# MathematicsWizard ™ # ElementaryAlgebra 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? Jump to Chapter: one, two, three, four, five, six, seven, eight, nine, or ten.

## Algebra 1: ElementaryAlgebra Test PrepChapter 1: RealNumbers

E Example titles for Ch 1: Real Numbers Time 1 Word problem, real numbers 2:25

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## Algebra 1: ElementaryAlgebra Test PrepChapter 2: Solving Linear Equations & Inequalities

E Example titles for Ch 2: Solving Linear Equations & Inequalities Time Note 1 distributive property in multiplication, parentheses 0:43 2.1 Combining Like Terms 2 distributing negative one, negative multiplication 0:59 3 simplify and collect like terms 0:34 2.2 The Addition Property of Equality 4 simplify and collect like terms, commutative property 0:48 5 simplify and combine like terms 0:38 2.3 The Multiplication Property of Equality 6 combine like terms 0:39 7 order of operations 1:15 8 solve for x in a linear equation, long division 2:07 2.4 Solving Linear Equations with a Variable on Only One Side of the Equation 9 solve for x in a linear equation, distributive property 3:19 2.5 Solving Linear Equations with the Variable on Both Sides of the Equation 10 solve for x, linear equation, distributive 1:13 11 solve for x in a linear equation, recognizing when there is no solution, no intersection 0:55 never true, not true for all x 12 solve for x in a linear equation, true for all x, when x = all real numbers, not "no solution", rather an infinite number of solutions 0:59 13 solve for x, in a multivariable linear equation 1:10 14 solve for x, in a multivariable linear equation 1:03 2.6 Formulas 15 solve for x, in linear equation, fractions, recognizing when x = 0 2:25 1) clear parentheses first, 2) clear fractions 16 solve for x, linear equation, fractions 0:34 17 exactly one solution --> conditional solution, no solution --> contradiction no intersection, solution x = all real values --> Identity 0:54 18 solve and graph an inequality 1:30 2.8 Inequalities in One Variable 19 solve and graph an inequality 1:27 20 solve and graph an inequality when no solution 1:02 21 solve for x, always true, x = any real number, infinite number of solutions 1:18 22 proportions, similar triangles 1:14 2.7 Ratios and Proportions 23 principle & interest, I=prt 1:24 24 Circumference of a circle equals 2*Pi*r 1:24 25 rate problem, r*t = d, travel, speed = rate, distance, time 1:48 Total Time of videos in this Chapter = 31:22

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## Algebra 1: ElementaryAlgebra Test PrepChapter 3: Applications of Algebra

E Example titles for Ch 3: Applications of Algebra Time Note 1 story problem, word problem, money 1:07 3.1 Changing Application Problems into Equations 2 story problem 0:43 3.2 Solving Application Problems 3 story problem, interest change, cost, price 0:22 4 story problem, interest change, cost, price 1:09 5 story problem, word problem, problem formulation 1:25 simple translation 6 story problem, word problem, problem formulation 0:36 simple translation 7 story problem, riddle problem, problem formulation 1:20 simple translation 8 story problem, word problem, problem formulation 0:47 simple translation 9 story problem, word problem, problem formulation, percent, ratio, proportion 1:36 simple translation 10 story problem, word problem, problem formulation 2:02 solve 11 consecutive odd numbers, integers 2:27 12 word problem, problem formulation, "the word is" 1:49 3.4 Motion, Money, and Mixture Problems 13 percent solution problem, mixing acid solutions 2:05 14 percent solution problem, mixing salt solutions 2:04 15 mixing candy bags for price, mixing problem 3:09 16 multiple rate problem, r1*t1=d1, r2*t2=d2, When does r1=r2?, or t1=t2?, or when does d1=d2? 1:36 multiple rates problem 17 when does d1 + d2= given constant total distance? 3:13 note: t1=t2 18 word problem, geometry refresher, Isosceles Trapezoid, symmetry problem, story problem. Note: in Euclidean space, every triangle has 180 degrees & every trapezoid has 360 degrees 2:33 3.3 Geometric Problems Total Time of videos in this Chapter = 30:03

