by judiethcarol&rocketcat
Three concepts to learn to reap many, many more points on every standardized math test--including the SAT:
1. slope (the graph, the ratio, the formula, the terms--and even the letter that is usually used to indicate the unknown number for slope:m)
2. order of operations (use the most common mnemonic to remember the order: PEMDAS (parentheses, exponents, mulitiplication, division, addition, subtraction)
3. Pythagorean theorem (Greek name and square roots, even names for the sides of the right angle triangle) This is a favorite for standardized test because the visualization, and the codes are standardized already. This is all about a triangle that has a right angle (90 degrees) and the longest side of the 3 sides of the triangle is across from that right angle.
That side of a right angle triangle has its own name. The longest side of a triangle with a 90 degree angle is the hypotenuse. This is generally the side with the label c. The other two sides have the name 'legs' in these right angle triangles. They generally have the labels: a and b. Even though the formula is usually written with a,b, and c. You need to remember that these are labels for the unknown numbers in this type of triangle. The letters could be different. They stand for particular sides of the triangle. On a standardized test they are probably going to call these sides a,b, and c with c being the longest side, the hypotenuse.
I'm not sure what makes my post disappear when I have been composing, but this has happened before.
Instead of talking so much about the classic problem about slope that is in today's example, let me tell you that there WILL be problems about slope. Part of what you can predict and learn before the mathematics test is in relation to problems about slope. Visualize the graphs, the steepness of skateboard ramps as opposed to the stretched out manageability of a wheelchair ramp.
Learn that the answer is a ratio. Use this concept to understand the formula and to remember the formula. Look at the same problem as a graph problem. The ratio is made up of the relationship of two coordinated points on a graph of the 'hill' or 'ramp' or 'mountain' you envision. The slope is the steepness--How steep is it? What you are finding, with slope, is the steepness ratio based upon how high UP you go vertically in relation to how FAR OUT you go on the horizon (the x axis).
VISUALIZE: Put a crossbar on top of the drawing of your hill or ramp. The measurement of how high is up and down, the y axis. The measurement of right and left (I sometimes call it east and west in my mind) is the distance you are going out (the 'run') to make the slope easier to manage (think wheelchair ramp). The ratio of the point up the y axis (rise) to the point you go out on the x axis (run) is the slope (m).
Maybe the fact that I had to start over in composing this because my graph and symbols for the formula was whisked away by the blog blotter is better anyway, as what you need to do for mathematics questions on the SAT is: to realize that so much is predictable that you need to be working on the obvious questions right now. Visualize EVERYTHING. Jot down little pictures to do this.
You can gain many more points in the medium and difficult level portions of the SAT in math if you use a few minutes a day for a few days to learn how to do the following types of questions:
1) There will be questions about slope involving ratios (because slope IS a ratio) and graphs. The formula to find the slope (steepness) of a ramp (think steep for skateboard and stretched out to make a manageable ramp for wheelcairs (run).
The more a steep (rise) ramp is stretched out (run), the less difficulty in climbing.
Slope questions will sometimes have coordinates on a graph (Yesterday's SAT is a nice, classic drawing!) SAT slope questions will sometimes just check if you can use the formula.
Now that we have talked about slope, come back to see me about some of the OTHER types of problems you will have on the SAT and other standardized tests in the math section. They include:
2) There will be questions checking whether you understand Order of Operations. Some of the questions will have only a couple of steps and still require that you notice the correct sequence. Remember: Doing the actual arithmetic incorrectly can still lose points for you--even if you understand a strange and difficult concept. The thing is: You will be tested to use proper order of operations with tiny problems and with big 'family' problems.
3) There will be mathematical questions that require your understanding of the Pythagorean Theorem. This looks fancy because it has that Greek name and it says that c squared is equal to a squared plus b squared. But what it is really about is a right angle triangle. So look up these problems with right angle triangles--and the terms used for the lines making these triangles (2 shorter sides are 'legs' and the longer side across from the right angle is the hypotenuse. A right angle is 90 degrees. If you are given any 'leg' or line length of the sides of the triangle, you can square the amounts and then find more answers by taking square roots.
Let's say, for example, that a squared plus b squared equals c squared. If a is 4 and b is 6, what is c?
Okay, we have 16 +36 = 42 Therefore, c is the square root of 42. What if your possible answers from which you were choosing were: 16, 4, or 12.20.
Please realize that if you need some quick help with your multiplication tables when you are in the middle of a problem about slope, you can quickly jot down the low numbers and figure while visualizing or you can use your calculator on the multiplication. This is an instance that jotting down will save you time so you can visualize the answer you are looking for by seeing what is too big and what is too small. But you have to know your mulitplication tables. If you have trouble remembering the multiplication tables while doing problems on a test, learn how to check your calculations quickly on the calculator. Use this as why using your pencil and paper on a standardized test can be faster. You can sometimes be more accurate using pencil and paper to figure because of the visualization going on in your mind.
You could eliminate all of these answers because the square root of 42 is going to be more than 4 and less than 16. You know this without doing anything, right, because if square 4 (4x4 )you get 16; but when you multiply 16 x 16--It's too big to be the square root of 42. You don't have to multiply it because you already know that even 12 is too big, right? How do you know? 12 x 12 =144. so the answer is not 16, a bigger number than 12! In fact, the square root of 42 is not something neat like the square root of 16 or the square root of 144 because you know that it is not 6 because 6x6 is 36; then the next number is 7. But 7x7=49. So the square root of 42 is going to be a number between 6 and 7. It will be 6 with a decimal portion (a fraction).
Summary: Practice these types of problems, in various formats of words, graphs, and symbols:
- Use the Order of Operations, mnemonic: PEMDAS.
- Use the formula and graph to find slope. Remember the answer is in the form of a ratio. Thre are two styles to write the RATIO.
- Use the Pythagorean theorem to solve problems relating to square roots
rocketcat&judiethApril2010x
