Author Archives: admin

Intro to Probability (SAT style)

In this video we'll learn what probability is, as well as a bunch of vocab words like "compound", "dependent", and "mutually exclusive". We'll also work a bunch of common examples, starting with colored marbles in a bag (with and without replacement), then moving on to coin tosses and dice.

This video appears on the page: Probability

Probability
Intro to Probability (SAT style)
Binomial Probability Formula

This chapter "probably" (lol) covers mutually exclusive events, dependent probability, and, or, colored rocks, coin flips, regular dice, weighted dice, and even the Binomial probability formula.

Part of the course(s): Math Analysis ,College Algebra ,Algebra 2 ,Pre-Calculus

Intro to Permutations & Combinations

This video starts with the differences between permutations and combinations, and shows you how to spot which type of problem you're looking at. Then I work a bunch of problems of each type, showing you how to list out all the possible combinations and permutations in an organized way, such as ABC, CBA, BCA, etc. Stay organized!

This video appears on the page: Permutations & Combinations

Binomial Expansions & Pascal's Triangle

These are problems like "Find the third term of the binomial expansion of (x+2)12" which would take forever to FOIL, but which can be done relatively painlessly (notice the word relative) using the combination formula nCr. Whatever you do, remember n-1: if you're looking for the sixth term, you plug in five for "r"!

This video appears on the page: Permutations & Combinations

Tricky Permutation and Combination Problems for SAT

This video is all about doing tricky SAT combinatorics problems without using any formulas. Instead, we'll just make blanks, then fill in numbers and multiply in a sort of truncated factorial technique. Examples include how many ways you can rearrange the letters of a word, form a committee of both parents and teachers, compose a password, and limited seating arrangements.

This video appears on the page: Permutations & Combinations

Combinations: a closer look

We touched on combinations in the intro video, but now we'll learn nCr notation: what it's for and how to use it. And since there's so much confusion out there about combinations vs the permutations of the last video, this video focuses on how combinations are different. Example problems include pizza toppings, student committees, and baseball batting order.

This video appears on the page: Permutations & Combinations

Permutations & Combinations (a.k.a. Combinatorics)
Intro to Permutations & Combinations
Permutations: a closer look
Combinations: a closer look
Tricky Permutation and Combination Problems for SAT
Binomial Expansions & Pascal's Triangle

Make nCr and nPr pay for what they've done by mastering them and using them to execute on your upcoming test. Also in this chapter: brush up for this common SAT question.

Part of the course(s): Math Analysis ,College Algebra ,Statistics ,Algebra 2 ,Pre-Calculus

Permutations: a closer look

In this video we get into the nitty gritty of nPr notation: what it's for and how to use it, including a bunch of example permutation problems about student council, sports teams, and family portraits. Also discussed are Circular Permutations, which is a gotcha question a lot of teachers use which applies only to items in a circle on something that rotates.

This video appears on the page: Permutations & Combinations

SAT-type Sequence Questions

I realize most students won't still remember their sequence formulas when the SAT comes around, but that's actually good, because SAT questions are usually designed so that the formulas wouldn't help you anyway!

This video appears on the page: Sequences & Series

Sigma Notation

Sigma is just a Greek letter (I assume it's Greek since it's on the front of every frat house in the world) that looks like a cross between Z and E, and when you see it in math class it translates roughly to "you're screwed". Kidding! It actually means "sum", as in, "add all this stuff up." It's not too bad once you see how it works, but most teachers seem unable to make it non-confusing.

This video appears on the page: Sequences & Series

Geometric Sequences & Series

In this video I cover how use all the formulas for geometric sequences and series. If you've already seen arithmetic sequences, this is going to be similar, except you'll definitely need a calculator, and the common difference gets replaced by the common ratio.

This video appears on the page: Sequences & Series

Arithmetic Sequences & Series

In this video I cover how use all the formulas for arithmetic sequences and series. We'll learn what an nth term is, how to find it, how to find the sum of an arithmetic sequence, how to find the "common difference" d, and how to find arithmetic means.

This video appears on the page: Sequences & Series

Intro to Sequences and Series

In this video we introduce geometric and arithmetic sequences, talk about the differences between explicit vs recursive formulas, and do lots of problems that don't require the formulas for arithmetic and geometric sequences.

This video appears on the page: Sequences & Series

Sequences, Series & Sigma Notation
Intro to Sequences and Series
Arithmetic Sequences & Series
Geometric Sequences & Series
Sigma Notation
SAT-type Sequence Questions (Word Problems)

Common confusion: a "series" is just a sequence with plus signs between the terms instead of commas. All other questions, check out the chapter page, which includes a free printable pdf of all the formulas for arithmetic and geometric sequences.

Part of the course(s): Math Analysis ,free videos edit ,Free Sample Videos , ,Test Image Problem ,College Algebra ,Algebra 2 ,Pre-Calculus ,Calculus

Hyperbolas

These hyper parabolas take conic craziness to another level, combining all the craziest stuff we've seen in graphing: asymptotes, foci, vertices, weird dashed-line boxes. Even a minus sign! Plus, you've got to just look at the equation and figure which way it opens. To find the foci, we're back to the usual Pythagorean theorem: a2+b2=c2.

This video appears on the page: Parabolas, Ellipses, Circles & Hyperbolas

Ellipses

In this rather long video we'll hit all the crazy details of the stretched-out circles we call ellipses: vertices, co-vertices, co-co-vertices (I made that one up), foci (that one's real), and the "constant sum". To find the foci of an ellipse, we'll use a mutant Pythagorean theorem unique to ellipses: b2+c2=a2.

This video appears on the page: Parabolas, Ellipses, Circles & Hyperbolas

Parabolas: Directrix & Focus

I saved parabolas for last because even though you probably think you know something about parabolas from past chapters, there are a couple new details, like focus and directrix, that are very similar to hyperbolas and ellipses.

This video appears on the page: Parabolas, Ellipses, Circles & Hyperbolas

Circles

In this video we'll see how to graph circles from their equations, as well as how to get a circle's equation from its graph. We'll also check out the distance and midpoint formulas, and use them for a circle word problem. Finally, we'll use completing the square to put a random circle equation in standard form.

This video appears on the page: Parabolas, Ellipses, Circles & Hyperbolas ,Circles in X-Y Coordinates

Intro to Conics

In this video I'll teach you to how to just look at an equation and know if it's a circle, ellipse, hyperbola or parabola, and we'll look at what they have in common. I'll also emphasize the most common mistakes students make with the conic formulas, as well as explaining the differences between the two common parabola equations you'll see.

This video appears on the page: Parabolas, Ellipses, Circles & Hyperbolas

Circles, Ellipses, Hyperbolas & Parabolas: The "Conics"
Intro to Conics
Circles
Ellipses
Hyperbolas
Parabolas: Directrix & Focus

In this chapter we'll emphasize the similarities and differences between the equations of these four shapes, and we'll discuss why conic sections are called that.

Part of the course(s): Geometry ,College Algebra ,Algebra 2