http://www.wyzant.com/resources/lessons/math/trigonometry/polar-and-rectangular-coordinates I am not done with it yet. I still need to show how simple it is to do the "same" calculations in the second, third, and fourth quadrants.
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You have most likely heard the advice "Follow your dreams!" in regards to finding success, satisfaction, and happiness. Unfortunately, this advice is a bunch of baloney and has lead to a generation of frustrated young people. I'll justify this statement with an example of the man in love with the outdoors. He loves camping, hiking, and communing with nature, and his teachers and parents always told him to follow his passions for success. Well unfortunately, park rangers don't make much money, and unless living in a trailer in the woods is going to satisfy his every desire, he will live a life filled with a longing for family, travel, and job security. Not to mention that this is also assuming he is any good at being a park ranger! Note that I'm not telling you to give up your passions. They are the things that fill our hearts and feed our souls. I'm telling you to bring your passions with you. So then if I don't follow my passions and put energy into... read more
See if there is one thing that I cannot stand, is seeing a student rush into a Stats class and stating that this class is remarkably easy because my friend said so. Too many times has a student come up to me and asked is statistics easy, and I reply "it most certainly is... for myself, because I studied my content for two years before retaking the course.". If you know that you are going to start a statistics class anywhere at any time your going to need the following items. 1. TI-83 or 84 preferably Now why one of these calculators? Students, if you are going to take a stats class be aware that there is a lot of data or numerical values that can be used to find the measures of central tendency and measures of dispersion. These calculators excel for data entry and double checking your answers on the very first test. *If your teacher says you cannot use this calculator, then get its cheaper cousin. TI-30XII Hint there usually blue and do not get... read more
A few years ago, I began to teach a noncredit science class at a local community college. One of the lessons was how to solve word problems. This is what the material gave us to teach the students. 1.Read questions carefully 2.Define terms, think about relationships 3.Identify key or clue words 4.Identify the problem to be answered 5.Analyze the problem 6.Plan a solution 7.Answer the question 8.Evaluate the solution Over time I began to realize that this was too much info to give, so I began looking for better ways to explain the process. I finally stumbled on an acronym that was simple and yet explain the steps in a concise way. The acronym was WORD which stood for: W- What does the question give you and does it want for answer (covers points 1, 3, 4) O- Organize the information. Most science questions have a distinct order to them that can either be organized or diagrammed to assist in ‘seeing the problem’... read more
I am a firm believer that one does not truly know something until she can put it into a new format. You can take notes from a book or from lectures all day, every day, but until you can put the information into a new shape, you haven't actually learned anything. Make a concept map, put facts and vocabulary into tables or categories, write flash cards, and/or rearrange the information in a new outline. Go really crazy and write a song or a poem, draw a picture, even make something in 3D. What you do or make depends on your learning style, but it has to be something new. I also believe that you only know something if you can summarize it. If you know enough about a subject to condense it into something really compact, like a “cheat sheet,” then you’re doing pretty well. You can capture its meaning in much less space than a textbook chapter. I actually do make “cheat sheets” for most of my tests. I condense all of the information I need for the test onto just a few pages,... read more
1) Learn well in school 2) If you fall behind, ask for help 3) Do not be afraid to ask a question 4) Start to study for the tests early 5) If you failed all of the above, hire me
Breaks from school are usually much needed and enjoyed. We get to spend time with friends and family, take that vacation that we've been planning for the past 6 months or just simply get to relax. While winter break is fun, we don't want to come back to school thinking "Huh? What is all this again?" Here are a few great ways to remain refreshed while over winter break. 1. Read a book. A couple weeks from school is a great opportunity to delve into a new world. Whether it be a mystery book or action-adventure novel, reading is a great way to keep your mind sharp. You have the chance to expand your vocabulary, discover new things and you can do it all at your own pace! Studies show that reading is not only good at keeping your mind sharp but it's healthy for your body overall. Reading is something that we do, it's an action and therefore some muscles in our body our working. It increases our attention span and makes us feel less sluggish. Instead of watching television... read more
