Algebra I
Algebra is a field of mathematics which involves the use of symbols in order to manipulate and resolve calculations which otherwise would be confusing. Through the use of algebraic manipulation one can isolate and determine the value of an unknown variable. These manipulations initially seem complex but with considerable practice they can become quite simple. While physics involves the user of higher mathematics such as differential calculus to determine the slope of a curve or integral calculus to determine the area under a curve, the vast majority of the problems in mechanics can be resolved with simple algebraic equations.
In continuation we present the lectures by Khan academy with respect to Algebra:
Content

11. Absolute value equations, functions, and inequalities
12. Expressions with rational exponents and radicals 13. Introduction to exponential functions 14. Introduction to polynomials 15. Polynomial factorization 16. Quadratic equations and functions 17. Rational and irrational numbers 
1. Introduction to algebra
2. Onevariable linear equations
3. Onevariable linear inequalities
4. Units of measurement in modeling
5. Twovariable linear equations
Pointslope form(yb)=m(xa)
Standard formax+by=c
Summary: Forms of twovariable linear equationsTake an overview of the three main forms of linear equations: slopeintercept, pointslope, and standard. Learn which form is most appropriate for different uses.

6. Functions
Introduction to functionsMake a first introduction to functions.
Evaluating functionsLearn how to find the value of a function for a given input value.
Inputs and outputs of a functionExtend your understanding of the relationship between the inputs of a function and the outputs of that function.

Functions and equationsUnderstand the subtle differences and similarities between functions and equations. In this exercise, we will see how an equation can be turned into a function.
Interpreting function notationSolve some word problems by interpreting expressions of modeling functions.
Introduction to the domain and range of a functionLearn what the domain and the range of a function are. Practice finding the domain and the range of a function given its graph.

Determining the domain of a functionDetermine the domains of functions according to various considerations.
Recognizing functionsRecognizing functions
Piecewise functionsIntroduction to piecewise defined functions
Maximum and minimum pointsLearn about maximum and minimum points of functions.

Intervals where a function is positive, negative,Learn about features of functions that have distinct graphical representations: intervals where the function is always positive or always negative, and intervals where the function is always increasing or always decreasing.
Interpreting features of graphsInterpret the graphs of functions in terms of the contexts that are modeled by the functions.

Average rate of changeLearn what's the average rate of change of a function and how to find it over given intervals.
Average rate of change word problemsSolve word problems that concern the average rate of change of a functional relationship.

7. Linear equations and functions word problems
Interpreting linear functions and equationsSolve word problems where you need to answer a question about a realworld relationship based on its mathematical model.
Comparing linear functionsCompare features of linear functions, such as slope and intercepts, where the functions are given in different forms—tables, graphs, or formulas.
Constructing linear models for realworld relationshipsLearn how to represent realworld relationships (that are described verbally) with linear graphs, equations, or functions.
Linear models word problemsSolve general word problems about realworld relationships that can be modeled by linear equations or functions.

8. Sequences
Introduction to sequencesLearn what sequences are, and about the explicit and recursive definitions of sequences. Evaluate sequences that are defined recursively.
Introduction to arithmetic squencesLearn about arithmetic sequences and their main features, the initial term and the common difference. Evaluate arithmetic sequences.
Constructing arithmetic sequencesLearn how to find the explicit or recursive formula of an arithmetic sequence.

Introduction to geometric sequencesLearn about geometric sequences and their main features, the initial term and the common ratio. Evaluate geometric sequences.
Constructing geometric sequencesLearn how to find the explicit or recursive formula of a geometric sequence.
Modeling with sequencesNow that we are able to solve any kind of system we are given, it's time to use that knowledge to solve some word problems.

9. Systems of linear equations
Introduction to systems of linear equationsLearn what "systems of equations" are and what counts as a solution to such a system.
Graphical representation of systems of equationsLearn how to solve a system of equations by considering its graph, which turns out to be a VERY effective method.
Equivalent systems of equations and the elimination methodLearn about the elimination method, which is a way manipulate systems of equations in order to solve them algebraically. This is actually very similar to the way we manipulate single equations in order to solve them!

