217.5 Graphing Linear Inequalities
9Graph the line given by the equation y = 20:21
10Graph y=3x-2, by freehand diagram1:56
11solve for y given a standard form equation of a line (2D), t-chart, test value chart2:35
12Graph the line 3x+5y=15, using x & y-intercepts, test chart1:49
13given a point and a slope, find an equation0:55Using the "point-slope formula"
14find equation of line passing thru 2 given points, find slope, find equation2:35
15given 2 equations of lines, determine if parallel or perpendicular?1:00
16Graph line given slope and intercepts1:14
17Graph line using slope intercept form1:54
18Define what is a function0:127.6 Functions
19Determine if a set of ordered pairs is a function. Identify the Domain and Range.0:53rare, but important
20Given a graph, determine it represents a function using vertical line test1:05
21Evaluate a function for a particular given value.1:30
22Given a function, graph using test values2:05
23Graph a given linear inequality2:11
24Graph a given linear inequality2:07
25Graph given formula of income as function of sales2:48
 Total Time of videos in this Chapter = 34:15  
 

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Algebra 1: Elementary Algebra Test Prep
Chapter 8: Systems of Linear Equations

EExample titles for Ch 8: Systems of Linear EquationsTimeNote
1Determine if a given point satisfies two given equations of lines3:25
2two lines which eventually intersect off page, consistent system, one solution, not parallel0:128.1 Solving Systems of Equations Graphically
3parallel lines, never intersect, no solution, inconsistent system0:13
4two lines on top of one another, dependent system, infinite number of solutions0:14
5solve two equations in two unknowns, determine how many solutions exist, recognizing parallel lines1:23
6solve two equations for y, determine how many solutions exist, recognizing non-parallel lines1:46
7solve two equations for y, determine how many solutions exist2:18
8What is Inconsistent? Any false statement. What is Dependent? Any statement that is always true.0:43
9Solve a system of two equations graphically. Graph using x & y intercepts.2:44
10Solve a system of two linear equations graphically. Graph using x & y intercepts.2:56
11Solving systems of equations graphically, finding intercepts, & finding if solution exist.2:36
12Solving systems of equations by substitution.1:088.2 Solving Systems of Equations by Substitution
13Solving systems of linear equations by substitution.2:27
14Solving a system of linear equations by substitution.2:11
15Solving systems of by the addition method.1:478.3 Solving Systems of Equations by the Addition Method
16Solving systems of linear equations by the addition method.1:44
17Solving a system of equations by the addition method.1:54
18Solving systems of equations by the addition method. Use the method of your choice.1:44graphing, addition, or substitution method?
19Solving systems of linear equations by the addition method. Use the method of your choice.1:54
20Solving a system of linear equations by the addition method. Use the method of your choice.2:50
21Rate Problem, Story problem, word problem, translating a word problem, r x t = d, trucks3:538.4 Systems of Equations: Applications and Problem Solving
22Rate Problem, Story problem, word problem, translating a word problem, r x t = d, candy, prices4:48
23Rate Problem, Story problem, word problem, translating a word problem, r x t = d, boats3:19
24Graph a system of linear inequalities, shading graph, solution of a system inequalities1:408.5 Solving Systems of Linear Inequalities
25Graph a system of linear inequalities, shading graph, solution of a system of inequalities1:26
 Total Time of videos in this Chapter = 51:15  
 

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Algebra 1: Elementary Algebra Test Prep
Chapter 9: Roots and Radicals

EExample titles for Ch 9: Roots and RadicalsTimeNote
1rewrite radical expression in exponential form0:239.1 Evaluating Square Roots
2rewrite an exponential expression in radical form0:25
3simplify & rewrite radical expressions0:169.2 Simplifying Square Roots
4simplify, re-write & equivalent radical expressions0:39
5simplify & rewrite equivalent radical expressions0:53
6rewrite equivalent radical expressions1:29
7multiply and simplify radical expressions1:209.3 Adding, Subtracting, and Multiplying Square Roots
8multiply and simplify radical expressions1:08
9multiply and simplify radical expressions0:32
10divide and simplify radical expressions0:519.4 Dividing Square Roots
11simplify a radical expression with a radical in the denominator0:47
12simplify a radical expression with a radical in the denominator1:06
13divide and simplify a radical expression with a radical in the denominator2:22
14multiply and divide, and then simplify expression with radicals in the denominator2:00
15multiply and divide, and then simplify expression with radicals in the denominator1:18
16add and subtract radical expressions1:25
17add and subtract radical expressions0:28
18solve an equation for a variable under a radical, and check for extraneous solutions1:289.5 Solving Radical Equations
19solve an equation for a variable under a radical, and check for extraneous solutions3:25
20solve a right triangle geometry problem, solve for x using Pythagorean Theorem1:209.6 Radicals: Applications and Problem Solving
21Given coordinates of two points, find the distance in Euclidean space between the two points.1:33distance formula
22evaluate an exponential expression0:40
23rewrite the product of radical expressions in exponential form and simplify0:419.7 Higher Roots and Rational Exponents
24Given area of a square find the length of a side0:35area of a square formula
25story problem, word problem, translate the problem, given a formula and some data, solve for a missing variable in a radical expression1:11
 Total Time of videos in this Chapter = 28:15  
 

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Algebra 1: Elementary Algebra Test Prep
Chapter 10: Quadratic Equations

EExample titles for Ch 10: Quadratic EquationsTimeNote
1Solve Quadratic Equation via radical method1:1610.1 The Square Root Property
2solve quadratic equation using the square root property1:02compare your solution with the factoring method solution
3solve quadratic equation by completing the square and using the square root property2:4710.2 Solving Quadratic Equations by Completing the Square
4solve quadratic equation by completing the square and using the square root property1:41complete the square
5solve quadratic equation using the quadratic formula and simplify2:3210.3 Solving Quadratic Equations by the Quadratic Formula
6solve quadratic equation using the quadratic formula and simplify3:05
7solve quadratic equation with the method of your choice0:54completing the square and the root property, quadratic equation, or factoring?
8State the Quadratic Formula0:30
9give an example of a perfect square trinomial1:05
10determine the number of real number solutions to the given quadratic using the discriminate1:31Recall: b2-4ac, from the quadratic formula. >0 exists 2 real, =0 only exists 1 real, <0 exists 2 imaginary solutions
11find the number of real solutions of a given quadratic equation using the discriminate1:04
12find the equation for the axis of symmetry for a given quadratic equation (1D example)0:44x = -b/2a, see quadratic formula
13find the equation for the axis of symmetry for a given quadratic equation (1D example)0:45
14determine if this graph opens upward or downward0:14coefficient of the squared term
15determine if this graph opens upward or downward0:15coefficient of the squared term
16vertex of a parabola0:12
17find coordinates of the vertex of a given parabola, x = -b/2a and y = (4ac - b2)/4a1:49see quadratic formula: x = xvrtx ± (yvrtx)1/2
18find vertex of a parabola using formula1:47
19graph vertex of a parabola using formula4:2510.4 Graphing Quadratic Equations
20graph parabola, recall vertex formulas, test points4:28
21graph parabola, recall vertex formulas, test points4:12
22story problem, word problem, find the length and width of an area, given the area and some relation4:07
23story problem, word problem, find the integers problem2:00
24story problem, word problem, find the numbers that satisfy a given relation1:59
25solve quadratic equation using quadratic formula2:5010.5 Complex Numbers
 Total Time of videos in this Chapter = 47:14  
 

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