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Some Algebra 1 teachers are crazy, putting all kinds of advanced Algebra 2 topics in Algebra 1. If what you're covering isn't listed above, click here for the Algebra 2 class page.
FOIL On Bigger Problems (trinomials)
These problems have more terms than basic FOIL, but the same principals apply. One: everything in the first parentheses has to get multiplied by everything in the other parentheses. Two: don't forget anyone! Once again, my patented "draw rainbows everywhere" technique should make it easier to remember. NOTE: Some or all of the problems in this video might be more advanced that what your class is doing, so if you start getting scared, hit stop!
Basic FOIL on 2-by-2 parentheses
In this video we'll learn the most common FOIL situation, multiplying parentheses that each have two terms in them (a.k.a. binomials). Most students don't have too much trouble with the concept of FOIL; the most common mistake is forgetting one of the terms. First, Outside, Inside, Last is one way not to forget any terms, but I'll also show you my favorite graphical technique: drawing rainbows over and under to keep track.
FOIL is an acronym that helps you multiply out parentheses in problems like (x-5)(x+2), and you've got to be able to do this before you can factor. This chapter covers the easier 2-by-2 FOIL problems, as well as 2-by-3 and beyond.
When a word problem talks about two things being "proportional", this is what they're talking about. Or maybe they're "inversely proportional". "Joint" variation just refers to when you have three things that are proportional or inversely proportional instead of just the two, which is basically just ratios in disguise.
Joint Variation: Three or More Variables
These problems are exactly like the problems in the previous video, except instead of 2 variables there are three or four. Either way, same series of steps! "Directly" will still mean multiply, and "inversely" will still mean divide, and "plug and chug" will still be in your future. CAUTION: this video won't make a ton of sense unless you watch the one before it, so I'd recommend that first.
Direct & Inverse Variation: Two Variables
These two types of problems always involve two letters (usually x and y) and usually start the same way: if the problem has the words "varies directly" in it (or says two things are "proportional"), you just write down "y=kx" and start plug-and-chugging. If the problem says "varies inversely" (or variables are "inversely proportional"), you write down y=k/x and start plug-and-chugging. Sound too easy? What can I say: the same four steps will get you through every one of these things.
Factoring Stuff Out (a.k.a. "distribution in reverse")
Instead of taking a problem like 2(x-3) and distributing it to 2x-6, we're going to do the exact opposite: start with 2x-6 and break it up into 2(x-3) by pulling out common factors. Seem like a waste? It's a necessary skill that you'll see throughout your math career, and it's a great lead-in for the more difficult type of factoring with two sets of parentheses, coming up in the next videos.
Hard Multi-Step Percent Problems (SAT)
When percent problems get hard, especially on standardized tests like the SAT, it's often because it's a two-step process. For example, a retail item is marked down once, then marked down again. Or, perhaps something gets bought and sold a couple times. Regardless of the exact question they're asking, the burn is always the same, and this video will show you how to always use the right denominator!
Percents As Decimals
I know I'm starting to sound like a broken record, but in this short video once again I'll pummel you about the head and shoulders with admonitions to use decimals rather than percents! And in this video, hopefully I make it look easy enough that you'll give it a try.
Percent Increase & Decrease
The exact wording of percent problems is super-important, so let’s get specific! “Percent increase” and “percent decrease” are common types of problems, as well as their closely related brothers, “increased by” and “decreased by”. We’ll also cover “percent more than” and “percent less than”, mostly using decimal methods rather than ratios.
Percents as Ratios
In this first video we'll take a look at how to solve basic percent problems using ratios and cross multiplication. I don't recommend using this method for long, though, since I've seen so many students struggling with this percents stuff years later while preparing for the SAT, who still set up equations with x/100. Use it to learn percents, but try and move on to the decimal methods in the later videos as soon as possible!
We'll start by comping percentages using basic ratios, then we'll move on to using a decimal-based approach since that's what you'll need for more advanced problems. I also point out the most common types of trick questions about percents, including common types of SAT questions, and computing interest. And if you're super-advanced, "compound interest", where you have to calculate how interest builds over n weeks, months, years, etc.
Ratios & Proportions (SAT)
Ratios are mostly word problems that lead to cross multiplication equations, and most students find them pretty basic. In this chapter we'll work some typical problems about marbles and pizzas, and I'll emphasize the one trick they always pull on the SAT. 7.RP.1
Ratios are mostly word problems that lead to cross multiplication equations, and most students find them pretty basic. In this chapter we'll work some typical problems about marbles and pizzas, and I'll emphasize the one trick they always pull on the SAT.
Cross Canceling vs Cross Multiplying (free)
Time to clear up the confusion on these two once and for all! Not sure why cross canceling (cancelling if you're European) had to get that name, since it really causes a lot of confusion with cross multiplication, and since if you do one when you should do the other, you'll get the question totally wrong. But hey, every book and teacher calls these things by these same confusing names, so hopefully this video will help!
Cross Multiplication
This is a pretty basic skill that you'll lose a lot in your math career, including Ratios, Percents, and Similar Triangles. Luckily, it's pretty easy to remember and use, with the exception of it sounding a lot like Cross Canceling, which is completely different yet has a very similar name. That's the subject of the next video.
Cross "multiplication" refers to what you do when you have two fractions across an equal sign from each other. You cross "cancel" when you are multiplying fractions. Confused yet? This chapter will sort you out.
Solving Equations With Distribution
In this video we work distribution problems similar to the last video with all the parentheses, except in this video the problems have equals signs as well, which means we can solve for the variable! But only after multiplying it out, combining like terms, then doing everything else we did in the solving basic equations chapter.