Author Archives: admin
Rate/Time Word Problems Using Tables
In this video I solve problems where a rower takes a journey with and against the current, and a plane flying with and against the wind. The key method I'll demonstrate is using a rate/time table to turn the hard word problem into a manageable rational equation.
Solving Rational Equations (x's in denominators)
This video pertains to finding common denominators when said denominators contain x's, x2's, and other factorable junk. With the aforementioned common denominators established, one is heretofore then able to perform the solving-related work for hire.
Rational equations are ones with x and/or x2 in the denominator, not too bad. The word problems that go with them are tougher, often involving "rate x time = distance" tables to help cook the books.
Quadratic Inequalities
This video is all about what to do when your quadratic "equation" suddenly has a "<" or ">" instead of an equals sign. Not surprisingly, to solve "quadratic inequalities" we'll use a fun combination of the "quadratic" methods from this chapter (factoring mostly) and solving inequalities stuff from the previous chapter.
Solving equations with only one square root
You may think that the key to solving equations with roots in them is to square away the root. And you'd be right. But there's another key too: checking your answers! That's because of the dreaded "extraneous solution", which can sap you of strength and points.
Solving equations with two square roots
The force is strong in these extraneous solutions. Plus there's all that FOILing to do. Beware: (x+2)2 does not equal x2 + 4! Gotta check it before you wreck it (the middle term, that is).
Rational Equations are the problems where you have a bunch of x's and x2's in the denominator of a giant fraction, and you have to find the least common denominator and simplify in order to solve for X. And I teach a great method using tables to solve nasty word problems involving stuff like boats rowing upriver and faucets filling tubs.
In this chapter we take a look at how to solve equations where the variable is under a square root or a radical. Often we'll be able to simply square both sides of the equation, but we'll always have to be careful to check for extraneous solutions.
Quadratic Word Problems
Teachers vary quite a bit on whether they make you do word problems requiring factoring to solve. I demonstrate a few here, about picture frames with constant borders and farmers trying to construct pens, to give you a flavor of how these things usually go. As always, learn the ones your teacher emphasizes in class!
The Quadratic Formula
On the down side, you'll have to memorize this puppy. On the up side, this formula is going to save your bacon a lot, both when solving equations that can't be factored and when something can be factored but you can't figure it out. My only warning: whatever you do, don't attempt to learn the quadratic formula song. You'll regret it.
Completing the square
While not the most useful quadratic method for most of the students I tutor, there are a few who like it. You should also learn completing the square if you're ever going to feel ready to try deriving The Quadratic Formula on your own. You know, for kicks.
Factoring Quadratic Equations
The best way to solve a quadratic equation (a.k.a. "find the x-intercepts of a parabola") is factoring, except in the rare case where there's no middle term and you can just square root both sides. (If you're not a fan of factoring, you should check out my factoring chapter.)
"Quadratic" means "squared", for some reason, so this chapter is about solving equations with x2's in them. You'll have to learn several tricky techniques -- square rooting, factoring, completing the square, and/or the Quadratic Formula -- but I give you tips to make them easier, and to decide which to use in different situations.
Absolute Value Inequalities
When you replace the "=" with a "<" or ">", unfortunately absolute value problems get a lot tougher. Or at least more complicated. These are fair game on the SAT, though, so gotta respect that. And the tricks I teach in this video seem to work for most students.
Absolute Value Equations
Absolute value equations are confusing when you see them, but they're not as bad as inequalities. Just get that absolute value alone on one side of the equations, then turn it into two separate equations as I explain in this video, and you'll never be the same.
Solving Absolute Value Equations & Inequalities
Absolute Value Equations
Absolute Value Inequalities
Absolute value signs (i.e. |x+3|) wreak havoc on equations and inequalities, often resulting in multiple answers and interval notation, but I'll give you simple steps to memorize for dealing with them. If you need to graph absolute value functions, check out the library functions page.
Systems of Inequalities with both X & Y
Systems, by now you've learned, means "two equations at once." And we get to color in one side of two lines at the same time! I know I said the chapter peaked last video, but this really is the best-best-best of inequalities. A key skill in linear programming.
Linear Inequalities with both X & Y
Finally, those problems where you have to color in one side of a line! I didn't mention these earlier because I didn't want to get anyone excited, but this is definitely as good as this chapter is going to get. It's all downhill from here.
Systems of Inequalities (with just X)
In this video we're given two inequalities aka compound inequalities instead of just one. We'll put them on the same number line, then decide how to do "and" vs "or". We'll then write the answer in interval notation, since we're crazy about that.