Recently, I've noticed other tutors asking questions about raising rates and client retention. Professional tutors learn how to provide this educational service and negotiate payment for services rendered. This website is great for providing leads and helping a new tutor get started. Attaining a level of education and specific tutor training will help beginners become effective professionals, not simply peer tutors with high GPAs. Successfully tutoring others who achieve high marks on writing assignments and exams takes preparation and time. This job requires more than just one hour with a student. When I first started tutoring I did not calculate all of my travel expenses, including my time, into my hourly rate. As I quickly gained experience, I began to realize that my clients appreciate and value my willingness to drive to their homes once or twice a week. Then gas prices began to slowly rise and I had another epiphany. My expenses are not just gasoline,... read more
Fun Related Rates / Optimization Question: Smallest Surface Area of a Square and Circle Cut From a Single Piece of Rope
Hello everyone, One of my Calculus students had an interesting Related Rates problem that I had to go home and think about for a while in order to figure out. The problem was set up as such: A 25 inch piece of rope needs to be cut into 2 pieces to form a square and a circle. How should the rope be cut so that the combined surface area of the circle and square is as small as possible? Here's what we'll need to do: 1. We will have to form equations that relate the length of the perimeter and circumference to the combined surface area. 2. We will then differentiate to create an equation with the derivative of the surface area with respect to lengths of rope. 3. Wherever this derivative equals 0 there will be a maxima or minima, and so we will set the derivative = to 0 and determine which critical points are minima. Let's start by looking at the problem conceptually... read more
You can find some really good resources for math test prep in the used bookstores in a college town. Some examples that I like are: (1) Humongous Book of ______________ Problems (fill in the blank with your math topic); (2) the REA Problem Solvers series; and (3) the Schaum's Outlines. If you don't live near a college town it might be worth a Saturday trip just to buy books. Alternately, all of these are available (used) through the Amazon Marketplace sellers at really low prices. You should preview each title of these book series that you might be considering to be sure you like the authors style. Each one is different. You may like one series' treatment of Pre-Calc but prefer a different series for Calculus. So how do you use these books ? They are an alternate resource for explanations of basic concepts and problem solving techniques. You should use them as 'hint mills' and sources of problems to make up your own practice exams. Sometimes you will... read more
A passenger vehicle passes a stationary police car traveling at 20 meters/ second, slowing at a rate of 1.2 meters/ second. After a 1 second delay, the police cruiser begins pursuit of the vehicle with a constant acceleration of 3 meters/ second. How long will it take for the police cruiser to catch the vehicle? For the complete solution, please reference the following link: Police Chase
As students, we all have heard the term 'critical thinking' at some point or another, but I think the question really is, do we understand what it is and how it affects us every day? Indeed, I have seen many different ways that critical thinking can be used every day and not just in our academic papers or assignments. But before getting to those everyday encounters with critical thinking, I think it is only fitting to define what critical thinking is. According to UniLearning, critical thinking is as the intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing and/or evaluating information gathered from, or generalized by, observation, experience, reflection, reasoning or communication as a guide to belief or action (UniLearning). Critical thinkers ask basic questions like: So what? Here the idea is to ask questions about the evidence or claims one is presented with. For example, say... read more
Don't change your sleep cycle! If you wake for school normally at time x continue to rise at the same time. Altering your sleep wake cycle is difficult at best to put back on track when school starts up again and will punish your concentration skills and memory. Use the free time in the morning to exercise (swimming is best but biking in a designated area or just go to the gym). Exercise will stimulate the brains endorphins/enkephalins (promotes feeling of well being/happy and decreases pain), lowers stress hormones (cortisol) build up over the semester and eliminates those added pounds you picked up during school time. Next, reading is important! Reconnect to the "real-world" by reading the local newsletters (most are free) in your community, you will find many afternoon and nighttime activities your friends, family and that special person can attend with you to explore the community for fun, you deserve it. Also city newspapers or news on your computers favorite... read more
Happy Holidays everyone! I hope all the students among you take this winter break time to relax and recharge your batteries for the coming year. Enjoy the season, Merry Christmas & a Happy New Year!
