Math 7A, Final Exam Answers

Weidong Post in Spring 2012, Teaching info
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You can find the answers to the final exam with the link below:

http://www.newtonchineseschool.org/teachers/wangweidong/Math7_2012_Spring_Fall_Asnwers.pdf

For those of you who have sent the tests to me, I have emailed them back to you, so you can talk about it with your kid and help them in the summer.

Enjoy the time off.

 

Math 7A, Lesson 16, 06/17/2012

Weidong Post in Spring 2012, Teaching info
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This is our last class for Spring 2012 semester and we had our final test.

We stopped at 4:30 and I let students finish their exams at home, as I didn’t want to keep studnets until 5pm. After all, today is the last day of school!

Please finish the exam at home, scan it and email me. I will grade and email you back the score.

For those of you who could not attend the class today, drop me an email and I will send you the test to finish at home.

It’s been a pleasure to have you guys in my class. Keep up the good work, and have a wonderful summer.

 

 

Weidong Post in Spring 2012, Teaching info
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We had review class today. Thanks to Ms. Cao, who covered for me today, as I needed to go to Support China Education report workshop. As you know, I, along with another teacher, took those 12 kids to China in April. Today they reported on their trip and learning experiece.

Please check the following link for the material we covered during the Spring semester:

http://blog.newtonchineseschool.org/wangweidong/teaching-plan-2/

We don’t have any specific review material, but students can go over their homework to refresh themselves.  We will have our final exam next week.

 

Math 7A, Lesson 14, 6/3/2012

Weidong Post in Homework, Spring 2012, Teaching info
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We continued our lecture on Probabilities.

We introduced the important concepts of dependant events and independant events. Dependant event is a group of outcomes where the outcomes depend on each other, while an independant event is a group of outcomes where the outcomes do not depend on each other.

If A and B are two independant events, then the probability of A and B happening is:

P(A and B) = P(A) * P(B)

If A and B are two dependant events, then the probability of A and B happening is:

P( A and B) = P(A) * P(B after A)

Important to note is that for dependant events, when A happens, it changes the outcome space so P(B after A) is no longer the same as P(B), that is, we need to take into consideration about A’s happening.

We further talk about the two importance concepts of Permutations and Combinations.

A Combination is a group of outcomes where the order does not matter. For example, mixing two kinds of paints taken from 4 possible paints. Because of fixing effect, picking Red first then Blue has the same result of picking Blue first then Red. So here the order of picking does not matter.

A Permutation is an arrangement of outcomes in which the order does matter. For example, picking two paints out of 4 possible pains with one paint for the background and the other paint for the design. Order here matters.

We introduced that concept of factorial of a natural number where it is the product of itself and all the natural numbers less than it. So 5! = 5*4*3*2*1. And in particular, we define 0! = 1.

With that we have the formulae to calculate number of permutations of taking r things out of possible n things as:

nPr = n! / (n-r)!

And the number of combinations of taking r things out of possible n things is:

nCr = n! / [(n – r)! * r!]

Homework is as follows:

http://blog.newtonchineseschool.org/wangweidong/files/2012/06/Math7_Spring_HW_L14.pdf

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

Weidong Post 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 Post 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 Post 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 Post 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

 

Math 7A, Lesson 10, 04/29/2012

Weidong Post in Homework, Spring 2012, Teaching info
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We covered Arithmetic Series today.

When we add a group of consecutive terms of an arithmetic sequence, we form an arithmetic series. For an arithmetic sequence with the first term as a and the common difference d, the sum of the first n terms of the sequenece is:

Sn = n(a1 + an)/2

That is, the sum is the average of the first and last terms, times the number of terms. We want the students to understand how we get to that formulae, not just memorize it (which is the least they should do).

We did quite some in-class exercises mixing the arithmetic sequence formulae for the nth term and the sum of the first n terms. Usually the steps go like this: first figure of how many terms we are talking about, then see if we have the first term and the last term, if so, we can already find the sum; if not, look at the givens and figure out the first term and the common difference.

Another set of problems usually give two conditions about some terms in an arithmetic sequence. Because we want to find out a and d, two conditions usually is all we need to find the unknown of a and d. With a and d, we can find any term in an arithmetic sequnce.

Homework is the following:

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

 

Math 7A, Lesson 9, 4/22/2012

Weidong Post in Homework, Spring 2012, Teaching info
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Today we started the 2nd half of the Spring semester where we will go over new material that is not in the “Algebra I” text book. The material can be found under:

http://www.newtonchineseschool.org/teachers/wangweidong/SequenceSeries_Part1.pdf

http://www.newtonchineseschool.org/teachers/wangweidong/SequenceSeries_Part2.pdf

http://www.newtonchineseschool.org/teachers/wangweidong/SequenceSeries_Part3.pdf

We talked about arithmetic sequence where any two consecutive numbers in the sequence have the common difference. For an arithmetic sequence with the first term as a and the common difference as d, its nth term is:

      an = a + (n-1)d

As I was telling the students, it takes two parameters, the first term and the common difference, to uniquely identify an arithmetic sequence.

We did some in-class exercise in determining such parameters.

For homework, click the link below:

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