Solving systems of equations with substitutionLearn about the substitution method, which is another way to manipulate systems of equations in order to solve them.
The possible number of solutions of systems of linear equationsLearn about the possible number of solutions of systems of linear equations. Spoiler: There can be a single solution, zero solutions, or infinite solutions. These different cases define the distinctions between "consistent" and "inconsistent" systems, and between "dependent" and "independent" systems.

Analyzing the solutions to systems of equationsLearn how to determine the number of solutions a system of equations has, without having to go through the entire solution process.
Solving any system of linear equationsUse everything you learned so far in order to solve any kind of system of equations!
Systems of linear equations word problemsNow that we are able to solve any kind of system we are given, it's time to use that knowledge to solve some word problems.

10. Twovariable linear inequalities
Checking solutions of twovariable inequalitiesChecking your answers in a two variable linear equality. Is (4, 3) a solution for y>x+1? In this tutorial from Khan academy, they check solutions for systems of inequalities.
Intervals where a function is positive, negative, increasing, or decreasingConstraining solutions of twovariable inequalitiesOnce you have set a value for one of your variables in a twovariable linear inequality (or system of inequalities), how can you find the range of values which are true for the other variable. For example, if x=3, and the equation is 2x+y<1 what number must y be?

Graphing twovariable inequalitiesMarking a graph with twovariable linear inequalities and systems of twovariable linear inequalities.
Modeling with linear inequalitiesIn a real life situation how can you write linear inequalities and systems of inequalities? Learn to use algebra or graphs to solve the problem.

11. Absolute value equations, functions, and inequalities
Solving absolute value equationsLearn how to solve absolutevalue equations. For example, solve 2x1=5.
Graphs of absolute value functionsLearn how to graph absolute value functions like f(x)=x+28.
Solving absolute value inequalitiesLearn how to solve absolute value inequalities. For example, solve x12+4<14.

12. Expressions with rational exponents and radicals
Introduction to rational exponents and radicalsIn this tutorial you will learn about radicals and about rational exponents and practice how to change back and forth from these two types of notation.
Simplifying numerical radical expressionsIn this tutorial you will simplify numerical expressions with radicals by removing all factors that are perfect squares from inside the radical.
Rational exponents and the properties of exponentsIn this tutorial you will rewrite variable expressions with rational exponents and radicals using the properties of exponents.

13. Introduction to exponential functions
Introduction to exponential growth and decayLearn about exponential growth and decay, and specifically how it always grows (or diminishes) by equal factors.
End behavior and graphs of basic exponential functionsLearn how an exponential function behaves as the value of its input increases to positive infinity or decreases to negative infinity. Learn how to graph basic exponential functions.

Interpreting formulas of basic exponential functionsLearn how to analyze the formulas of basic exponential functions in order to find their common ratio, initial value, and other parameters.
Interpreting graphs and tables of basic exponential functionsLearn how to analyze the graphs, or tables of values, of basic exponential functions in order to find their common ratio, initial value, and other parameters.

Constructing basic exponential modelsLearn how to construct exponential functions to model realworld situations.
Solving basic exponential modelsLearn how to construct exponential functions and then analyze them to model and solve realworld problems.
Comparing exponential and polynomial functionsLearn how distinguish between linear and exponential growth, and learn the differences between the end behavior of polynomial and exponential functions.

14. Introduction to polynomials
Intro to polynomialsLearn about polynomial expressions: What are they? How are they constructed? What can we do with them?
Adding & subtracting polynomialsLearn how to add and subtract polynomial expressions with one variable.
Adding and subtracting polynomials: two variablesLearn how to add and subtract polynomial that involve two variables. For example, x^3 + xy + 3y  (x^3 + 6xy + 2y^2).

Multiplying monomialsMultiplying monomials by polynomialsLearn how to multiply a polynomial expression by a monomial expression. Monomials are just polynomials with a single term!
Multiplying binomialsLearn how to multiply two binomials together. For example, (3x * 7) * (3x^2 + 10x + 2).
Special products of binomialsLearn about the special types of products of binomials: perfect squares and the difference of two squares. These will be very helpful once you tackle more advanced expressions in Algebra.

Multiplying binomials by polynomialsLearn how to multiply a polynomial expression by a binomial expression.
Polynomials word problemsSee a few examples of how we can represent realworld situations with polynomials.

