Today, I've decided to post a blog to review for my midterms. This will be a big help for me, as well as anyone else who really needs it.
Now, to get this out there, my teacher (whom I've never said before) is Mr. Battaglia, and he uses standards to grade us on how we did. For this blog, I will go through some of the standards confusing for most people and I will try to give a quick summed up explanation of how it works.
Let the Standards Begin!
Converting Between Non-metric Units
To convert between metric units, it is imperative to understand that you need conversion factors before you do anything. For example, you cannot convert from feet to yards unless you know that there are 3 feet in a yard.
Now, to better explain this, I will need an example. Let's say that you want to know how many yards is equal to 12 feet (This is an easy one so I can help you understand this better). For this example, we need to know that 3 feet is equal to 1 yard. To convert, there are 2 different methods.
- Cross-Multiplying: To cross multiply, you are basically setting up 2 different fractions and multiplying diagonally. For the example given above, we can do 12ft./x yd.. = 3ft./1yd. We would then cross-multiply and come up with 12 = 3x. Then, the answer is as easy as dividing 12 by 3, and finding out that x = 4yds. When doing cross-multiplication, it is important to remember that you must put the same part of the fractions on the same part. What I mean, is that, if you look at my example, you can see that both the feet parts are in the numerators, and both the yards parts are in the denominators. You cannot have one feet part in the numerator and one feet part in the denominator. Your answer will not come out correctly.
- Dimensional Analysis: The second method to solve these types of problems is to do dimensional analysis. To do so, we will use the same example shown above. When doing dimensional analysis, you would also use fractions. However, you set them up much differently. This time, you would do 12ft./1 = 1yd./3ft. Notice how one feet part is in the numerator and one feet part is in the denominator. There is also no x (variable). This time, instead of cross-multiplying, we would multiply like we would with any other fractions.You would do 12ft. x 1yd./1 x 3ft. This time, since feet are in the numerator and denominator, the feet cancel, leaving you with 12yd./3. Now, your answer is as easy as dividing, and it would come to the same answer of 4 yards.
Converting Between Metric Units
To convert between metric units, we do things a little differently. This time it is easiest to just do KHDUDCM which stands for King Henry Drinks Unlimited Delicious Chocolate Milk. This will help you when converting due to the fact that each letter stands for a metric unit. (Note: There are more metric units larger and smaller than these, so this isn't always the best way to convert). The letters stand for Kilometer, Hectometer, Decameter, Unit, Decimeter, Centimeter, and Millimeter.
Let's get another example. How many millimeters is equal to 5 meters? To do this, all we are going to do is start at U (since meters is a unit) and move the decimal place 3 to the right due to the fact that you would move three on KHDUDCM scale to get from Units to Millimeters. This would make your answer
5000 millimeters.
Note: You can move right and left depending on which way you need to convert. Going right tends to make the number bigger, and going left makes it smaller.
However, this is only the easy way. It is also possible to use dimensional analysis with this when using even bigger or smaller units.
Converting Between Standard and Scientific Notation
For this standard, you kinda have to think about it. Logic almost always plays some kind of a role in science.
Anyway, to convert between the two, we are going to have to slide the decimal place like we've done before. Let's say our number is 5,000,000, and we want to convert to scientific notation. Really, all we would do would be to slide the decimal place to the left until we get to the 5. Then, we would count how many times we slid. For this example, we slide 6 to the left. Now, the question is, do we have a negative exponent or a positive exponent. Well, we have to think about it. Positive exponents make the number bigger, while negative exponents make the number smaller (if we were going from scientific notation to standard). So, if we put this together logically, we can realize that we need to use a positive exponent, making our answer 5 x 10^6 or 5 E 6 (they mean the same thing).
If that was a little too confusing, let me explain going from scientific to standard. Let's say our number is
5 x 10^6. I am purposely using the same example from above to help you understand. Again, think about it. Positive exponents make a number bigger, so if we work opposite of what I showed above, we would move the decimal 6 times to the right, adding zeros and making the number bigger so that it is 5,000,000.
I'll do one more example. This time, you want to know the standard from of 2 x 10^-3. This time, you would notice the exponent. This is your hint to tell you that you need to make the number smaller because negative exponents make numbers smaller. This time, you would move the decimal 3 times to the left, making your answer 0.002.
Extra Help With the Different Types of Graphs
Our three types that we learned were position vs. time graphs, velocity vs. time graphs, and acceleration vs. time graphs. Since I'm pretty positive that acceleration vs. time graphs will not be on the exam, I won't be discussing it (unless you need it).
Notes for Position vs. Time graphs:
- The slope is equal to the velocity.
- The y-intercept is the starting point.
- The x-axis (as far as I've observed) is the reference point.
- Displacement is equal to final position - initial position.
Notes for Velocity vs. Time graphs:
- The slope is equal to acceleration.
- The y-intercept is the starting velocity.
- Displacement is equal to the area under the curve.
Other types of graphs that we've done include:
- Linear: a straight line.
- Proportional: When x doubles, y doubles (or anything like that) and it goes through the origin.
- Direct: When x increases, y increases.
- Indirect: When x increases, y decreases.
- Inverse Proportional: When x doubles, y halves.
What the graphs look like:
- Quadratic: Looks like the letter "U" or and upside-down letter "U".
- Polynomial: Basically either a quadratic or a curvy line.\
- Inverse Square: The curve that never touches the x-axis and the y-axis, EVER.
- No Relation: Usually something like a scatter plot. (Scatter plots are graphs that are basically just graphs covered in dots).
Explaining the Meaning of Slopes
Slopes can be explained with a "for every" statement. If your slope is 2 for a position vs. time graph (meters per second), your slope would be 2 meters/second (this would also be the unit for the slope in case you needed help with units). To explain with a "for every" statement, you would say, "For every second time increases, the position increases by 2 meters."
Explaining the Meaning of y-intercepts
Y-intercepts can also be explained, but in a different way. If your y-intercept is 5 for a position vs. time graph (meters per second), you can see that your position is 5 and your time is 0. To explain, you can say "At a time of 0 seconds, the position is at 5 meters. This would be your starting position."
In Conclusion...
To end my blog, I just want to let anyone out there know that I really hoped this helped. If you have any questions, you would like me to explain something a more, or you would like me to explain another topic, just let me know in any method (comments, email, etc.).
Also, anyone out there who has to take this exam, I wish you the best of luck! You will all do fantastic!