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## Algebra 1: ElementaryAlgebra Test PrepChapter 4: Exponents and Polynomials

E Example titles for Ch 4: Exponents and Polynomials Time Note 1 exponent product rule 0:47 4.1 Exponents 2 simplify expression with exponents inside and outside of parentheses 0:50 3 simplify rational expressions involving exponents, exponent quotient rule 0:38 4 rational expressions, with exponents, parentheses and order of operations 1:12 5 simplify expression with negative exponents, parentheses 0:54 4.2 Negative Exponents 6 zero exponents and order of operations 0:39 7 simplify multivariable exponential rational expressions 1:20 8 scientific notation 2:10 4.3 Scientific Notation 9 using scientific notation to simplify expressions 1:34 10 polynomials include singular nomials AKA monomial, but does not include 4x-1 1:24 11 polynomials, binomials like 4x + 5 1:02 12 polynomials dont include negative exponents of the highest degree (convention) 0:25 13 descending order, degree of each term of a polynomial 0:52 14 simplify sum of polynomials 1:00 4.4 Addition and Subtraction of Polynomials 15 subtracting polynomials 0:53 16 subtracting polynomials 0:46 17 multiply a monomial times a binomial polynomial 0:29 4.5 Multiplication of Polynomials 18 FOIL, multiplying polynomials 0:57 19 FOIL, multiplying polynomials, binomial times a binomial 0:54 20 multiply a binomial times a trinomial polynomial 1:39 21 divide a polynomial 0:53 4.6 Division of Polynomials 22 divide a trinomial polynomial by a monomial 1:10 23 polynomial division, divide a trinomial by a binomial 1:57 24 long division of polynomials 2:05 25 compare half-lifes, dividing monomials with exponents 2:24 Total Time of videos in this Chapter = 28:54

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## Algebra 1: ElementaryAlgebra Test PrepChapter 5: Factoring

E Example titles for Ch 5: Factoring Time Note 1 What's the difference between: Greatest common factor (GCF), Lowest common denominator (LCD), and Lowest Common Multiple (LCM) 1:55 2 Identify the GCF given various expressions 1:26 3 factor binomial like 5x2y3 - 15x5y2 1:55 5.1 Factoring a Monomial from a Polynomial 4 factoring trinomials 1:25 5 factor by grouping 1:29 5.2 Factoring by Grouping 6 factor by grouping, good example 1:51 7 factor a trinomial using FOIL into a pair of binomials 1:57 5.3 Factoring Trinomials of the Form ax2 + bx + c, when a = 1 8 factor a trinomial using FOIL into binomial factors 3:30 AKA "trial and error" 9 factor trinomial first by common factor then FOIL 0:58 5.4 Factoring Trinomials of the Form ax2 + bx + c, a ∋ 1 10 factor trinomial first by common factor then FOIL 1:38 11 factor multivariable trinomial by FOIL 2:28 12 factor a Difference of Squares by "Similar Results" 1:21 5.5 Special Factoring Formulas and a General Review of Factoring 13 factor a Difference of Cubes by "Similar Results" 1:21 remember to plug back in & test 14 solve an equation by factoring to find zeros 1:07 15 solve an equation by factoring to find zeros 0:37 16 solve by factoring a Difference of Cubes to find zeros 1:11 17 solve by factoring trinomial with FOIL to find zeros 1:00 5.6 Solving Quadratic Equations Using Factoring 18 solve trinomial by factoring with FOIL to find zeros 0:52 19 solve by setting equal to zero and factoring with FOIL to find zeros 1:24 remember to test results 20 solving right triangles with Pythagorean Theorem, Difference of Squares, and discarding non-physical solutions 2:09 5.7 Applications of Quadratic Equations 21 solving right triangle with Pythagorean Theorem, complicated example, discarding non-physical results, and making sure you answer the actual question 4:20 22 mystery integers problem, word problem, story problem, solution by factoring, finding zeros 4:39 23 mystery integers problem, word problem, story problem, solution by factoring, finding zeros 1:25 24 word problem, story problem, problem formulation, solution by factoring, finding zeros, discarding non-physical solutions 1:56 25 given formula, apply correctly to solve, discarding non-physical solutions 0:57 Total Time of videos in this Chapter = 44:51

