赵一兵

This class will have midterm on Nov. 3. For more details, please contact Zhao Laoshi at yz32@yahoo.com

In today’s class, I guided students to work on factorization of algebraic expressions, especially the special expression factorization, such as a^2+2ab+b^2, a^2-b^2, etc.
In the quadratic expression factorization, students learned the definition of quadratic expression and the standard form, special quadratic expression factorization, and the method of factoring quadratic expressions with leading coefficient of 1.

Here is the homework to practice the factorization

Ch. 3
2. b, f, h
7. d, h
8. c, e
9. a, b, c, d
10. a, c, e, f, g
11. a, c, g, h
13. a, b, c, g, h
15.
18. a, b, c, e, f

Ch. 4
1. a, b

In today’s class, students studied expansions of Algebraic expression, especially the method of handling “sign” in algebraic expressions. A few special products were introduced that are so important in the quadratic expression section. By using those special products, we are able to compute some type of numbers without calculator. In addition, reverse applications of those special products are helpful in the factorization of certain types of algebraic expressions, such as some quadratic expression factorization. Limited class practices should be good guidance for students to deal with more questions.

Here is the homework assignment for the contents that students studied today.

Workbook 8A

Ch.3
1. b, c, g, h, j
2. a, c, e, g, i
3. a, c, e, g, h
4. a, c, d, f, h
5. b, d, e, f
6.
7. a.b.c.f.g
8.
9. e, f, g, h,j
11. b,e, h
12, a, b, d, e ,g, h

Today, students continued to work on exponent computation and 
simplification, especially with fractional exponents. Simply 
speaking, all laws of exponents that were introduced to students 
last week are also valid for the fractional exponent. Most 
importantly, the relation of radical number and expression and 
fractional exponents is the explanation of the meaning of fractional 
exponents. 

Solving exponent equation by using the idea of "the same base" was
the good practice in exponent contents. Students learned to solve
different type of simple same base exponent equations.

Additionally, students learned how to use scientific notation to 
present very big numbers or very small numbers.

Here is the homework assignment:

Workbook 8A
Chapter 1
2. (a) (b) (c) (d) (h)
4. (c) (h)
5. 6.
7. (b) (c) (d) (f) (h)
8. (a) (d) (f) (h)

Optional: (challenging)
16. (d), 17; (c) (e); 18. (e)

In the first class, we reviewed the basics, including number tree, order of operation, commutative, associative, distributive property, and factoring, equation, exponent. The exponent is very important knowledge and will be used in Algebra studying.

In exponent section, we started with the integer exponents. The law of exponents, the core of exponent, were reviewed in the class. It is more effective to memorize those laws.

Homework for today’s class

AOPS Introduction to Algebra textbook

PP.12, 1.3.1, 1.3.3

PP.17, 1.4.4, 1.4.5

PP.36, 1.6.1, 1.6.2 (a), (d)

In the first class, students worked on exponent and related computation/simplification. Today’s class is shorter because of the distribution of workbooks. The integer exponent was the first topic that students started with. During the introduction of exponent laws, students learned how to apply these laws in the application of algebraic expressions, and how to avoid some common problems in solving exponent questions. In order to handle such important topic without problems, memorizing the “Laws of exponents” is the key. In addition, doing more practices is so important.

Homework for today’s topic:                                                                                                        Workbook 8A, Chapter 1                                                                                                                      1. a, b, c, d, e, f                                                                                                                                         2. e, f, g                                                                                                                                                      3. a, b, c, d,e                                                                                                                                               4. a, b, e, f                                                                                                                                              18. a, c, d