The holidays are an exciting time of year! However, when the calendar turns, we're all expected to be ready to procede with classes, schoolwork, and early mornings! If there are any academic areas that you KNOW you need assistance with, be sure to create an action plan during the winter break that you will benefit from and put to use when our calendars read the month of JANUARY. ** Some of the questions you should be asking yourself and others around you: - How can I better balance studies with everything else that is going on, day to day? - Am I reaching out for extra help with my teachers and tutors in the areas that I know I need more guidance? - What after-school and personal activities will benefit me the most in the months ahead? - How can I make better use of my time at home during the school weeks to better prepare for tests and quizzes? - Am I ready for the various standardized tests that my school requires? Don't... read more
I use this "trick" with students who know their basic math but need to increase their speed and accuracy. I play "math war". It is based on the card game war, but builds math speed. The basics: Remove all face cards (leave the Aces) Deal the cards as you would in the game "war" Players flip the top card and the first player to call out the sum of the cards wins that round Count the number of cards at the end. The best thing is that it can be modified to "odds/evens" (is the sum odd or even) or even multiplication. They can build their speed and still play the game. It can be modified to more than 2 players or many other ways. Hope this helps and gives some ideas Mike
I think most kids in this country learn that the Japanese poetic form known as haiku is a three line poem with seventeen syllables in the pattern of 5-7-5. I doubt if many of them ever learn any of the other equally important elements of the form. Furthermore, the differences in the English syllable and the Japanese onji, render this syllable counting method ineffective when attempting to create an English equivalent to the Japanese form. Below, I have included a description of the traditional form. But I have also included a strategy to best employ the natural nuances of the English language in creating an effective verse of haiku in English. Ultimately, the best way to explore this form is to read and engage a lot of haiku. Differences Between the Onji and the Syllable The Japanese word onji means “sound symbol,” not “syllable.” Japanese onji are generally shorter than most English syllables. In some cases, it takes two or three onji to write what... read more
I. Identify an Issue To have an argument in a formal sense, you must begin with an issue, a subject about which there are at least two clearly differing opinions. For example, “drunk driving” is not an issue for debate. However, reasonable people disagree about which policies are most likely to discourage people from driving while intoxicated. Use the following questions to determine whether you have chosen an issue worth pursuing in your writing: 1. Is the issue clearly debatable? 2. Can you explore the issue with something more than pure speculation? (Claims that can’t be verified often make for interesting philosophical discussion, but they don’t lend themselves fully to argument.) 3. Is the issue more than a matter of pure taste or preference? (An author’s own values and beliefs need to be supported in argumentative writing with sound reasoning or evidence.) 4. Does the issue avoid assumptions that are so deeply or universally... read more
Winter break is approaching and I am sure most students and teachers are more than ready for to rest, relax and rejuvenate. But how do you do that and keep your brain sharp and ready for when your return to school? The answer is very simple . Do something interesting and fun that requires you to read ,to write or to learn something new. Whether you read that book you have been putting off, keep a journal everyday , take a trip to Mexico and practice your spanish, play Words with Friends on Facebook or Zumba. Just make sure you do something . The old saying , " If you don't use it, you will lose it ." Is so true. So my three tips for keeping your brain sharp ? Do something exciting or fun that requires you to read, to write or to learn something new.
One of the best ways to keep your brain humming over winter break is to read, read, read! Reading from a variety of sources keeps your gray matter in great shape! Online sources are varied, so that makes it very easy to find topics and issues that are interesting and different in topic, tone and style. One thing that you can do to challenge yourself is to read an article, Blog or website and take a few moments to think about the audience it is meant to appeal to. Everything that is written has an audience in mind and if you can learn to pay attention to the content and its intended audience, it will improve your critical thinking skills.