15. Polynomial factorization
Introduction to factorizationLearn what factorization is all about, and warmup by factoring some monomials.
Factoring monomialsLearn how to write a monomial as a factor of two other monomials. For example, write 12x^3 as (4x)(3x^2).
Common monomial factorsLearn about common monomial factors and how to find the greatest common factor of two monomials. For example, find the greatest common factor of 6x^2y and 9xy^2 (answer: 3xy).

Factoring polynomials by taking common factorsLearn how to take a common monomial factor out of a polynomial expression. For example, write 2x^3+6x^2+8x as (2x)(x^2+3x+4).
Factoring quadratics 1Learn how to factor quadratic expressions with a leading coefficient of 1. For example, factor x²+3x+2 as (x+1)(x+2).
Factoring quadratics 2Learn how to factor quadratic expressions with a leading coefficient other than 1. For example, factor 2x²+7x+3 as (2x+1)(x+3).

Factoring polynomials with quadratic formsLearn how to factor quadratic polynomials of the form ax^2+bx+c as the product of two linear binomials. For example, write x^2+3x10 as (x+5)(x2). Learn how to identify these forms in more elaborate polynomials that aren't necessarily quadratic. For example, write x^44x^212 as (x^2+2)(x^26).
Factoring quadratics: Difference of squaresLearn how to factor quadratics that have the "difference of squares" form. For example, write x²16 as (x+4)(x4). Learn how to identify this form in more elaborate expressions. For example, write 4x²49 as (2x+7)(2x7).

Factoring quadratics: Perfect squaresLearn how to factor quadratics that have the "perfect square" form. For example, write x²+6x+9 as (x+3)². Learn how to identify these forms in more elaborate expressions. For example, write 4x²+28x+49 as (2x+7)².
Factoring polynomials with special product formsFactor polynomials of various degrees using factorization methods that are based on the special product forms "difference of squares" and "perfect squares." For example, factor 25x⁴30x²+9 as (5x²3)².

16. Quadratic equations and functions
Solving quadratic equations by taking square rootIn this tutorial you will learn about the most basic way of solving quadratic equations.
Solving quadratic equations by factoring and using structureIn this tutorial, you'll learn some pretty elaborate ways of solving quadratic equations, by harnessing the mighty strength of algebra.

Solving quadratic equations by completing the squareYou're already familiar with factoring quadratics, but have begun to realize that it only is useful in certain cases. Well, this tutorial will introduce you to something far more powerful and general. Even better, it is the bridge to understanding and proving the famous quadratic formula.
Solving quadratics using the quadratic formulaLearn how to solve any quadratic equation with the most general tool of all, the quadratic formula!

Features of quadratic functionsLearn about the features of quadratic functions, and how to find them given the formula of the function. Also learn about the different forms of quadratic functions: standard, vertex, and factored.
Graphing quadratic functionsIn this tutorial, we will learn how to graph quadratic functions given in different forms.
Transforming the graphs of quadratic functionsLearn how function transformations affect the graphs of quadratic functions.
Interpreting quadratic modelsUse all the knowledge you gained about quadratic equations and functions in order to solve some word problems about real world contexts that are modeled by quadratic functions.
Systems of quadratic equationsLearn how to solve systems of two equations in two variables, where at least one of the equations is quadratic.

17. Rational and irrational numbers
Irrational numbersLearn what irrational numbers are. Also learn how to classify numbers as whole, integer, rational, and irrational.
Proofs concerning irrational numbersLearn some proofs about the existence of irrational numbers.
Sums and products of rational and irrational numbersDetermine whether various combinations of rational and irrational numbers are rational or irrational themselves.

18. Seeing structure in expressions
Evaluating expressions with unknown variablesLearn how to evaluate expressions with variables whose values are unknown, by using another information about those variables. For example, given that a+b=3, evaluate 4a+4b.
Manipulating expressions with unknown variablesLearn how to rewrite expressions with variables whose values are unknown, by using another information about those variables. For example, given that a+b=0, express a*b in terms of b alone.

Reasoning about expressions with unknown variables
Learn how to study algebraic expressions containing variables whose values are unknown, and how to derive new facts about those expression by using other information. For example, given two positive integers b and c where b>c, determine which expression is greater: b/(b+c) or 0.5.