Video Links

Refresh your memory with these videos! They go in order by chapter.

Chapter 1: algebraic expressions

Intro to order of operationsThis example shows the steps and clarifies the purpose of order of operations: to have ONE way to interpret a mathematical statement.

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Writing expressions with variablesLearn how to write simple algebraic expressions.

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Evaluating expressions with two variablesWe've done a few examples together where we were faced with 1 variable. Why not try one that has 2 variables?

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Quadrants of the coordinate planeLearn about the 4 quadrants that make up a coordinate plane.

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Chapter 2: Equations

Worked example: Solving proportionsLearn the reasoning behind solving proportions. We'll put some algebra to work to get our answers, too.

Intro to ratiosA ratio is a comparison of two quantities. Learn how to find the ratio between two things, for example apples to oranges.

Growing by a percentageIn this example we grow a whole number by a percentage of itself. Growing by percentage is a common skill often used when figuring how much is owed or earned with interest.

Worked example: two-step equationsSal solves the equation -16 = x/4 + 2. It takes two steps because he first has to subtract 2 from both sides and then multiply both sides by 4.

Linear equations 3Linear equations with multiple variable and constant terms

Chapter 3: inequalities

One-step inequalities: -5c ≤ 15In addition to solving the inequality, we'll graph the solution. Remember to swap if you mutiply both sides of the inequality by a negative number.

Two-step inequalitiesTwo-step inequalities are slightly more complicated than one-step inequalities (duh!). This is a worked example of solving ⅔>-4y-8⅓.

Compound inequalities examplesSal solves several compound linear inequalities.

chapter 4: functions

Interpreting a graph exampleLearn to interpret the graphs of a linear functions.

Relations and functionsLearn to determine if a relation given by a set of ordered pairs is a function.

What is the range of a function?Sal introduces the concept of "range" of a function and gives examples for functions and their ranges.

What is the domain of a function?Functions assign outputs to inputs. The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0. We can also define special functions whose domains are more limited.

Worked example: Evaluating functions from equationLearn how to evaluate f(x)=49-x² at x=5.

chapter 6: Systems of equations

Systems of equations with graphingSal shows how to solve a system of linear equations by graphing and looking for the point of intersection.

Solving linear systems by substitution (old)An old video where Sal introduces the substitution method for systems of linear equations.

Solving systems of equations by elimination (old)An old video where Sal introduces the elimination method for systems of linear equations.

Systems of equations with elimination (and manipulation)In some cases, we need to slightly manipulate a system of equations before we can solve it using the elimination method. So how it's done in this video.

chapter 7: exponents and polynomials

Exponent rules introIntroduction to exponent rules including basic product and quotient rules.

Exponent rules part (composite problems)Learn about exponent rules with an introduction to composite problems

Negative exponentsLearn how to rewrite expressions with negative exponents as fractions with positive exponents.

Polynomials introPolynomials are sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer. For example, 3x+2x-5 is a polynomial. Introduction to polynomials. This video covers common terminology like terms, degree, standard form, monomial, binomial and trinomial.

Adding polynomialsSal simplifies (5x² + 8x - 3) + (2x² - 7x + 13x).

Subtracting polynomialsSal simplifies (16x+14) - (3x² + x - 9).

Multiplying binomials by polynomialsSal expresses the product (10a-3)(5a² + 7a - 1) as 50a³+55a²-31a+3.

Chapter 9: Quadratic functions

Vertex & axis of symmetry of a parabolaSal rewrites a quadratic equation in vertex form and shows how it reveals the vertex of the corresponding parabola.

The quadratic formulaWith the quadratic formula, we can solve any quadratic equation! Learn how to use it with an example.

Solving quadratics by taking square rootsSal solves the equation 2x^2+3=75 by isolating x^2 and taking the square root of both sides.

chapter 8: factoring

(Intentionally after Chapter 9 on this website. This is the order in which it's taught)

Greatest common factor explainedHere's a nice explanation of greatest common factor (or greatest common divisor) along with a few practice example exercises. Let's roll.

Factoring polynomials: common factorSal factors 4x⁴y-8x³y-2x² as 2x²(2x²y-4xy-1) by taking the greatest common factor.

chapter 11: exponential functions and simplifying square roots

Intro to geometric sequencesSal introduces geometric sequences and their main features, the initial term and the common ratio.

Intro to exponential functionsIn exponential functions the variable is in the exponent, like y=3ˣ. Here we introduce this concept with a few examples.

Compound interest introductionLearn about the basics of compound interest, with examples of basic compound interest calculations

Exponential decay introAn exponential function a⋅rˣ is growing (increasing) if r>1 and decaying (decreasing) if 0

Graphs of square-root functionsSal graphs y=√x. Then, he shows a few examples of how we can shift and stretch the graphs of y=√x and y=x^2, and how the equations of those graphs look.

Simplifying square rootsRoots are nice, but we prefer dealing with regular numbers as much as possible. So, for example, instead of √4 we prefer dealing with 2. What about roots that aren't equal to an integer, like √20? Still, we can write 20 as 4⋅5 and then use known properties to write √(4⋅5) as √4⋅√5, which is 2√5. We *simplified* √20.

Intro to rationalizing the denominatorWhen we have a fraction with a root in the denominator, like 1/√2, it's often desirable to manipulate it so the denominator doesn't have roots. To do that, we can multiply both the numerator and the denominator by the same root, that will make the denominator an integer. For example, we can multiply 1/√2 by √2/√2 to get √2/2

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