Mastering Algebra 2

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Teacher: Terri
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Unit 1 - Fundamentals of Algebra

0 Course Introduction 04:01

Basic Information about this course

1 Unit 1-1 Solving One Variable Equations 14:40

In this lesson, we will review the process of solving multi-step, one-variable equations including equations with variables on both sides, equations with decimals, and equations with fractions. We will go over how to remove decimals and fractions from equations. This should all be a review of topics learned in Pre-Algebra and Algebra I.

2 Unit 1-1 Review 06:38

Review of problems from section 1-1

3 Unit 1-2 Solving Inequalities 10:55

In this lesson, we will review how to solve multi-step one-variable inequalities and graph their solutions on a number line. We will also learn to identify inequalities that have no solution and ones where all real numbers are solutions. This again should be a review of material learned in Algebra I.

4 Unit 1-2 Review 06:34

Review of problems from section 1-2

5 Unit 1-3 Solving Absolute Value Equations 13:57

In this lesson, we will learn how to solve absolute value equations. We will identify when these equations have no solutions. We will also identify extraneous solutions.

6 Unit 1-3 Review 07:30

Review of problems from section 1-3

7 Unit 1-4 Solving Compound Inequalities & Absolute Value Inequalities 18:55

In this lesson, we will solve "and" & "or" inequalities & graph them on a number line. We will identify special cases that overlap, have no solution, and have all real numbers as solutions. We will then solve absolute value inequalities. We will then identify absolute value inequalities that have no solution and those with all real numbers as solutions.

8 Unit 1-4 Review 06:41

Review of problems from section 1-4

9 Unit 1-5 Problem Solving 25:46

In this lesson, we will review the steps to problem-solving and the language of mathematics. We will then use that information to solve word problems involving numbers, geometry, and consecutive integers.

10 Unit 1-5 Review 06:23

Review of problems from section 1-5

11 Unit 1-6 Relations & Functions 17:08

In this lesson, we will learn how to determine if a given relation is a function and give the domain and range of that relation. We will do this when the relation is given as a set of ordered pairs, a mapping diagram, and a graph. We will also evaluate functions for a given value. This should all be a review from previous courses.

12 Unit 1-6 Review 04:41

Review of problems from section 1-6

13 Unit 1-7 Function Operations 17:57

In this lesson, we will add, subtract, multiply, and divide functions. In doing so, we will also review how to distribute a binomial through a trinomial. We will also learn how to compose functions. This should also be a review of items learned in previous courses.

14 Unit 1-7 Review 05:57

Review of problems from section 1-7

Unit 2 - Systems of Equations

15 Unit 2-1 Solving Systems of Linear Equations 22:16

We will solve systems using both the substitution and elimination methods. 

16 Unit 2-1 Review 07:49

Review of problems from section 2-1

17 Unit 2-2 Solving Value & Mixture Problems 29:02

In this lesson, we will go over 2 types of application problems for systems of equation. Value problems involve two items that have a value (like coins) or a cost (like two types of tickets) associated with them. Mixture problems involve substances that are solutions or mixtures that have a given percentage concentration of a substance. These can involve mixing two different concentrations together to produce a given quantity of another concentration or starting with a given quantity of a particular concentration and then adding or removing an unknown quantity of another concentration to produce a certain concentration.

18 Unit 2-2 Review 09:22

Review of problems from section 2-2

19 Unit 2-3 Uniform Motion Problems 29:42

In this lesson, we will go over how to solve problems that involve the formula Distance = Rate x Time. We will go over the three structures that these application problems come in.

20 Unit 2-3 Review 08:57

Review of problems from section 2-3

21 Unit 2-4 Systems of Linear Inequalities 29:14

In this lesson, we will review how to graph linear inequalities. We will then use this skill to solve linear programming problems that involve maximizing or minimizing a function given certain constraints.

22 Unit 2-4 Review 09:12

Review of problems from section 2-4

23 Unit 2-5 Solving Systems with 3 Variables 27:20

In this lesson, we will learn 2 methods of solving systems of equations with 3 variables: the elimination method and the substitution and elimination method.

24 Unit 2-5 Review 09:49

Review of problems from section 2-5

25 Unit 2-6 Solving applications with 3 variables 23:26

In this lesson, we will learn how to set up systems of equations for application problems with three unknowns. We will then use the skills learned in the previous lesson to solve those equations. 