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## Algebra 1: ElementaryAlgebra Test PrepChapter 6: Rational Expressions and Equations

E Example titles for Ch 6: Rational Expressions and Equations Time Note 1 simplify rational expressions, divide out common factors 0:48 6.1 Simplifying Rational Expressions 2 simplify rational expressions, divide out common factors 0:47 3 simplify rational expressions with exponents 1:36 4 simplify rational unfactored expressions, factor, divide out common factors 1:22 5 [unavailable] 0:00 6 multiplication of rational expressions, factor, divide out common factors 1:34 6.2 Multiplication and Division of Rational Expressions 7 Division of rational expressions, factor, divide out common factors 1:33 8 Division of rational expressions, factor, divide out common factors 1:26 9 Division of rational expressions, factor, divide out common factors 1:53 10 adding rational expressions, Least Common Denominator 1:04 6.3 Addition and Subtraction of Rational Expressions with a Common Denominator and Finding the Least Common Denominator 11 subtract rational expressions, Least Common Denominator 1:09 6.4 Addition and Subtraction of Rational Expressions 12 subtract rational expressions, Least Common Denominator 1:32 13 subtract rational expressions, Least Common Denominator 2:01 14 subtract rational expressions, Least Common Denominator 4:22 15 simplify complicated fraction, eliminate simpler fractions from numerator and denominator 1:34 6.5 Complex Fractions 16 simplify complicated fraction, eliminate simpler fractions from numerator and denominator 1:30 17 simplify complicated fraction, eliminate simpler fractions from numerator and denominator 1:19 18 [unavailable] 0:00 19 [unavailable] 0:00 20 solve 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 zeros 3:36 6.6 Solving Rational Equations 21 story problem, word problem, r × t = d, translate problem, formulate problem, rate problem, When does r1=r2?, or t1=t2?, or when does d1 = d2? 2:39 6.7 Rational Equations: Applications and Problem Solving; farming 22 mystery number problem, word problem, story problem, translate problem, formulate problem, solve 2:36 6.8 Variation 23 story problem, word problem, triangle problem, translate problem, formulate, solve, discard non-physical solutions 2:44 triangles 24 story problem, word problem, r × t = d, translate problem, problem formulation, rate problem 4:05 exorcise 25 story problem, word problem, formula, wavelength 2:18 Total Time of videos in this Chapter = 43:28

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## Algebra 1: ElementaryAlgebra Test PrepChapter 7: Graphing Linear Equations

E Example titles for Ch 7: Graphing Linear Equations Time Note 1 What is a Graph? 0:17 7.1 The Cartesian Coordinate System and Linear Equations in Two Variables 2 Cartesian coordinate system 0:32 3 standard form of a linear equation (of a line in 2D), point-slope form of equation of a line (2D), point-slope formula 0:38 7.2 Graphing Linear Equations 4 determine what point satisfies an equation of a line, i.e. test each of the possible given solutions 2:27 5 find slope of a line intersecting two given points 0:58 7.3 Slope of a Line 6 find slope and y-intercept of an equation of a line, given standard form 1:22 7.4 Slope-Intercept and Point-Slope Forms of a Linear Equation 7 given slope, and y-intercept, determine the equation of a line through that point with that slope 0:30 8 Graph the line given by the equation x = - 4; What values of y allow for x to equal -4 ? 0:21 7.5 Graphing Linear Inequalities 9 Graph the line given by the equation y = 2 0:21 10 Graph y=3x-2, by freehand diagram 1:56 11 solve for y given a standard form equation of a line (2D), t-chart, test value chart 2:35 12 Graph the line 3x+5y=15, using x & y-intercepts, test chart 1:49 13 given a point and a slope, find an equation 0:55 Using the "point-slope formula" 14 find equation of line passing thru 2 given points, find slope, find equation 2:35 15 given 2 equations of lines, determine if parallel or perpendicular? 1:00 16 Graph line given slope and intercepts 1:14 17 Graph line using slope intercept form 1:54 18 Define what is a function 0:12 7.6 Functions 19 Determine if a set of ordered pairs is a function. Identify the Domain and Range. 0:53 rare, but important 20 Given a graph, determine it represents a function using vertical line test 1:05 21 Evaluate a function for a particular given value. 1:30 22 Given a function, graph using test values 2:05 23 Graph a given linear inequality 2:11 24 Graph a given linear inequality 2:07 25 Graph given formula of income as function of sales 2:48 Total Time of videos in this Chapter = 34:15

