Thursday, April 12, 2012

How Mathematics Help Brain Concentration & Memory


Math is one of those charged words that make people either excited or queasy. For the people who have no trouble thinking logically and can problem solve using different skill sets math is a fun and engaging exercise that helps form new ideas, solve complex problems and create new ways of thinking. However math can also be very intimidating and reduce even intelligent people to tears trying to factor for "x".

Unfortunately the way math is taught in most public school systems it really is a matter of you get it or you don't. While some people genuinely display a high aptitude for mathematics it doesn't mean that people who aren't as gifted with numbers can't grasp the basic concepts of math and use simple problems to help improve several areas of their brains including spatial relationships, cognitive ability and problem solving.

A common gripe regarding math is heard by plenty of school children who rightly ask 'when will I ever need this'. It's a fair question since life isn't laid out like an equation and we rarely are asked by a retail clerk if we'd like to see a variable of the product we are interested in. However, what math essentially teaches us is how to use our brain's ability to problem solve, which is absolutely necessary to make it through every day life.

When looked at from a mathematical perspective life is really a series of problems for us to overcome: what will we eat, how will we get the food to eat, how do we prepare the food, what do we do with leftover food... these apparently mundane and trivial tasks are actually quite complex functions in the brain that require a string of neurons and code that make us capable of going to a store, buying a chicken, cooking it and storing the leftovers. Surprisingly enough these simple tasks can become rather difficult when stress is factored in. Being able to streamline our thoughts to make better decisions is where math problems come in to play.

When you train your brain by using simple math problems you actively exercise several areas of the brain that are responsible for decision making, thought processes and critical analysis. Math whether it is geometry, algebra or calculus sharpens the mind by forcing the brain to think differently for ways to solve different problems. The more skilled you get at solving problems the more difficult challenges you will be prepared for. Instead of seeing numbers and variables try to look at math as tasks that need solutions. Another trick to making math easier to understand is to not only think of the numbers in terms of money (a concept most people can grasp) but as your money therefore making it relevant to you specifically. When you see how math affects every aspect of daily life then you will begin to understand how equations aren't set up to confuse you but to help train your brain to think through problems using all the resources your brain contains.


Wednesday, April 11, 2012

Do SAT Preparation Courses Really Work?


For decades, colleges have relied upon the SAT Reasoning Test as a tool for determining a student's eligibility for enrollment. Not surprisingly, courses of all shapes and sizes have emerged professing the ability to markedly improve student scores. In parallel to the claims of the SAT preparation courses has been the mantra of those who suggest that, not only are SAT courses unable to significantly raise test scores, but that the SAT is a "pristine" exam immune to such efforts. In order to answer the question "Does SAT preparation really work?" it is necessary to carefully consider the positions of both camps.

One might argue that, as a seasoned SAT expert, author, and instructor, I have a particular interest in promoting the virtues of SAT prep courses in general, but this could not be further from the truth. What almost three decades of SAT preparation expertise has instilled in me is an interest in promoting effective SAT courses and steering students away from so many ineffective options. Those courses that routinely fail to produce desired results are detrimental to the test preparation industry as a whole! Any objective discussion of SAT preparation success or failure must begin with a consideration of statistics. Some "experts" have suggested a very simple study involving a few hundred students, some of whom receive coaching and some of whom do not. The results can then be statistically analyzed to determine whether or not SAT preparation really works. Sounds simple, logical, and fair, right? Wrong! In fact, such a simplistic compilation would result in grossly inaccurate, misleading data and erroneous conclusions. While I applaud the idea of an unbiased, statistical evaluation, a truly fair and accurate study would prove to be profoundly complicated and complex.

Here's why. In order to begin such an analysis, one would first have to sift through literally hundreds of SAT courses to find a suitable preparation vehicle. The sad truth is that a great number of SAT courses simply do not work, and some of them are miss the mark entirely. Approximately fifteen years ago, one of the major financial periodicals published an eye opening expose' concerning the plethora of ineffectual and, perhaps, fraudulent SAT coursework on the market at that time. I dare say that, today, those numbers seem to be on the increase. Armed with false promises and fictitious data, such organizations bilk customers out of thousands of dollars, yet are no longer limited to small, local, no-name organizations. Students who unknowingly subscribe to such programs typically assimilate little or no insight into the nature of the SAT test itself and realize little or no score improvement. Whenever I interview students who have come to me after completing any SAT course, I routinely ask a few fundamental questions such as "How many sections comprise a typical SAT?" Amazingly, more than half of those students are completely unaware of the structure of the exam! Would it be fair, then, to include data from such courses in a statistical analysis?