26 Unit 2-6 Review 07:16

Review of problems from section 2-6

Unit 3 - Matrices

27 Unit 3-1 Matricies 18:03

Learn what a matrix is, how to write the dimensions of a matrix, how to identify elements in a matrix, how to add matrices, and how to solve basic matrix equations.

28 Unit 3-1 Review 04:14

Review of problems from section 3-1

29 Unit 3-2 Matrix Multiplication 22:40

Learn how to solve matrix equations involving scalars and how to multiply matrices.

30 Unit 3-2 Review 06:29

Review of problems from section 3-2

31 Unit 3-3 Determinants & Inverses 19:29

Learn how to find the determinant of 2 x 2 matrices and 3 x 3 matrices and how to find the inverse of a 2 x 2 matrix.

32 Unit 3-3 Review 04:31

Review of problems from section 3-3

33 Unit 3-4 Using Matrices to Solve Systems 25:59

Use matrix inverses to solve systems with 2 variables and use Cramer's Rule to solve systems with 2 or 3 variables

34 Unit 3-4 Review 07:09

Review of problems from section 3-4

Unit 4 - Quadratics

35 Unit 4-1 Factoring Quadratic Expressions 25:31

Review of factoring quadratic expressions including all trinomials and binomials that are a difference of squares.

36 Unit 4-1 Review 04:26

Review of problems from section 4-1

37 Unit 4-2 Solving Quadratic Equations 14:33

Learn how to solve quadratics using the factoring and square root methods.

38 Unit 4-2 Review 05:24

Review of problems from section 4-2

39 Unit 4-3 Complex Numbers 17:15

Learn how to write square roots of negative numbers in terms of i and how to add, subtract, multiply, & divide complex numbers

40 Unit 4-3 Review 04:49

Review of problems from section 4-3

41 Unit 4-4 Completing the Square & the Quadratic Formula 26:43

Learn how to solve quadratics by completing the square and by using the quadratic formula. Also learn how to tell what type of solutions a quadratic will have based on the discriminant.

42 Unit 4-4 Review 05:26

Review of problems from section 4-4

43 Unit 4-5 Solving Systems involving Quadratics 16:27

Learn how to solve systems of equations where one or both of the equations have square terms.

44 Unit 4-5 Review 05:41

Review of problems from section 4-5

Unit 5 - Radicals

45 Unit 5-1 Simplifying Radicals & Roots 17:17

Simplify square roots and higher order roots that contain numbers and letters

46 Unit 5-1 Review 05:05

Review of problems from section 5-1

47 Unit 5-2 Adding, Subtracting, Multiplying, & Dividing Roots 16:56

Add, Subtract, Multiply, & Divide roots

48 Unit 5-2 Review 05:35

Review of problems from section 5-2

49 Unit 5-3 Multiplying & Dividing Binomial Radical Expressions 13:27

Use double distribution to multiply binomials containing radicals and use conjugates to divide binomials containing radicals

50 Unit 5-3 Review 06:23

Review of problems from section 5-3

51 Unit 5-4 Rational Exponents 12:59

Learn how to convert back and forth between roots and exponential form. Simplify expressions with rational exponents.

52 Unit 5-4 Review 03:00

Review of problems from section 5-4

53 Unit 5-5 Radical Equations 20:49

Learn how to solve equations with roots and radicals in them.

54 Unit 5-5 Review 08:21

Review of problems from section 5-5

Unit 6 - Rational Expressions & Equations

55 Unit 6-1 Multiplying & Dividing Rational Expressions 25:16

Learn how to simplify, multiply, and divide fractions with variables

56 Unit 6-1 Review 08:05

Review of problems from section 6-1

57 Unit 6-2 Adding and Subtracting Rational Expressions 19:30

Learn how to add and subtract fractions with variables

58 Unit 6-2 Review 07:37

Review of problems from section 6-2

59 Unit 6-3 Complex Fractions 11:39

Learn how to simplify expressions that combine addition and subtraction with division but are written as a complex fractional expression

