Wednesday, April 25, 2012

Using the quadratic formula

Why find a personal tutor?

Employing a private tutor was once the preserve of the prosperous few. These days, private teaching is a support available much more widely than any other time. People searching for private instructors have better choices along with personalized help available for learners in a lot of different subjects.
Private tutoring can consist of a specialist teacher attending the actual learners home. Using the growth of the net and high speed broadband, private teaching can also be available online. Several private instructors use a combination of individualized tutoring given on the students home (or any other mutually decided location) along with the possibilities that online studying offers.
Precisely why find a non-public tutor?
Educational institutions, schools, colleges and universities obviously teach peeople. Sometimes it really is individual consideration that really helps make the difference. The effectiveness of one-to-one tutoring, the foundation of nearly all private educating, should never be overlooked. Its not hard to discover why private instructing can be so successful. An experienced instructor will be able to identify where a student has expertise gaps or difficulties 
Private teaching  can be particularly useful for kids, young learners and adults. The increase of on-line tutoring has had help to millions of individuals..
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From homework assistance to more particular subject teaching or test prep, personal teaching  can create a big difference to educational and also career outcomes. In a competing world where qualifications and also achievement count, private tutoring is an option well worth thinking about.
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Thursday, April 12, 2012

Study Skills for Success: Study Smarter, not Harder

Far too many people study harder rather than smarter and end up burning out. Sitting and passing exams is supposed to get you ahead in life – not make you tense and a nervous wreck.
With simple and effective techniques you can massively increase your ability to pass exams. Here are a few tips to get the most out of your study time.
Use lots of color. Using color in note taking and study will increase your ability to remember and recall information. It makes your notes more exciting to reread and learn.
Use felt pens of different thicknesses, colored pencils and crayons. Use your favorite colors, highlight key information, and make notetaking fun.
Talk about the information as much as possible. When you say information out loud, it is reinforced in the brain. Have you ever asked someone to remind you to do something? Do they usually need to remind you? Not usually. When you say something out loud it comes out of your mouth and back into the brain through your ears. Talk about the information you are learning to yourself, friends, family, or even the dog! Just say it out loud.
Study at “my best thinking time.” Are you a morning, afternoon or late night person? Study when you are most alert. If you prefer to stay up late at night, study at this time. One of the worst times to study is the one hour after school. Take time to refresh and relax before doing homework or study.
Study the information you don’t know. This may sound obvious and is a major key to successful study. Take out old test and exam papers and learn the information you got wrong. When you get your test marks back, celebrate if you have a pass mark. However it is the questions you got wrong that are the most important to learn. This is how you will improve.
Study for 20 minutes with 5-minute breaks. Having short study times increases the retention of information and avoids the brain ‘chunking out’ or forgetting. During a five minute break, eat brain food, get some fresh air, or do some quick exercise to keep the blood and oxygen flowing to the brain. Always leave your study environment during this five-minute break to give the brain some variety and a change of focus.
Frame important information. Putting a frame around information makes the brain focus within the frame and can raise comprehension. This is such a simple strategy and works. If you are a doodler and often draw all over the page when listening or thinking, doodle frames around the edge of the page – it will increase your ability to recall and remember the information within the frame.
Review your notes one day after learning them. Reviewing or periodic revision of material is needed to reactivate the stored memories and prevent information from being buried under other data. The more recent, regular, and fun the review is the easier it will be to recall. Research shows if you go over your notes the next day, your recall can stay at up to ninety percent, however waiting three days before you re-visit your notes drops recall down to thirty percent
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Thursday, April 5, 2012

How to Find the Volume of a Shape Using the Washer Method

Geometry tells you how to figure the volumes of simple solids. Integration enables you to calculate the volumes of an endless variety of much more complicated shapes. If you have a round shape with a hole in the center, you can use the washer method to find the volume by cutting that shape into thin pieces. Each slice has a hole in its middle that you have to subtract. There’s nothing to it.

Here you go.
A sideways stack of washers — just add up the volumes of all the washers.
A sideways stack of washers — just add up the volumes of all the washers.
Just think: All the forces of the evolving universe and all the twists and turns of your life have brought you to this moment when you are finally able to calculate the volume of this solid — something for your diary. So what’s the volume?
  1. Determine where the two curves intersect.
    So the solid in question spans the interval on the x-axis from 0 to 1.
  2. Figure the area of a cross-sectional washer.
    In the above figure, each slice has the shape of a washer so its area equals the area of the entire circle minus the area of the hole.
    The area of the circle minus the hole is
    where R is the outer radius (the big radius) and r is the radius of the hole (the little radius).
  3. Multiply this area by the thickness, dx, to get the volume of a representative washer.
  4. Add up the volumes of the washers from 0 to 1 by integrating.
Focus on the simple fact that the area of a washer is the area of the entire disk,
minus the area of the hole,
When you integrate, you get
This is the same, of course, as
which is the formula given in most books. But if you just learn that by rote, you may forget it. You’re more likely to remember how to do these problems if you understand the simple big-circle-minus-little-circle idea.