Let us not forget to include many high school-generated prep courses among the ineffective. Those make-shift (albeit well-intentioned) programs, which the schools once offered free of charge but can now cost hundreds of dollars, lure thousands of students each year! The problem with these courses is that, by and large, high school mathematics and English teachers (not SAT experts) present the coursework. While these teachers may be highly-skilled educators with considerable knowledge and expertise in specific subjects (algebra, geometry, writing, grammar, etc.) they are generally untrained in the explicit reasoning skills necessary to master the SAT. Practically every student whom I have interviewed who has attended such a course has felt that the preparation was at best a waste of time. Indeed, some have emerged discouraged, disgruntled, and opposed to any further preparation! Are we also to include those data in an objective analysis?

And what about the group-oriented programs that routinely hire SAT instructors of limited insight and experience? A few years ago, a woman boasting of a whopping six-months' SAT instructional experience, called me requesting employment. Although I certainly did not hire her, I would bet that a number of companies would be perfectly willing to do so in spite of her extremely limited experience (expertise is so very important that I never permitted any of my tutorial staff to teach SAT prep). Are those companies to be ranked equally with the one-to-one preparation of seasoned SAT experts? To understand this, let's consider dining as an analogy. No one would believe a fast-food chain to be comparable in quality to a five-star restaurant, but the fast food joint does have several major advantages. A large fast-food chain can serve far more customers than can a single dining establishment, and can do so at a considerably lower price. A customer willing to sacrifice quality for price and availability would be far better served at such an establishment.

Does the analogy extend to SAT preparation, however? In some cases it does. A number of SAT experts are simply too high-priced ($400-$500 per hour) for the average customer, and have chosen to offer their services to those willing and able and afford them. When it comes to SAT coaching, however, price is not at all a definitive indicator of quality. Some of the most highly skilled experts offer their services at relatively moderate prices (comparable to those of the "fast-food" courses), while certain neophytes are happy to charge exorbitant prices! Clearly, no rational person can justify lumping such diverse data into the same statistical bundle while, at the same time, professing to objectively analyze the general effectiveness of SAT preparation coursework.

In addition to discussing the disparity in quality among SAT programs, we must also consider that of the students themselves. Even the best of SAT courses will inevitably entertain a certain number of unmotivated clients, and compliance has always been a primary component of SAT preparation. Although a number of SAT "programs" promise success with little or no study or homework (indeed, some profess to prepare a student in a weekend or two) no legitimate SAT course can offer something for nothing. A student unwilling to complete his or her assigned work is unlikely to show a major improvement in score. There are also certain numbers of students with inherent learning difficulties. Those students may to show less improvement than students of average ability. Is it fair, therefore, to include all students in an overall analysis?

This brings me to another important factor in determining the success or failure of an SAT preparation course. Just how does one evaluate improvement? Unaware that I am an SAT instructor, a representative from another SAT prep company contacted me recently peddling his company's services on the promise that a student will improve his or her score by at least 100 points. So I asked him, "If a student came to you with a prior score of 2300, do you promise a perfect score of 2400 upon the completion of your coursework?" Not surprisingly, his answer was "Well...er...no." I then asked him whether a student can expect a 2300 if he or she started with a 2200. Although I did not set out to put this fellow on the spot, I did intend to point out the sheer ludicrousness of his company's promises. As SAT scores increase, incremental improvements are, naturally, much smaller. Indeed, a fifty point increase from 2100 to 2150 may be just as significant and may require just as much diligent study and effort as does a 200 point increase from 1700 to 1900! So where exactly does one begin to evaluate the significance of score improvement? In the absence of complicated statistical adjustments, gifted students with high initial SAT or PSAT scores would actually diminish numerical averages even though those students may have experienced satisfying increases in total score!

Unaware of such statistical complexities, well-intentioned parents routinely inquire as to a particular instructor's rate of success. Understandably, potential clients would like to know the average increase in score that they can expect after taking a particular course. I am sure that, to some of these folks, my answer must sound somewhat convoluted. On one hand, I can certainly say that the majority of my students show a marked improvement in score, but I cannot present any hard numbers without meticulously filtering the data. In the absence of my deleting unmotivated and learning disabled student performances and adjusting for high initial scores, the numbers would be misleading, and I am sure that this dilemma extends to other SAT courses as well. Therefore, when a parents make such a request (as all prospective clients should), I give them a reasonable estimate of expectation based upon students who are similar in scholastic performance, motivation, etc. to their students.

Hopefully, one can now begin to appreciate the fallacies and limitations associated with simple statistical analyses. Depending on the variables selected and controlled, a simplistic compilation and analysis could produce dramatically varying results which would, in turn, lead to erroneous conclusions. If one were somehow able, however, to eliminate from the equation all of the factors that would unfairly diminish the averages, it is my contention that one would notice a remarkable average increase in performance after completing a legitimate, high-quality SAT program taught by a seasoned SAT expert, but the experimental conditions would, by definition, remain extraordinarily complex.