60 Unit 6-3 Review 07:05

Review of problems from section 6-3

61 Unit 6-4 Solving Rational Equations 18:47

Learn how to solve rational equations

62 Unit 6-4 Review 07:44

Review of problems from section 6-4

63 Unit 6-5 Applications involving rational expressions 22:32

Learn how to solve direct, inverse, and joint variation problems using the ratio method and learn how to solve work problems

64 Unit 6-5 Review 06:18

Review of problems from section 6-5

Unit 7 - Polynomials

65 Unit 7-1 Introduction to Polynomial Functions 24:06

Learn how to name polynomials by degree and number of terms, convert between standard and factored form, find the zeros of a polynomial in factored form, and write a polynomial function from its zeros

66 Unit 7-1 Review 06:39

Review of problems from section 7-1

67 Unit 7-2 Special Factors & Products 19:53

Learn how to factor sums and differences of cubes and how to expand binomials using Pascal's triangle and the binomial theorem.

68 Unit 7-2 Review 07:07

Review of problems from section 7-2

69 Unit 7-3 Dividing Polynomials 29:40

Learn how to divide polynomials with long division and synthetic division

70 Unit 7-3 Review 06:42

Review of problems from section 7-3

71 Unit 7-4 Solving Polynomial Equations 15:35

Learn how to solve polynomial functions by using factoring to find quadratics that can be solved.

72 Unit 7-4 Review 06:59

Review of problems from section 7-4

73 Unit 7-5 Theorems about Roots of Polynomials 29:52

Learn how to use the rational root theorem to find all the roots of a polynomial function. Also write polynomials given their irrational and/or imaginary roots.

74 Unit 7-5 Review 11:54

Review of problems from section 7-5

Unit 8 - Graphing Functions

75 Unit 8-1 The 4 Basic Functions & Function Inverses 18:10

Learn how to graph quadratic, absolute value, cubic, and square root functions. Also learn how to find the inverse of a function and show that two functions are inverses

76 Unit 8-1 Review 05:22

Review of problems from section 8-1

77 Unit 8-2 Shifting, Reflecting, and Stretching Graphs 21:15

Learn how to graph shifts, reflections and stretches of quadratics, absolute value functions, cubics, and square root functions.

78 Unit 8-2 Review 05:43

Review of problems from section 8-2

79 Unit 8-3 More on Graphing Quadratics 18:58

Learn how to graph quadratics that are written in standard form, write the equation of a quadratic from its graph, and graph quadratic inequalities.

80 Unit 8-3 Review 07:23

Review of problems from section 8-3

81 Unit 8-4 Graphing Polynomial Functions 21:42

Learn how to graph polynomial functions.

82 Unit 8-4 Review 05:48

Review of problems from section 8-4

83 Unit 8-5 Graphing Rational Functions 21:37

Learn how to graph rational functions.

84 Unit 8-5 Review 07:13

Review of problems from section 8-5

Unit 9 - Exponents & Logarithms

85 Unit 9-1 Exponential Functions 26:52

Learn how to graph exponential functions and how to write and solve basic exponential equations.

86 Unit 9-1 Review 05:43

Review of problems from section 9-1

87 Unit 9-2 Logarithmic Functions 18:39

Learn how to convert equations from logarithmic form to exponential form and vice-versa. Also learn how to graph logarithmic functions.

88 Unit 9-2 Review 04:30

Review of problems from section 9-2

89 Unit 9-3 Properties of Logarithms 12:21

Learn the properties of logarithms and the change of base formula

90 Unit 9-3 Review 04:06

Review of problems from section 9-3

91 Unit 9-4 Solve Exponential & Logarithmic Equations 21:41

Learn how to solve both exponential and logarithmic equations

92 Unit 9-4 Review 05:49

Review of problems from section 9-4

93 Unit 9-5 Applications of Exponential Equations 24:34

Learn how to solve problems involving continuous compounding, half-life, and doubling time.

94 Unit 9-5 Review 06:08

Review of problems from section 9-5

Unit 10 - Basic Trigonometry

95 Unit 10-1 Right Triangle Trigonometry 29:58

Learn the 6 trigonometric ratios and use them to find missing sides and angles in right triangles

96 Unit 10-1 Review 07:12

Review of problems from section 10-1

97 Unit 10-2 Special Right Triangles 15:21

Learn how to find missing side lengths in 45-45-90 and 30-60-90 triangles. Also learn the relationship between sine and cosine.

