Trust me, I’ve haven’t aced every math test I’ve taken. Both as a student (ions ago!) and a math tutor, I’ve found that these things really help when “studying” for taking a math test or final. The main thing is that you don’t “study”, you “work problems” to prepare:
If you are lucky enough to have your old tests for the semester (or year, if the final covers the whole year), retake them again!! Cover up the answers and go for it! I know it seems like a lot of work, but it’s the surefire way of knowing if you really get the stuff. If you don’t have time to go through all the tests, go through the ones that were at the beginning of the learning period and also the ones where you didn’t do the greatest.
If you can’t get your old tests back, try to work any packets, homework, or chapter reviews covering the material. Just pick out one or two problems covering each concept.
If you’re having trouble with any of the concepts when working problems, create a “cheat sheet” (not for the test! lol) of notes that you need to study. Remember that some things (actually a lot of things) in math you have to memorize – that’s OK.
Glance over your notes one more time to see if you missed anything after doing steps 1 and 2 above. This is not good enough though; you may think you know how to work a problem by looking at your notes, but you don’t really know unless you actually try it! If you’re unsure about a concept, you might even check out She Loves Math!
One more thing – Reviews can be deceiving!! Don’t rely on them; many times, they don’t cover everything on the test!
Good luck, and let me know if you have any questions about anything. And of course, when you’re taking the test, skip over any problems that stump you, put a big circle on it, and come back to it. Time can be your enemy with math tests and we’ve all had those brain lapses. Try not to let those times affect the rest of the test.
Happy Mathing and have a wonderful summer! I hope to do a lot of She Loves Math writing this summer!
When solving linear inequalities, you can solve as if you have an equality. You must have the variable on the left hand side when you use these rules to know where to graph:
When you have the less than sign (<), you want to graph to the left (both start with “le”); when you have the greater than sign (>) you graph to the right.
You can also graph in the direction where the inequality sign is pointed.
You can also plug in a number to see if it works: if it works, it should be on the colored part of the number line – like 3 is for the inequality “x < 4” (since 3 is less than 4).
Here are some examples, including the solutions in Interval Notation. Remember that with Interval Notation, you always go from lowest to highest number with “(“ (soft brackets) if the inequality doesn’t hit the point, and “[“ (hard brackets) if the inequality does hit the line. If you have to skip over any numbers, you do so by using the “U” sign, which means union, or put the things together.
Note that when you solve an inequality, you pretend like the inequality is an equal sign. The only thing you have to worry about is multiplying or dividing by a negative number; when you do this, you have to reverse the inequality symbol (change < to >, or > to <). You can see an example of this in the last equation below. The reason we need to do this, is when we have a negative coefficient(what comes before the variable), we’d eventually have to move the variable with it’s coefficient to the other side and make it positive, so it would be on the other end of the inequality sign.
At this point, we are not multiplying or dividing by variables (since we don’t know the signs of them); we will learn how to do that later.
I always loved foreign language in school, and like to think of math like just one more language, when it comes to (the dreaded!) word problems. So in the Algebra Word Problems Section, I put together a Math-to-English Translation Table, which covers some of these conversions:
An Example: “Find the Numbers” Word Problem (only using 1 variable):
The sum of two numbers is 18. Twice the smaller number decreased by 3 equals the larger number. What are the two numbers?
Ok, so we always have to define a variable, and we can look at what they are asking. The problem is asking for both the numbers, so we can make “n” the smaller number, and “18 – n” the larger.
Do you see why we did this? The way I figured this out is to pretend the smaller is 10. (This isn’t necessarily the answer to the problem!) But I knew the sum of the two numbers had to be 18, so do you see how you’d take 10 and subtract it from 18 to get the other number? See how much easier it is to think of real numbers, instead of variables when you’re coming up with the expressions?
We don’t need to worry about “n” being the smaller number (instead of “18 – n“); the problem will just work out this way!
I always like to teach the major units of the metric system with a King Henry mnemonic (a mnemonic is a way to use familiar words to remember something). The following table will help you with the different units used with the metric system. The middle column is the standard unit (main measurement), or the base unit. Note that the units beginning with “dec” have to do with tens or tenths, the units that start with “cent” or “hect” have to do with hundreds or hundredths, and the units that start with “milli” or “kilo” have to do with thousands or thousandths. These are Latin and Greek stems of words.
So this means that 1 meter is the same as 10 decimeters which is the same as 100 centimeters, and so on. It also means that there are 1000 meters in a kilometer (since a meter is of a kilometer). If you get confused between “deca” and “deci” remember that a decathlon is a series of 10 events in sports.