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MfM Math Discussion, Help & Advice

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MiKeY188

S For So Not Mature
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Whats this thread for:
I know theres some people who are good at Math and some who arnt so good. This thread is where you can receive Help, advice and discuss problems which you may be having on any Math matter.


Algebra is a branch of mathematics that uses mathematical statements to describe relationships between things that vary over time. These variables include things like the relationship between supply of an object and its price. When we use a mathematical statement to describe a relationship, we often use letters to represent the quantity that varies, since it is not a fixed amount. These letters and symbols are referred to as variables. (See the Appendix One for a brief review of constants and variables.)

The mathematical statements that describe relationships are expressed using algebraic terms, expressions, or equations (mathematical statements containing letters or symbols to represent numbers). Before we use algebra to find information about these kinds of relationships, it is important to first cover some basic terminology. In this unit we will first define terms, expressions, and equations. In the remaining units in this book we will review how to work with algebraic expressions, solve equations, and how to construct algebraic equations that describe a relationship. We will also introduce the notation used in algebra as we move through this unit

The basic unit of an algebraic expression is a term. In general, a term is either a number or a product of a number and one or more variables. Below is the term
 
eldiablov

eldiablov

Contributor
Why would you start with the definition of something that everybody goes through at their first year at school?
 
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chrono6456

New Member
Write but do not evaluate an integral for the area inside the polar equation r=2cosθ and outside r=cosθ

Can someone also explain to me what it really means for a series to converge or diverge?
 
eldiablov

eldiablov

Contributor
I never said you go through the definition, I said you go through mathematics at your first year. So you should be able to define it yourself ...
 
Hardrive

Hardrive

Contributor
chrono6456 said:
Write but do not evaluate an integral for the area inside the polar equation r=2cosθ and outside r=cosθ

Can someone also explain to me what it really means for a series to converge or diverge?
Click to expand...
areaz.jpg


For a series to converge, it means that when you add up all the numbers in the series, they approach some finite number. When a series diverges, it means the exact opposite, that the numbers are not approaching a finite number. You should know (and be able to use):
  • The nth term test
  • The geometric series test (and the sum of a geometric series)
  • The direct comparison test
  • The p-Test
  • The integral test
  • The direct comparison test
  • The limit comparison test
  • The alternating series test (and remainder theorem)
  • The ratio test

If you need any more help (especially on sequences and series), just ask. I'm taking the AP Calculus BC exam on Wednesday, so I'm pretty fresh about all of this right now.
 
Seth

Seth

MD Party Room
Sir_Axxewraith said:
Can somebody explain what the fuck quadratic expansion is used for in real life situations.
Click to expand...

The speed of a falling object is a quadratic function.
 
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chrono6456

New Member
I'm taking BC calc too on wednesday, I have little to worry, over 40% of people taking it get 5s and all you need is a 60% to get a 5, or 50% to get a 4.

I get high enough scores on multiple choice practices that I probably will only need to get roughly a 50% or better on the free responses to get a 5. I just hope theres no lagrange error on one of them :confused:
 
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chrono6456

New Member
What is the difference between the trapezoidal rule and the trapezoidal sum?

I was doing the 2008 free resposne questions, and on the second problem, part b I think, it asks you to use the trapezoidal sum.

I used the trapezoidal rule (b-a/2n)yadda yadda, and got it wrong, because int he scoring guidelines, they don't have the (b-a)/2n out infront
 
Hardrive

Hardrive

Contributor
chrono6456 said:
What is the difference between the trapezoidal rule and the trapezoidal sum?

I was doing the 2008 free resposne questions, and on the second problem, part b I think, it asks you to use the trapezoidal sum.

I used the trapezoidal rule (b-a/2n)yadda yadda, and got it wrong, because int he scoring guidelines, they don't have the (b-a)/2n out infront
Click to expand...

Trapezoidal rule and trapezoidal sum are the same. Typically, I don't use the set formulas, I just add them up myself. So, to do a trapezoidal sum, I just add up a lot of area of trapezoids, to avoid having to learn the formula.

There are a few pitfalls I can see happening in this problem. First off, I can see someone only evaluating the integral, when the problem explicitly says to evaluate the average value of the function in the first four hours (from t=0 to t=4). To do this, use the mean value theorem. Secondly, I can see errors when typing into the calculator.

So, to do 2 b from the 2008 BC free response, I would do:
traprule.jpg
 
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chrono6456

New Member
Thanks for that, sort of makes sense.

Here's to hoping we get open ended problems on Wednesday with a taylor expansion, euler approximation, and slope field. Although they are confusing, if you know it, they are so easy, and can't be made too complicated.

God I pray there will be no homogeneous functions or dot stuff (unless its super simple)
 
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