July 29, 2011
Vacation
The Math Geek will be on vacation until next Saturday, 8/6/11. Anyone may ask questions during this time, but they will not be answered until my return. I apologize for any inconvenience.
July 20, 2011
Wolfram Alpha
This website is an invaluable resource for calculus (or any math or any other class, really) students: http://wolframalpha.com/
Find answers to questions in an immense variety of areas: Mathematics, Statistics, Physics, Chemistry, Engineering, Finance, Weather, Music, Nutrition; it can do almost anything!
Take a look at examples of many things it can do: http://www.wolframalpha.com/examples/
Find answers to questions in an immense variety of areas: Mathematics, Statistics, Physics, Chemistry, Engineering, Finance, Weather, Music, Nutrition; it can do almost anything!
Take a look at examples of many things it can do: http://www.wolframalpha.com/examples/
The Power Rule
This is a calculus lesson based on a question:
The derivative of a function ƒ(x) = xn is ƒ'(x) = n * xn-1. If it is easier to remember think of it as dragging the exponent down (to multiply the x by) and then subtracting one in the exponent.
Here are some examples to clarify:
The power rule is used to find the derivative of (or "differentiate" or "find the instantaneous rate of change of") an algebraic expression of the form x to a numerical power, or xn.Would you be able to explain how to derive a square root?
The derivative of a function ƒ(x) = xn is ƒ'(x) = n * xn-1. If it is easier to remember think of it as dragging the exponent down (to multiply the x by) and then subtracting one in the exponent.
Here are some examples to clarify:
July 09, 2011
Fractions
In this lesson I will show you how to add, subtract, multiply, and divide fractions. Then I will show you how to simplify your answers.
Addition/Subtraction
These are done almost the same way. First, you find a common denominator (you need the same number on the bottom of both fractions). Then, you add or subtract across the top of the fractions and keep the bottom the same.
The hardest part of this is the common denominator. If you are good with numbers, you are trying to find the smallest number that both denominators can multiply to. If you are not good with numbers (don't know the times tables or need to use a calculator often), simply multiply the two bottom numbers. REMEMBER: whatever you do to the bottom you must also do to the top, and whatever you do to the top you must also do to the bottom.
I'll provide a few examples.
Addition/Subtraction
These are done almost the same way. First, you find a common denominator (you need the same number on the bottom of both fractions). Then, you add or subtract across the top of the fractions and keep the bottom the same.
The hardest part of this is the common denominator. If you are good with numbers, you are trying to find the smallest number that both denominators can multiply to. If you are not good with numbers (don't know the times tables or need to use a calculator often), simply multiply the two bottom numbers. REMEMBER: whatever you do to the bottom you must also do to the top, and whatever you do to the top you must also do to the bottom.
I'll provide a few examples.
July 01, 2011
Order of Operations
I'm starting off with the order of operations because I feel that this is the beginning of math. Yes, there are the actual operations of addition, subtraction, multiplication, division, and exponents. Those are what I consider pre-math.
The purpose of the order of operations is to simplify an expression (hint, if you ever come across a question on a homework or test that says "simplify" or "simplify the expression," this is what it is talking about). In other words, we want to make something ugly into something pretty.
In order to do that, we use the order of operations, which is:
Parentheses
Exponents
Multiplication/Division
Addition/Subtraction
The purpose of the order of operations is to simplify an expression (hint, if you ever come across a question on a homework or test that says "simplify" or "simplify the expression," this is what it is talking about). In other words, we want to make something ugly into something pretty.
In order to do that, we use the order of operations, which is:
Parentheses
Exponents
Multiplication/Division
Addition/Subtraction
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