Math 7A, Lesson 13, 5/20/2012

Weidong Posted in Homework, Spring 2012, Teaching info
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We moved on to Probability this Sunday.

We talked about experimental probability where we use the number of times an event happens to compare with total number of trials.

We talked about theoretical probability where we compare number of ways an event can happen to the total number of equally likely outcomes. The key word here is “equally likely”.

Important fact: P(an event happens) + P (the event not happening) = 1

We then talked about “Odds”, odds for winning is defined as the probability of winning over the probability of not winning, while odds against winning is defined as the probabilty of not winning over the probability of winning.

Odds can be bigger than 1, while probabilities cannot be over 1. We can easily convert from odds to probability.

Homework is the following:

http://blog.newtonchineseschool.org/wangweidong/files/2012/05/Math7_Spring_HW_L13.pdf

 

 

Material for Probability, The Last Part of Our Study

Weidong Posted in Spring 2012, Teaching info
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We are moving on to the last part for this year: Probability.

You can find the material for this part below:

http://www.newtonchineseschool.org/teachers/wangweidong/Probability.pdf

 

Math 7A, Lesson 12, 5/13/2012

Weidong Posted in Homework, Spring 2012, Teaching info
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Today we are onto geometric series, which talks about the sum of the first n terms of a geometric sequence. Given a geometric seuqnece with a as its first term, and r as its common ratio, the sum of its first n terms can be written as:

Sn = a(r^n – 1)/(r-1)

We talk about whether a series is convergent (which means the sum is bounded by a constant), or divergent (the series always go bigger or smaller), or it is un-determinant.

When r > 1, the series is divergent;

When r = 1, it is a constant sequence, Sn = a*n, so it is divergent;

When -1 < r < 1, or |r| < 1, the series converges to a/(1-r);

When r = -1, the series jumps between 0 and a, so it is undeterminant;

When r < -1, the series jumps between positive and negative, so it is also undeterminant.

The homework is as follows:

http://www.newtonchineseschool.org/teachers/wangweidong/HomeworkGeometricSeries.pdf

 

 

Math 7A, Lesson 11, 5/6/2012

Weidong Posted in Homework, Spring 2012, Teaching info
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We started goemetric sequence today. A geometric sequence is defined by its first term and a common ratio. For a geometric sequence, any two consecutive numbers have the same ratio, the common ratio.

With the first term as a and the common ratio as r, the nth term is: an = ar^(n-1).

With this, we can proof the following properties for a geometric sequence:

1.  the square of nth term equals the product of (n-k)th term and (n+k)th term;

2. if {an} and {bn} are two geometri sequences, then {anbn} and {an/bn} are geometric sequences as well.

We can use the given nth term formulae to solve a variety of problems about geometric sequences.

Note, when working on sequences, it is important to make it right with the subscripts.

Homework is as follows:

http://www.newtonchineseschool.org/teachers/wangweidong/HomeworkGeometricSequence.pdf