That said, let us turn our attention to those who, even to this day, insist that it is virtually impossible to significantly improve an SAT score. In 1995, the same year that the College Board changed the test title from SAT to SAT 1 and altered the test format, I began to hear rumors that the new design was supposed to be preparation-proof. Those rumors turned out to be utter nonsense (the newer format actually proved somewhat easier to prep than was its predecessor), but it is interesting that someone, somewhere, had felt compelled to circulate them. Thankfully, one hears such nonsense less frequently today than a decade ago, but some folks still believe in the "pristine" nature of the SAT and continue to disseminate the rumors. Although, we may never know the source of that myth, we are well aware of its impact... every year, the misassumption that the SAT is not teachable prevents some sadly misled students from actively working to improve their scores!

In the early 1990s, rumors began to circulate suggesting that the College Board (the company that designs and administers the SAT), in an effort to promote the purity of the SAT test design, might have been one of the original proponents of this myth. These rumors may have been the result of the notion that, if the College Board were to have admitted that SAT preparation courses were valuable assets in improving scores, such an admission would be tantamount to an acknowledgement that the test was not even close to being the "pristine" evaluation tool that, ideally, many people thought that it should have been. Such an admission would, in turn, open wider the Pandora's Box of cultural and economic bias claims... "The rich can afford the prep courses that will ultimately get a student into a prestigious college or university." Nonetheless, whether or not College Board originally promoted the notion of a pristine test, it clearly has not done so for many years. As a matter of fact, the College Board currently markets its own SAT preparation coursework, an indirect suggestion, that one can, indeed, improve one's scores through study and practice!

Yet, in spite of overwhelming evidence substantiating the value of good, solid, SAT-specific preparation, there are still those who diminish or even deny it. Although relatively few in number today, those who would oppose SAT preparation coursework tend to fall into one of two categories: parents who, after subscribing to such a course, have witnessed poor results, and high school counselors and teachers who, years ago, had fallen for the rumors but who have never taken a hard look at the facts.

And those facts are becoming more and more evident each year...the SAT would seem to be a test that yields readily to proper study protocols. Pragmatically speaking, is it not reasonable to suggest that, if SAT preparation truly cannot significantly improve a score, then no one would improve as a result of such preparation? The fact that so many students do improve, however, attests to the value of SAT prep. Although statistics suggest that a score may increase by as much as forty points (about four correct answers) by simply retaking the test, those statistics do not account for the 100-400 point increases that seasoned, professional SAT experts routinely produce. Moreover, merely retaking the test without concerted study is no more than a toss of the dice; a student may or may not improve (and may do even worse). I recall a seventeen year-old high school student who had come to me after taking the test five times and getting roughly the same score at each sitting. That is not an isolated incident, either. Rarely have I seen a student improve his or her score by merely retaking the test!

Clearly, therefore, there are important factors to consider before subscribing to an SAT preparation course. An inappropriate or hasty decision is likely to result in a dismal, discouraging outcome. The following is a list of criteria that I recommend any student interested in preparing for the SAT Reasoning Test take into consideration:

1. Accept the fact that not all SAT prep courses (including some of the more popular ones) are likely to produce substantial results. Avoid the temptation to subscribe to a particular course simply because "everyone else is" or because "the company has made an elaborate presentation at your high school or because you have seen or heard advertisements promising results.

2. Seek a one-to-one or small group environment with a specific, seasoned SAT expert (not merely "someone on staff"), and be sure to inquire as to the number of years that the instructor has coached SAT.

3. Plan on several months' training (typically one or two sessions per week). Most students simply cannot assimilate SAT skills in a few short sessions or in an accelerated program of daily coaching.

4. Be committed to a concerted practice regimen... Input increases the probability of a desired outcome.

5. Beware of programs that "guarantee" results. Some courses may promise a small increase in score that may sound substantial to an unsuspecting client. Does the guarantee really mean, however, that a client will get a full refund if the student does not achieve a certain score, or does it simply mean that the student can sit through additional classes free of charge? The important point here is that there is no way that any SAT program can be certain that a student will show marked improvement.

6. Be suspicious of courses eager to accommodate a student's every whim. While such "feel-good" programs may appear to be client-oriented, they are probably not results-oriented. Remember that students will typically do as little work as they are permitted to do, so it is up to the instructor to maintain a reasonable amount of control and to expect a specific level of compliance.

Although I certainly allow for a limited amount of flexibility, as a general policy I will not work with students unwilling to accept all of the terms listed above. Experience has taught me that any student who does not commit to a strict protocol will simply waste time and money and will occupy an appointment slot that a serious student could use. For students eager and willing to put their shoulders to the wheel, however, SAT prep can be a remarkably rewarding venture. The key is to shop carefully, be selective, and work hard.


Tuesday, April 10, 2012

I Am Having Trouble in Math Class, I Want to Ace My Mathematics Final, I Studied All Night


Okay so, let's say you are having trouble in your mathematics classes, and you want to ace the final exam, but you are just having one heck of a time trying to memorize all the equations you need for all the different types of problems. Well, if you have solid algebra skills, and are good at factoring, you should do fine as soon as you learn the formula's right? I agree and so maybe we should discuss a little bit about how the logical part of your brain works, and why staying up all night, the night before your exam may not be so wise.