98 Unit 10-2 Review 04:13

Review of problems from section 10-2

99 Unit 10-3 Angles of Elevation & Depression 17:29

Learn how to solve application problems involving angles of elevation and depression.

100 Unit 10-3 Review 07:31

Review of problems from section 10-3

101 Unit 10-4 Radians & The Unit Circle 25:58

Learn how to convert angle measures between degrees and radians. Also learn how to find the reference angle for any given angle. Use the unit circle to find the exact values of sine and cosine.

102 Unit 10-4 Review 03:02

Review of problems from section 10-4

Unit 11 - Advanced Trigonometry

103 Unit 11-1 Graphing Trig Functions 14:56

Learn to graph sine, cosine, and tangent functions

104 Unit 11-1 Review 05:05

Review of problems from section 11-1

105 Unit 11-2 Area and the Law of Sines 16:28

Learn how to find the area of a triangle when given 2 sides and an included angle and learn how to use the law of sines to find sides and angles of triangles

106 Unit 11-2 Review 05:19

Review of problems from section 11-2

107 Unit 11-3 Law of Cosines 20:42

Learn how to use the law of cosines to find missing sides and angles in triangles

108 Unit 11-3 Review 05:49

Review of problems from section 11-3

109 Unit 11-4 Problem Solving with Trigonometry 12:23

Solve application problems using the Law of Sines and the Law of Cosines

110 Unit 11-4 Review 07:33

Review of problems from section 11-4

Unit 12 - Conic Sections

111 Unit 12-1 Parabolas 29:47

Learn the definition of a parabola and how to find a parabolas focus and directrix.

112 Unit 12-1 Review 10:27

Review of problems from section 12-1

113 Unit 12-2 Circles 11:00

Learn how to write the equation of a circle, how to find the center and radius of circle from its equation, and how to graph a circle.

114 Unit 12-2 Review 04:25

Review of problems from section 12-2

115 Unit 12-3 Ellipses 16:29

Learn how to write the equation of an ellipse, how to find its foci, and how to graph an ellipse.

116 Unit 12-3 Review 04:54

Review of problems from section 12-3

117 Unit 12-4 Hyperbolas 15:39

Learn how to graph hyperbolas and find their foci.

118 Unit 12-4 Review 04:54

Review of problems from section 12-4

Unit 13 - Probability & Statistics

119 Unit 13-1 Permutations & Combinations 17:55

Learn how to calculate permutations & combinations

120 Unit 13-1 Review 04:06

Review of problems from section 13-1

121 Unit 13-2 Probability 15:15

Learn how to calculate basic probability and relative frequency

122 Unit 13-2 Review 04:42

Review of problems from section 13-2

123 Unit 13-3 Multiple Event Probability 14:10

Learn how to compute "and" probability and "or" probability for overlapping events

124 Unit 13-3 Review 03:57

Review of problems from section 13-3

125 Unit 13-4 Conditional Probability 16:02

Learn how to compute conditional probability

126 Unit 13-4 Review 04:41

Review of problems from section 13-4

127 Unit 13-5 Analyzing Data 25:14

Learn how to find the mean, median, mode, range, interquartile range, percentiles and standard deviation of a set of values. Also learn to make a box-and-whisker plot.

128 Unit 13-5 Review 03:54

Review of problems from section 13-5

Unit 14 - Sequences & Series

129 Unit 14-1 Arithmetic Sequences 10:28

Learn about arithmetic sequences

130 Unit 14-1 Review 02:28

Review of problems from section 14-1

131 Unit 14-2 Geometric Sequences 12:02

Learn about geometric sequences

132 Unit 14-2 Review 03:11

Review of problems from section 14-2

133 Unit 14-3 Arithmetic Series 16:40

Learn about arithmetic series

134 Unit 14-3 Review 04:48

Review of problems from section 14-3

135 Unit 14-4 Geometric Series 12:24

Learn about geometric series

136 Unit 14-4 Review 03:37

Review of problems from section 14-4

Course Overview

This “Algebra 2” video course covers all of the content students need to successfully complete High School Algebra 2. It covers the requirements of the Common Core and also goes beyond common core requirements by preparing students for new topics that are dealt with in Pre-Calculus and Calculus. This is a full year’s math course!