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## Algebra 1: ElementaryAlgebra Test PrepChapter 8: Systems of Linear Equations

E Example titles for Ch 8: Systems of Linear Equations Time Note 1 Determine if a given point satisfies two given equations of lines 3:25 2 two lines which eventually intersect off page, consistent system, one solution, not parallel 0:12 8.1 Solving Systems of Equations Graphically 3 parallel lines, never intersect, no solution, inconsistent system 0:13 4 two lines on top of one another, dependent system, infinite number of solutions 0:14 5 solve two equations in two unknowns, determine how many solutions exist, recognizing parallel lines 1:23 6 solve two equations for y, determine how many solutions exist, recognizing non-parallel lines 1:46 7 solve two equations for y, determine how many solutions exist 2:18 8 What is Inconsistent? Any false statement. What is Dependent? Any statement that is always true. 0:43 9 Solve a system of two equations graphically. Graph using x & y intercepts. 2:44 10 Solve a system of two linear equations graphically. Graph using x & y intercepts. 2:56 11 Solving systems of equations graphically, finding intercepts, & finding if solution exist. 2:36 12 Solving systems of equations by substitution. 1:08 8.2 Solving Systems of Equations by Substitution 13 Solving systems of linear equations by substitution. 2:27 14 Solving a system of linear equations by substitution. 2:11 15 Solving systems of by the addition method. 1:47 8.3 Solving Systems of Equations by the Addition Method 16 Solving systems of linear equations by the addition method. 1:44 17 Solving a system of equations by the addition method. 1:54 18 Solving systems of equations by the addition method. Use the method of your choice. 1:44 graphing, addition, or substitution method? 19 Solving systems of linear equations by the addition method. Use the method of your choice. 1:54 20 Solving a system of linear equations by the addition method. Use the method of your choice. 2:50 21 Rate Problem, Story problem, word problem, translating a word problem, r x t = d, trucks 3:53 8.4 Systems of Equations: Applications and Problem Solving 22 Rate Problem, Story problem, word problem, translating a word problem, r x t = d, candy, prices 4:48 23 Rate Problem, Story problem, word problem, translating a word problem, r x t = d, boats 3:19 24 Graph a system of linear inequalities, shading graph, solution of a system inequalities 1:40 8.5 Solving Systems of Linear Inequalities 25 Graph a system of linear inequalities, shading graph, solution of a system of inequalities 1:26 Total Time of videos in this Chapter = 51:15

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## Algebra 1: ElementaryAlgebra Test PrepChapter 9: Roots and Radicals