First, it is perfectly natural to have trouble sleeping the night before an important day, and a math final is exactly that, as how well you do in math matters very much in success in life. Now you might feel better if you stay up all night studying, and you will be telling yourself that you are really learning and you are going to ace that test, but the reality is that you are more likely to do poorer on it if you lack concentration and make silly mistakes causing you to miss answers.

You see, proper human health sleep is required, and just like any long-distance truck driver will tell you it is a matter of conditioning how long one can stay up and remain in solid concentration. If you don't often stay up all night studying, I wouldn't make a special exception for the test, no matter how much caffeine you throw into your system.

The U.S. Navy had done many tests in World War II, and during the Vietnam War, along with the U.S. Air Force on how long pilots could stay mentally prepared for combat. There were all sorts of chemicals induced into the brain, and even to this day they study these kinds of things. It is amazing what the human brain can do when put under certain circumstances.

Still, proper sleep, even 10 hours before the test, with 2-hours to become fully awake will help you do better on that test and improve your concentration during the test. Those folks who do stay up and all night will find that much of their memory may not work as well as they had hoped for during the test, therefore even though they have put in all that time studying, they may not do as well.

Mathematics and classes which require logic skills are not the ones you should pull all-nighters for the night before the final exams, because they require a lot of concentration, and accuracy, something that you lose when you don't get enough sleep, and Red Bull, aside, I'd recommend not to go there. Study and learn your math the right way, it's one of the most important subjects. Please consider all this okay?


Monday, April 9, 2012

I Am Having Trouble in Math Class, I Want to Ace My Mathematics Final, I Studied All Night


Okay so, let's say you are having trouble in your mathematics classes, and you want to ace the final exam, but you are just having one heck of a time trying to memorize all the equations you need for all the different types of problems. Well, if you have solid algebra skills, and are good at factoring, you should do fine as soon as you learn the formula's right? I agree and so maybe we should discuss a little bit about how the logical part of your brain works, and why staying up all night, the night before your exam may not be so wise.

First, it is perfectly natural to have trouble sleeping the night before an important day, and a math final is exactly that, as how well you do in math matters very much in success in life. Now you might feel better if you stay up all night studying, and you will be telling yourself that you are really learning and you are going to ace that test, but the reality is that you are more likely to do poorer on it if you lack concentration and make silly mistakes causing you to miss answers.

You see, proper human health sleep is required, and just like any long-distance truck driver will tell you it is a matter of conditioning how long one can stay up and remain in solid concentration. If you don't often stay up all night studying, I wouldn't make a special exception for the test, no matter how much caffeine you throw into your system.

The U.S. Navy had done many tests in World War II, and during the Vietnam War, along with the U.S. Air Force on how long pilots could stay mentally prepared for combat. There were all sorts of chemicals induced into the brain, and even to this day they study these kinds of things. It is amazing what the human brain can do when put under certain circumstances.

Still, proper sleep, even 10 hours before the test, with 2-hours to become fully awake will help you do better on that test and improve your concentration during the test. Those folks who do stay up and all night will find that much of their memory may not work as well as they had hoped for during the test, therefore even though they have put in all that time studying, they may not do as well.

Mathematics and classes which require logic skills are not the ones you should pull all-nighters for the night before the final exams, because they require a lot of concentration, and accuracy, something that you lose when you don't get enough sleep, and Red Bull, aside, I'd recommend not to go there. Study and learn your math the right way, it's one of the most important subjects. Please consider all this okay?


Sunday, April 8, 2012

How to Approach Math Word Problems on the Pharmacy Tech Exams


The Big Secret: Don't think about the problem until you write down all of the factors.

Sounds too easy, right? But it's where everyone gets stuck. Start by carefully reading over the entire question from start to finish and decode the important factors. Then, go back and slowly read it again, writing down only the necessary factors. Factors aren't just numbers, but also things like days, percent signs, p.m., or whatever will help keep things straight for you. Also, neatly write numbers below or above numbers that will be added or subtracted and set-up any fractions.

Write an Equal sign where it belongs

This is critical; the equal sign is like a trigger to our brains that we've been taught since 3rd grade. Now that the problem is written in terms with an equal sign in place, the light will generally go on and you'll start working the problem. From here, the only hang-ups you may encounter are things like not knowing conversions or needing to convert to all like factors. Even if you write down the factors wrong the first time, you'll likely see how to re-arrange them and get started.

Sloppy writing is not allowed in math:

Your success at math is contingent on writing all of the factors neatly and organized. When you come across a math word problem, the first thought that should come into your head is to grab for a piece of paper to write it out. As you jot it down, write neatly and leave yourself some space between lines.Beware: Exam writers prey on your bad habits.