This course includes:

  •         14 UNITS
  •         68 NOTE SHEETS TO BE USED ALONGSIDE THE VIDEO LESSONS
  •         OVER 1000 PRACTICE EXERCISES/PROBLEMS!
  •         68 VIDEO-LESSONS
  •         68 REVIEW VIDEOS EXPLAINING SOLUTIONS TO PRACTICE PROBLEMS
  •         68 EXERCISE ANSWER KEYS SHOWING ALL WORK
  •         29 ONLINE QUIZZES AND EXAMS
  •         29 QUIZ/EXAM ANSWER SHEETS/KEYS
  •         OVER 20 HOURS OF VIDEO-LESSONS!

Course Goals

Upon course completion, students will be able to solve multistep one variable equations and inequalities, solve absolute value equations and inequalities, determine if relations are functions, perform operations on functions, solve systems of 2-3 equations, graph linear and quadratic inequalities, perform operations on matrices, use matrices to solve systems of equations, solve quadratic equations over the set of complex numbers, solve systems of non-linear equations, perform operations on radical expressions, convert radical expressions to rational exponents and vice-versa, perform operations on rational expressions, perform operations on polynomial expressions, use the Rational Root Theorem to find all of the roots of a polynomial function, graph functions and their shifts, reflections, and stretches, solve exponential and logarithmic equations, use trigonometry to find sides and angles of all types of triangles, find the foci and directrix of parabolas, graph circles, find the foci and graph ellipses and hyperbolas, learn how to find probability of multiple events, determine conditional probability, find all the measures of central tendency and dispersion of sets of data, find specified terms in arithmetic & geometric sequences, evaluate arithmetic & geometric series, and solve various types of application problems.

Target Audience

This video-course is primarily intended for 9th through 11th graders

Course Requirements

Students taking this course will need to have completed Algebra 1

Course Topics

Unit 1 Fundamentals of Algebra

Solve multi-step one variable equations

Solve and graph one-variable inequalities

Solve absolute value equations

Solve compound inequalities

Solve absolute value inequalities

Solve application problems involving one variable equations

Determine if a relation is a function

Find the domain and range of a relation

Add, subtract, multiply, and divide functions

Perform compositions of functions

Unit 2 Systems of Equations  

Solve systems of equations with two variables

Solve value and mixture application problems using systems of equations

Solve uniform motion problems using systems of equations

Solve systems of linear inequalities

Solve linear programming problems

Solve systems of equations with 3 variables

Solve application problems using systems of equations with 3 variables

Unit 3 Matrices

Add & subtract matrices

Solve basic matrix equations

Multiply matrices

Find the determinant of a matrix

Find the inverse of a matrix

Use matrices to solve systems of equations with 2 or 3 variables

Unit 4 Quadratics

Factor quadratic expressions

Solve quadratic equations by factoring

Solve quadratic equations by the square root method

Perform operations on complex numbers

Solve quadratic equations by completing the square

Solve quadratic equations using the quadratic formula

Solve systems of equations involving quadratics

Unit 5 Radicals

Simplify radicals and roots

Add, subtract, multiply, and divide radical expressions

Multiply and divide binomial radical expressions

Convert radical expressions to expressions with rational exponents

Solve radical equations

Unit 6 Rational Expressions

Multiply & divide rational expressions

Add & subtract rational expressions

Simplify complex fractions

Solve rational equations

Solve application problems involving rational equations

Unit 7 Polynomials

Name polynomials by degree and number of terms

Write polynomial functions given their zeros

Factor sums and differences of cubes

Expand binomials using the Binomial Theorem

Solve polynomial equations by factoring

Use the Rational Roots Theorem to find all the zeros of a polynomial

Unit 8 Graphing

Find the inverse of a function

Graph shifts, reflections, and stretches of quadratic, absolute value, square root, and cubic functions

