Today’s topics are exponential growth functions and exponential decay functions.

An exponential growth function can be written as the following:

y = C(1+r)^t

where t represents time, r is called growth rate (r > 0), 1+r is called growth factor, C is in the initial value.

A good example to help understand the exponential growth function is the simple bank annual interest. r will be the annual interest rate, t represents number of year, C is the initial deposit, and y is the total amount after t years.

Similarly, an exponential decay function can be written as the following:

y = C(1-r)^t

where t represents time, r is called decay rate (1 > r > 0), 1-r is called decay factor, C is the initial value.

A good example would be car losing value as 10% per year.

This lesson finishes the chapter 8. Next time we will do a review of what we have learned in the first 6 lessons, to get ready for the mid term exam two weeks from now, on 11/6.

Here is the homework:

http://blog.newtonchineseschool.org/wangweidong/files/2011/10/Math7_Fall_HW_L6.pdf

Dear Parent/Student:

Today we first went over the exponential functions again as some students found that part of the homework difficult. We then continued our Exponents study with section 8.3 and 8.4. We further talked abut the division properties of exponents:

a^m / a^n = a ^ (m-n), a <> 0 and

(a / b)^m = a^m / b^m, b <> 0

We did some exercises on simplifying expressions with exponents. I think students are still not good at dealing with negative exponents and how to make a negative exponents positive with: (a /b) ^ (-m) = (b / a)^m. This takes practice to get better.

We then talked about scientific notation where a positive number can be represented as C*10^n, where 1<= C < 10, and n is an integer. We talked about how to convert from a decimal number to a scientific notation number and vice versa, how to do multiplication and division with scientific numbers.

Below is this week’s homework:

http://blog.newtonchineseschool.org/wangweidong/files/2011/10/Math7_Fall_HW_L5.pdf

²Today we started Chapter 8 about Exponents and Exponential Functions.

We covered the first two sections: Multiplocation Properties of Exponents, and Zero and Negative Exponents.

Basic take-aways are:

• a^m * a^n = a^ (m+n)
• (a^m)^n = a^(m*n)
• (a * b)^m = a^m * a^n
• a^0 = 1, a ≠0
• a^(-n) = 1 / a^n, a ≠0

I didn’t get chance to cover the real world use cases. One example is like, there are two circular fields, one’s radium is twice the other, what is the area ratio. To solve it, you assume the smaller one’s radium as r, so the ratio is π(2r)²/πr² = 4.

I also had less time to go over the exponential functions, so if the student feels uncomfortable about the homework questions on exponential functions, they can skip. But if the parent can help explain, that will be great. I will circle back next time.

Homework is below:

http://blog.newtonchineseschool.org/wangweidong/files/2011/10/Math7_Fall_HW_L4.pdf

Today we covered section 7.5 and 7.6 from the book.

we talked abou the special cases for a system of linear equations: systems with no solution and systems with infinite solutions, and how they relate in graphing. That is, if a system has no solution, then it contains parallel lines (which dont intercept); if a system has infinite solutions, they it contains identical lines (they overlap).

We then talked about graphing for a linear inequality. From there, we talked about graphing for a system of linear inequalities, where the solution is normal a region. We did exercises in the classroom on how to graph and identify the solution region.

Lastly, we did the reverse problem: given a region, find the corresponding system of linear inequalities: frst find the lines that bound the region, you should find that many number of linear inequalities. Then for every the line, use the solution region information to help you determine the the inequality sign to use.

I found some students are still not familiar with how to use the given two points to come up with the linear equation for the line. You will need to work on it.

For homework, get it here: http://blog.newtonchineseschool.org/wangweidong/files/2011/09/Math7_Fall_HW_L3.pdf

Today we covered Section 7.3 and 7.4 from the book, about solving a linear system y linear combination, and the applications of linear systems.

To step a linear system by combinations, follow the following 4 steps:

1. Arrange the equations with like terms in columns;

2. Multiply one or both of the equations by a number to obtain coefficients that are opposites to one of the variables;

3. Add the equations from Step 2. Combining like terms will eliminate one variable. Solve the remaining variable;

4. Substitute the value obtained from Step 3 into either of the original equations and solve for the other variable;

5. Check the solution in each of the orginal equations.

We did some classroom exercises together. Thanks go to those students who volunteered. As I told them, don’t be afraid to make mistakes and it is totally OK to make mistake.

We talked about the importance of the last step, to check, as this is the step where you can find out if you have made any mistake, and get a chance to fix the mistake.

For the word problems, we talked about three steps to come up with the equations:

1. Have a verbal model by drawing squares with words in them;

2. Pick variables x and y to represent some values;

3. Come up with the algebraic model which contains two equations.

Then use any approach to solve the equations.

For homework, find it below:

http://blog.newtonchineseschool.org/wangweidong/files/2011/09/Math7_Fall_HW_L2.pdf

I have given back to the students the skill reviews we did in the last Sunday. You can review it with your kid.

Again, feel free to contact me for any question.

Welcome to Fall 2011 semester Math 7A class!

Today we had a quick skill review test to go over some concepts taught in Math 6. This serves two purposes: for me, it is to know the level each student comes with; for student, it is for him/her to know whether he/she is ready and what he/she is missing.

We went over the review and talked more about one variable linear equation, its graph, and one variable linear inequality.

We then went over the content in 7.1 and 7.2 on solving 2-variable linear system (2 2-variable linear equations) by graphing and substitution.

For solving the system by graphing, you first graph the first equation, then graph the 2nd equation in the same coordinate system. The intersection is your solution, so you estimate the interception. Last step is to take the estimated solution and plug it back into the original equations to make sure that they both work.

For solving the system by substituion, you first take  one equeation and rewrite it so that one variable is represted by the other. Then you substitute this variable in the other equeation with the represenation you got from the first step. Now you have an one-variable linear equation. Solve it, then solve the other variable. Again, the last step is to take the solution and plug in back into the origianl equations to make sure that they both work. This step will help you identify potential errors.

For the homework, please download the following pdf file and print it out. Homework is due next Sunday.

http://blog.newtonchineseschool.org/wangweidong/files/2011/09/Math7_Fall_HW_L1.pdf