When I create practice math word problems for the free practice exams, I have to think up three dummy answers. How do I do it? It may sound sadistic, but I try to consider what answers would come up if someone was sloppy. I think about things like if a factor was left out, or if someone did the equation in a rush, or their head. Exam writers who write for official exams do the same thing. After all, the exams are used to weed out unqualified applicants. If you want to pass the exam, get in the practice of writing things down completely, neatly and organized.

When you get to a question that's a math word problem.

First, relax and know that all of the facts are in there for you to solve it. Then take a deep breath and follow these steps: Don't try to rush or use a short-cut

Read it at least twice

Write down the only necessary factors

Put an equal sign where it belongs

Do the Math

Need some more Pharmacy Tech math practice?

For more FREE help with Pharmacy Technician Math, visit http://www.pharmacy-tech-study.com. You'll find a complete review of math including fractions, percentage concentration calculations, algebra and much more.


Saturday, April 7, 2012

Here's a Way How You Can Compare Different Graphing Calculators


The cost of graphing calculators that are widely used in schools and colleges can vary a lot. In fact, these changes are dependent on built-in algorithms and customizable options that are present in these calculators. It is these options that make calculators a desirable device to solve complicated math that one gets to encounter almost daily. According to a rough estimate, these calculators can cost you anywhere between $55 and $250. When there is such a difference in the price rate of these models, it is apparent that the costlier ones have added features that are totally absent in lower range models. Hence, it is very important to compare different graphing calculators to get the best out of them.

One of the best ways to kick start your comparing process is to look at the onboard memory of the calculator. Don't be surprised to see plenty of options here. HP is a known player in this segment. This manufacturer produces calculators with different memory capacities. They have calculators that have a memory capacity of 32KB all the way up to 1.3MB. The greater the memory capacity, larger will be its storage capacity for calculator games, onboard notes and other extra applications. If you are sure that you will not be required to add extra notes or programs, get a lower-capacity model through which you can save lots of money.

Connectivity options are another aspect you need to go through while comparing different graphing calculators. This is particularly a relevant factor for anyone who intends to upload custom programs. Make sure that you compare the 4-pin connectivity, 10-pin, and USB for each of these graphing calculators. At the end of the day, the chosen calculator has to be able to hook up to your computer easily.

You also need to watch out for different built-in equations and functions. Most of these details can be found out in the packaging itself. The manufacturer in all probability would have indicated the type of math it is designed for. Most of the graphing calculators that are manufactured these days are able to carry out simple tasks related to statistics and algebra. However, to carry out complicated tasks related to calculus, trigonometry, and geometry you might need the help of higher-end graphing calculators.

Once you buy a graphing calculator you cannot leave behind its accessories far too away. While you are doing shopping for graphing calculators make sure that you don't place too much attention at its sticker price. You might always feel the need for extra batteries for power, cables for computer, and even a carrying case for portability. Opting for a package that gives all these accessories and more at a higher price is a far better option than picking all of them individually and at different prices. If you want to make use of your graphing calculator for specific tests like ACT or SAT, make sure that the chosen calculator is on the approved list. For this, you will need to check the manufacturer's website or calculator's package.


Friday, April 6, 2012

What Makes Algebra So Difficult For Kids To Understand And Challenging for Teachers To Teach?


At first glance this seems to be another Chicken or the Egg situation. Are kids not understanding because Algebra is a subject that is difficult to teach or is Algebra difficult to teach because kids have so much trouble understanding it? In reality, there is some truth to both of these issues; and, theoretically, solving one will solve the other as well. So, exactly what is it that makes Algebra so unique?

Algebra is like a giant question mark in the brain of every freshman who walks into the classroom. These 14- and 15-year old students enter the classroom having absolutely no expectations of what they are going to be learning; and teaching Algebra successfully is one of the greatest educational challenges existing today.

Students in elementary school know just exactly what math was covered in each grade and what is coming next year. Addition, subtraction, multiplication,... They know. In high school, at the end of Geometry, Trigonometry, and Calculus, students can explain to you what the course was about. But Algebra is a different kind of animal. Too often Algebra teachers assume their students know what Algebra is, so Day One of school is Section One of Chapter One in the textbook and off they go on their unknown journey. Sadly, many students are as clueless at the end of the school year as they where at the beginning as to what they have been studying. Some students can tell you they solved(?) equations, they factored something, and they graphed things. Some students can actually be good at Algebra skills, but still have no idea why they were doing any of it. That's very sad.

The numerical skills required in Algebra (the HOW) are really pretty basic. It is the understanding of the WHY and WHEN that students don't get. But is this a student issue or a teacher issue?