Graph quadratics in standard form

Graph polynomial functions

Graph rational functions

Unit 9 Exponents & Logarithms

Write & graph exponential equations

Convert between exponential and logarithmic forms

Graph logarithmic functions

Solve exponential and logarithmic equations

Solve application problems involving exponential equations

Unit 10 Right Triangle Trigonometry

Find the exact value of all 6 trigonometric ratios

Find missing sides & angles of right triangles

Solve 30-60-90 and 45-45-90 right triangles

Solve angle of elevation & angle of depression problems

Convert between radians and degrees

Find reference angles for any given angle

Use the unit circle to find exact values of sine and cosine

Unit 11 Advanced Trigonometry

Graph sine, cosine, and tangent functions

Find the area of a triangle using trigonometry

Use the Law of Sines to find missing sides and angles

Use the Law of Cosines to find missing sides and angles

Solve application problems using the Law of Sines and the Law of Cosines

Unit 12 Conic Sections

Find the focus and directrix of parabolas

Write the equation of a circle given its center and radius

Find the center and radius of a circle from its equation

Graph circles, ellipses, and hyperbolas

Write the equation of an ellipse

Find the foci of an ellipse

Write the equation of a hyperbola

Find the foci of a hyperbola

Unit 13 Probability & Statistics

Compute permutations & combinations

Find basic probability

Find multiple-event probability

Find “or” probability

Find conditional probability

Find all the measures of central tendency and dispersion for sets of data

Unit 14 Sequences & Series

Identify and find given terms in arithmetic sequences

Identify and find given terms in geometric sequences

Find the arithmetic mean and the geometric mean

Evaluate arithmetic series

Write series in summation notation

Evaluate geometric series

  • Teacher: Terri
  • Areas of expertise: Mathematics
  • Education: MA - Mathematics from Marshall University and BA - Mathematics Education from Aurora University
  • Interests: Gaming, Science Fiction, Traveling
  • Skills: I am good at learning to use different computer programs
  • Associations: Illinois State Secondary Math Teaching Certificate
  • Issues I care about: The quality of education provided to everyone

I have been helping students learn math since I was in 5th grade. That year, I had a teacher who was tenured and did not teach us anything. He would just go to the board and write the assignment and then sit back down. Luckily, I was able to figure out how to do the problems from the examples in the book. The other students noticed and asked me for help. I have been helping others learn math ever since. Even though most of the students I taught over my 10+ years of teaching in a classroom setting did not like math. Most of them noted that I made it more understandable for them. I love it when previous students come up to me and thank me for helping them to be better at math.

Test Preparation Document

Test Preparation Document

Digital Quizzes and Tests Answer Keys Document

Digital Quizzes and Tests Answer Keys Document

Unit 1 Problem Solutions

Worked out solutions to all problems from Unit 1

Unit 1 Quiz & Test Solutions

Worked out solutions to the quizzes and test in Unit 1

Unit 2 Problem Solutions

Worked out solutions to all problems from unit 2

Unit 2 Quiz & Test Solutions

Worked out solutions to the quiz and test in Unit 2

Unit 3 Problem Solutions

Worked out solutions to all problems from Unit 3

Unit 3 Quiz & Test Solutions

Worked out solutions to the quiz and test in Unit 3

Unit 4 Problem Solutions

Worked out solutions to all problems from unit 4

Unit 4 Quiz & Test Solutions

Worked out solutions to the quiz and test in Unit 4

Unit 5 Problem Solutions

Worked out solutions to all problems from unit 5

Unit 5 Quiz & Test Solutions

Worked out solutions to the quiz and test in Unit 5

Unit 6 Problem Solutions

Worked out solutions to all problems from unit 6

Unit 6 Quiz & Test Solutions

Worked out solutions to the quiz and test in Unit 6

Unit 7 Problem Solutions

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Unit 7 Quiz & Test Solutions

Worked out solutions to the quiz and test in Unit 7

Unit 8 Problem Solutions

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Unit 8 Quiz & Test Solutions

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Unit 9 Problem Solutions

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Unit 9 Quiz & Test Solutions

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Unit 10 Problem Solutions

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Unit 10 Quiz & Test Solutions

Worked out solutions to the quiz and test in Unit 10

Unit 11 Problem Solutions

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Unit 11 Quiz & Test Solutions

Worked out solutions to the quiz and test in Unit 11

Unit 12 Problem Solutions

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Unit 12 Quiz & Test Solutions

Worked out solutions to the quiz and test in Unit 12

Unit 13 Problem Solutions

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Unit 13 Quiz & Test Solutions

Worked out solutions to the quiz and test in Unit 13

Unit 14 Problem Solutions

Worked out solutions to all problems from unit 14

Unit 14 Quiz & Test Solutions

Worked out solutions to the quiz and test in Unit 14

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