Often times experienced mathematicians tend to get comfortable with certain problem-solving strategies. For example, in a problem one might use a system of equations to solve a problem rather than employing a simpler more easy way to solve it. Though using system of equations are great, knowing how to solve problems using different approaches is important, not just for oneself, but for their students.
Take for example the following problem: A farmer has both pigs and chickens on his farm. There are 78 feet and 27 heads. How many pigs and how many chickens are there?
Solution 1: (Using Algebra System of Equations)
4p+2c=78 (pigs have 4 feet and chickens have 2 feet with 78 feet in total)
p+c=27 (27 heads mean that the number of chicken and pigs total 27)
Then by algebra p=27-c. Therefore by substitution, 4(27-c)+2c=78. 108-2c=78. 2c=30. c=15. Since, c=15, p+c=p+15=27. p=12. Therefore, the farmer has 15 chickens and 12 pigs...
Not all of us can memorize what we study therefore I come up with a few details that can help us to know the unit circle without memorize it.
1-For the (x, y) coordinates in the unit circle, always know or remember the four major coordinates point between the horizontal line (-1, 0) left and (1, 0) right and the vertical line (0, 1) up and (0, -1) down. Also, between the x-axis and the y-axis the middle angle, coordinate point always (√2/2, √2/2) in the entire unit circle; also, watch your sign in quadrant two through quadrant four. In addition, just remember your last angle coordinate point always going to be what you're starting with in the order side of your vertical or horizontal line.
2- There are three angles between x and the y axis, and the difference between them is 15° degree as well as for the radians, the difference between them is π/12. Also, from the...
Most people that I know feel that multiple choice questions on a test are a double-edged sword. On one hand, the right answer is somewhere right in front of you; you just have to pick it. On the other hand, multiple choice questions will do everything within their power to confuse you and lead you away from that right answer. Here are a few of my strategies for getting it right:
*50/50 - Does anyone watch Who Wants to Be a Millionaire anymore? I know I don't, but I do remember it. So, for those of us who either watch or remember it, think about the 50/50 lifeline. They'd eliminate two wrong answers out of the four potential choices. This is a great place to start! Eliminate anything that you know to be blatantly wrong. If possible, I like to physically cross it out on my test (in pencil, in case I change my mind). That way, you know what you can ignore when selecting your answer.
*Absolute words - This means words that are superlative or absolute, like "always," "never,"...
Throughout the course of my own education, and now as a semi-educator myself, I have picked up various handy ways to assist with memorization.
The first and probably best "memory assistant" is music. It doesn't have to be good, or really even "musical." But putting whatever you're trying to memorize to music is vastly helpful!
In high school, I memorized the presidents of the United States (in chronological order) by putting them to a song. I can still sing it to this day.
I can also recite the alphabet backwards by simply putting a tune to it.
The best thing to do is write out the words to your song, then sing it repeatedly - taking away a few of the written words each time. You (or whoever you're helping) won't forget it!
Similarly, rhymes are very helpful too! Remember the old favorite "i before e, except after c, or when sounding like 'ay,' as in neighbor or weigh"? I'll bet you do... because it rhymes!
Lastly, mnemonic devices...