Students issues to consider:

(1) knowledge of multiplication facts is the #1 indicator of success in Algebra, yet many students enter Algebra with weak multiplication skills,

(2) most students are lacking the ingrained sense of "I am smart enough" that they possessed when learning language,

(3) many students have lost the persistence they demonstrated when learning to walk, talk, and read,

(4) most students lack a pre-school math foundation similar to what parents provide for language skills,

(5) unlike all previous math courses in which only 25% of the material is new (never seen before), the amount of new material being covered in Algebra is approximately 75% of the course which seems to be too much for them to absorb,

(6) the pace required to cover so much new material seems too fast for students to absorb, and

(7) many Algebra students see no practical application to their lives, so they view it as unnecessary to learn. Have I missed any student issues? Probably, but you get the point.

Teacher issues to consider:

(1) the assumption that students already know what Algebra is is incorrect,

(2) teachers sometimes don't recognize that the problem is weak basic skills until the damage is done,

(3) the large amount of new material to be covered does not allow for proper processing but teachers do not have a choice about removing some of the subject matter,

(4) some teachers are weak at task analysis, (5) a few teachers have trouble explaining a topic several ways to deal with the different ways students learn, and

(6) No Child Left Behind has caused immeasurable harm to mathematics education and the learning environment. Again, you get my point even If I missed something.

In spite of all the issues I just listed, it should be noted that this "problem" has existed literally forever. The failure rate was 50% when I started teaching in 1972 and it still is. Many attempts have been made over the years to solve these issues. Nothing has been successful. So the answer to the initial question is: we don't know. If we knew, the issues would get solved.


Thursday, April 5, 2012

Elementary Algebra


'Elementary' as the name suggests, is the 'basics of algebra'. Beginners start with elementary algebra. If a person has no knowledge beyond that of arithmetic (basic calculation that involves addition, subtraction, multiplication and division), he has to start with Elementary Algebra.

In algebra, we use variables instead of numbers. Variables help in generalizing the concept of problem solving so that in case we have different values, but a similar situation, then simply changing the values of variables will help.

There are many laws that have been derived from years of study and inference that make algebra very easy for calculation. The very basic rule is that the polynomial of highest degree will be placed to the leftmost, and the degree decreases as we move from left to right. The constants (numbers) are to the right hand side (RHS) of the "=" and all the variables at the left hand side (LHS). A system is 'solvable' if there are at least as many equations (or statements) as the number of unknown variables.

To master the art of algebra, one must study the properties of real numbers thoroughly (associative, distributive etc.).

Examples of Linear Equations: 3x + 100 = 250.

Examples of Quadratic Equations: (x+1)(x+2)= 12.

Examples of System of Linear Equations: 3x + y = 25, x - 2y = 5.

Apart from all the positive points in algebra, another is that it also defines "unsolvable problems". If an equation does not have any possible solution, then the system of equations is unsolvable.

Similarly, there can be system of equations that have multiple or infinite solutions. Such systems are classified as "undeterministic"

Systems with more number of variables and lesser number of equations are called "undetermined". Such systems also fall into the category of undeterministic because they're solution cannot be determined, but since its because of lack of information it is placed into a different category of equations.

Similarly, the system of equations with more number of equations than variables is called "overdetermined". In this category, we have repetition of information. Usually there are factors of the same equations repeated.

Now, proceeding with the examples will give you more experience in this field. Remember "there are no short cuts in mathematics, only practice".

Starting algebra from the basics and then moving to the complex variations would be better in case you're a learner and scared of mathematics. After all, we all aim at reducing our problems, don't we?

Happy problem-solving!


Wednesday, April 4, 2012

Mastering Algebra - The Equation of the Circle


As one of the conic sections, the circle is probably the most important of these curves. When studying analytic geometry (the relationship between the algebraic formula for a curve and the actual graph) students are required to learn how to recognize the circle as well as to graph it. Here we discuss the simplest way to recognize this curve, put it into suitable algebraic form, and graph it on a coordinate grid.

The formal definition of the circle is the locus, or site, of points that are all equidistant from another fixed point. The set of points forming the circle outline its circumference; the fixed point is the center. The distance from the fixed point, or center, to any point on the periphery of the circle is the radius.

When in standard form, the equation of the circle takes on the following form: (x - h)^2 + (y - k)^2 = r^2. The center is located at the point (h,k) and the radius is r. Once we get the algebraic equation into such form, graphing could not be easier, as we simply plot the point (h,k) on our grid, and then go r units from this point up, down, to the left, and to the right. We then do our best to connect these points by a smooth circle.

To put the equation into standard form often requires a technique known as completing the square. As in life, the things we usually need require some work to get and this is no different in mathematics. Most equations are not so neat and tidy so as to be in standard form at first blush; therefore, we need to manipulate the equation a bit to get it into good form. This is not difficult however, and we shall show by example how this is done. Once in standard form, the center and radius are obvious and the graph becomes readily accessible.

Take the equation x^2 + y^2 + 2x + 4y - 4 = 0. This is obviously not in the form (x - h)^2 + (y - k)^2 = r^2. However, with a little manipulation, we can put this into such form. This procedure works no matter what the equation, as long as the equation is that of a circle. The only things that change are the numbers. Thus once you follow this procedure, you can put any equation which will produce a circle into standard form.