E Example titles for Ch 9: Roots and Radicals Time Note 1 rewrite radical expression in exponential form 0:23 9.1 Evaluating Square Roots 2 rewrite an exponential expression in radical form 0:25 3 simplify & rewrite radical expressions 0:16 9.2 Simplifying Square Roots 4 simplify, re-write & equivalent radical expressions 0:39 5 simplify & rewrite equivalent radical expressions 0:53 6 rewrite equivalent radical expressions 1:29 7 multiply and simplify radical expressions 1:20 9.3 Adding, Subtracting, and Multiplying Square Roots 8 multiply and simplify radical expressions 1:08 9 multiply and simplify radical expressions 0:32 10 divide and simplify radical expressions 0:51 9.4 Dividing Square Roots 11 simplify a radical expression with a radical in the denominator 0:47 12 simplify a radical expression with a radical in the denominator 1:06 13 divide and simplify a radical expression with a radical in the denominator 2:22 14 multiply and divide, and then simplify expression with radicals in the denominator 2:00 15 multiply and divide, and then simplify expression with radicals in the denominator 1:18 16 add and subtract radical expressions 1:25 17 add and subtract radical expressions 0:28 18 solve an equation for a variable under a radical, and check for extraneous solutions 1:28 9.5 Solving Radical Equations 19 solve an equation for a variable under a radical, and check for extraneous solutions 3:25 20 solve a right triangle geometry problem, solve for x using Pythagorean Theorem 1:20 9.6 Radicals: Applications and Problem Solving 21 Given coordinates of two points, find the distance in Euclidean space between the two points. 1:33 distance formula 22 evaluate an exponential expression 0:40 23 rewrite the product of radical expressions in exponential form and simplify 0:41 9.7 Higher Roots and Rational Exponents 24 Given area of a square find the length of a side 0:35 area of a square formula 25 story problem, word problem, translate the problem, given a formula and some data, solve for a missing variable in a radical expression 1:11 Total Time of videos in this Chapter = 28:15

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## Algebra 1: ElementaryAlgebra Test PrepChapter 10: QuadraticEquations

E Example titles for Ch 10: Quadratic Equations Time Note 1 Solve Quadratic Equation via radical method 1:16 10.1 The Square Root Property 2 solve quadratic equation using the square root property 1:02 compare your solution with the factoring method solution 3 solve quadratic equation by completing the square and using the square root property 2:47 10.2 Solving Quadratic Equations by Completing the Square 4 solve quadratic equation by completing the square and using the square root property 1:41 complete the square 5 solve quadratic equation using the quadratic formula and simplify 2:32 10.3 Solving Quadratic Equations by the Quadratic Formula 6 solve quadratic equation using the quadratic formula and simplify 3:05 7 solve quadratic equation with the method of your choice 0:54 completing the square and the root property, quadratic equation, or factoring? 8 State the Quadratic Formula 0:30 9 give an example of a perfect square trinomial 1:05 10 determine the number of real number solutions to the given quadratic using the discriminate 1:31 Recall: b2-4ac, from the quadratic formula. >0 exists 2 real, =0 only exists 1 real, <0 exists 2 imaginary solutions 11 find the number of real solutions of a given quadratic equation using the discriminate 1:04 12 find the equation for the axis of symmetry for a given quadratic equation (1D example) 0:44 x = -b/2a, see quadratic formula 13 find the equation for the axis of symmetry for a given quadratic equation (1D example) 0:45 14 determine if this graph opens upward or downward 0:14 coefficient of the squared term 15 determine if this graph opens upward or downward 0:15 coefficient of the squared term 16 vertex of a parabola 0:12 17 find coordinates of the vertex of a given parabola, x = -b/2a and y = (4ac - b2)/4a 1:49 see quadratic formula: x = xvrtx ± (yvrtx)1/2 18 find vertex of a parabola using formula 1:47 19 graph vertex of a parabola using formula 4:25 10.4 Graphing Quadratic Equations 20 graph parabola, recall vertex formulas, test points 4:28 21 graph parabola, recall vertex formulas, test points 4:12 22 story problem, word problem, find the length and width of an area, given the area and some relation 4:07 23 story problem, word problem, find the integers problem 2:00 24 story problem, word problem, find the numbers that satisfy a given relation 1:59 25 solve quadratic equation using quadratic formula 2:50 10.5 Complex Numbers Total Time of videos in this Chapter = 47:14

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