First isolate both the x and y terms and write as such: x^2 + 2x + y^2 + 4y - 4 = 0. Now bring the -4 over to the right side, and write as such: x^2 + 2x + y^2 + 4y = 4. We now complete the square on x and y by taking half of the coefficient of each and squaring both terms. Half of 2 is 1 and half of 4 is 2. Squaring each of these terms give 1 and 4, respectively, and adding them to both sides of the equation results in x^2 + 2x + 1 + y^2 + 4y + 4 = 4 + 5 = 9. Now we have two perfect square trinomials in x and y. These are always factorable into a form which puts both the x and y terms into standard form for the equation of the circle. The x^2 + 2x + 1 becomes (x + 1)^2 and the y^2 + 4y + 4 becomes (y + 2)^2. Notice that the h and k are -1 and -2, the opposite of what is inside parentheses. Notice also that the 1 and 2 are the terms which were derived by halving the coefficients of the x and y terms.

Thus we have x^2 + y^2 + 2x + 4y - 4 = 0 becomes (x + 1)^2 + (y + 2)^2 = 9. Observe that 9 is 3^2. Consequently, we have (x + 1)^2 + (y + 2)^2 = 3^2. Looking at this equation, we see that the center is (-1, -2) and the radius is 3. From this equation, we plot the center and move 3 units up, down, left, and right. We then draw a smooth curve. This procedure is exactly the same for every circle equation. The only things that change are the numbers.

You now have the tools to slay any circle equation or graph. Just follow the simple procedure above and you will be able to conquer any algebra problem that involves putting circle equations into standard form and graphing. After all, you probably have many other things to put your attention to, such as getting that new iPhone. Now you don't have to worry about circles any more. Enjoy.


Tuesday, April 3, 2012

High School Algebra Finally Pays Off - The Body Fat Equation


When approaching your goals for a better you, every game plan needs to start with determining where you are, and where you want to end up. We're going to talk about some ways to assess where you are -- right now -- so that you can make sure that the goals you have set (or will set) are reasonable. And yes, this will be on the test!

Whenever going into battle, a commander will send out reconnaissance experts to collect information on the size and strength of the enemy. We will continue to use a "battle" theme in this article, because your fight to lose weight and lose fat is nothing short of that.

Just as the commander needs to have a good assessment of what he or she is facing, we need to have an accurate assessment of our current situation so that we can set proper and appropriate goals. An inappropriate goal can insure failure, or worse, cause us physical harm.

If your goal is to look like a swimsuit model in time for your Hawaiian vacation a month and a half from now, you'd better not need to lose more than a few pounds. If your goal is to lose ten pounds per week for the next six weeks, you're simply not being practical.

With that said, what is 'reasonable'? You probably know how much you weigh, but do you know what percentage of your overall weight is fat?

The best way to know is to see a doctor or go to a gym that can calculate your body fat percentage. Normal body fat levels for women are between 22 - 25% and between 15 - 18% for men. Lean people will be slightly less, and athletes even lower. In lieu of that, there is a simple calculation that serves as a good guide, but is no where near as accurate.

This method is called the BMI or Body Mass Index and was created by the National Institutes of Health in 1998. The BMI uses your height and your weight to generate a factor that suggests whether you are underweight, normal, overweight or obese.

The BMI is generalized, so it cannot take frame size into account. If you have a large frame, your BMI will seem worse than it is, if you have a small frame, your BMI will seem better than it is. Use it as a guide and then add a portion of common sense.

In order to calculate your BMI, use the following equation:

BW = Body Weight in Pounds

HI = Height in Inches

(BW / (HI * HI) ) * 703

You will need a calculator to solve this equation.

If you failed algebra, here is the equation in English:

Divide your body weight in pounds (BW) by the square* of your height in inches (HI) and multiply that result by 703.

Once you've calculated your BMI, use the following guidelines to find out how you measure up:

BMI 18.5 AND 24.9 AND 30 You are in the "Obese" zone.

Again, this gives you a rough guide, but it also gives you (possibly) a more realistic view of your current situation.

This more realistic idea will help you to set more realistic and achievable goals, which lead to a greater degree of success!

( * - The "SQUARE" of a number means the number times itself. The "square" of 4 is 16.)


Monday, April 2, 2012

Math Tutoring for the Real World


If you're the parent of a student who is having a difficult time with math, you're familiar with the complaint that equations seem "pointless." Students want to know how solving equations with variables will help them in the real world. Students aren't sure that real people in the real world use math to solve real problems in their daily lives.

Students need to understand that logic used to solve math equations is a skill that will benefit them throughout life. Even in non-math situations, it is often necessary to isolate the unknown factor in a scenario to understand logically how to go about solving a certain problem. Math methodology lays the foundation for good problem-solving skills. In fact, many potential employers will require applicants to take a general math quiz before being hired. This realism makes the subject matter more enjoyable and easy to learn.

Many students who are struggling in their math work need additional tutorial assistance. In fact, hundreds of thousands of children having difficulty with a subject in school are currently being tutored in the United States for a variety of reasons:

· Many students didn't master basic skills which need to be re-taught to them

· Some have a learning disability which poses challenges to the mastery of math and slows down progress in school

· Others have weak organizational skills which result in difficulty with keeping on schedule with studying and completing assignments

· Some students have medical, social, emotional, behavioral and/or family problems which result in their struggling to keep up with their peers

· And still others simply desire to get ahead

Very often, all it takes to improve a student's low math grades is the right approach. Once that happens, it's as if a light comes on: suddenly everything falls into place! Even students who have been performing very poorly in math can finally experience the joy of "getting it."

Where can parents and students go for good quality math tutoring? Many parents find local tutors but rates can be as high as $175 per hour and not always effective.

An October 16th, 2007 Tutoring Report appeared on the NBC Today Show which described the dilemma many parents face in providing affordable quality tutoring.

As part of its overview of available services, the NBC Today Show explained that new internet technology is available to provide effective online tutoring services which enable students to get high quality one-on-one tutoring in the convenience of their own home at affordable prices.

With some online tutoring services, students can receive supplemental materials such as DVDs featuring complete review by expert teachers of the subject they are studying in school and unlimited practice exercises. In addition, online services may provide students access to new white board technology which enables them to watch the tutor's lesson and talk to them as if they were face to face with the tutors.

The NBC Today Show interviewed the Foley family in Peekskill, New York where Mrs. Foley acknowledged that she could not afford the costs of chain tutoring company services and therefore opted for an online tutoring program which was affordable and also gave her a full 30 day guarantee.

The two Foley daughters who used the program found that their math grades had a dramatic increase after using the online tutoring service and the DVD math reviews. In the interview, one of the Foley teenage girls said that she found the tutoring service easy to use and a really effective service.

Although no one wants their child to struggle, the good news is that solutions are available for math help. Parents should realize that the knowledge and sense of achievement that a tutoring program can bring to the student will pay big dividends for years to come. Not only will it help earn a better grade, but it will also lay a critical foundation for future success, including help with college admissions exams.


Sunday, April 1, 2012

How to Solve Easy Math Word Problems


Frank Howard Clark said, "I think the next best thing to solving a problem is finding some humor in it." What Mr. Clark would like to convey with this is that the way to solving easy math word problems is by having fun with the problems. And in having fun with them, there are two simple steps in solving math word problems:

Step 1: Translate the words into a numeric expression or equation

Math word problems can be converted into a series of expressions or equations containing a combination of mathematical expressions. To be able to translate these word problems you have to follow these steps:

1. Read the problem very well and in its entirety. Get the full perspective of the problem. Reading it in full will give you an idea of what the real problem is.

2. List all the factors provided. Make a list of all the given variables including units of measurement if available. Having all these information available will show you if you need to do any conversion like from miles to kilometers, pounds to kilograms, etc.

3. Define what needs to be answered. Be sure to know what you are looking for or what the problem needs to answer.

4. Organize your solution. Provide the procedures or steps you will take to find the answer to the problem. Showing the step-by-step procedure will help you track all the variables and expressions you are using.

5. Be aware of the key words. In translating and solving the problem, you should be aware of the basic key words in translating words into algebraic equations, such as:

Addition: added to, increased by, more than, sum of, total of, combined with

Subtraction: decreased by, subtracted from, less than, difference of, reduced by, fewer than

Multiplication: multiplied by, times, product of

Division: divided by, quotient of, remainder of, percentage, ratio of, per

Certain key words suggest specific mathematical operations that should be done to the given factors or variables.

6. Plot the expression or equation. Plot the expressions or equation properly following the order of operations.

Step 2: Solve the mathematical equation

To solve a mathematical equation, follow the order of operations by level:


compute first all those inside parentheses or the innermost expressions
compute those with exponents, raised to a power or root of
multiply or divide from left to right
add or subtract from left to right

It would be easy to solve the equation by writing down the answers for each level before going to the next level. Here is an example:

X = ((2 * 3) + (32) + (20/4) - (2 * 6)) * 2 + (3 * 8) - (4 * 5)

X = ((6) + (9) + (5) - (12)) * 2 + (24) - (20)

X = (6 + 9 + 5 - 12) * 2 + (24 - 20)

X = (8) * 2 + (4)

X = 8 * 2 + 4

X = 16 + 4

X = 20

From the sample equation above you will the order operations that were followed in solving the equation.

With these two simple steps to follow there is no need for you to just stop and stare and pray for divine intervention to be able to solve a math word problem! Now you can safely say that Math is easy and that it isn't hard to solve math word problems.