Midterm exam today.
I will grade and give back the exams next Sunday, will spend some time going over some parts of the exam.
For those students who could not come, here is the test. Do it at home: 85 minutes, closed-book.
http://blog.newtonchineseschool.org/wangweidong/files/2012/11/Math-7A-2012-Fall-Midterm-Exam.pdf
Today is the review day and we went over what we have learned this semester in the first 6 lessons: Indices (Exponents); Algebraic manipulations; Leanr and quadratic equations.
We will have our midterm exam next week on 11/4. Please go over your homework. To help you prepare, you can also do the following on your workbook:
Page 11, Test Paper 1, question 1 through 8, and Page 32, Test Paper 2, question 1.
Today we mainly focused on quadratic expression factorization (因式分解). This is a skill that is very useful in quickly solving quadratic equations. While it is not hard, it does take practice to get good at. So we spent most of the time letting the students going exercises.
Basically, for the simple form of x^2 + bx + c (that is, the coefficient in front of x^2 is 1) to be able to be factored as (x + p) (x + q), then p + q must be equal to b and pq (p times q) must be equal to c. So the basic steps are, first look at the factors for c and find two whose product is c, then check if their sum equals to b, if so, you have it. If not, try different pairs.
Then for the general form of ax^2 + bx + c (a <> 0), it is the same idea but a little more complicated. For it to be factored into (px + m)(qx + n), then pq (p times q) must be equal to a, mn( m times n) must be equal to c and pn + qm must be equal to b. The basic steps are, first look at the factors for a and pick two so that its product is a, then pick two factors of c so that its product is c, then check if the cross multiplication of those two pairs is b.
A cross multiplication chart will help
px +m | +pnx
X |
qx +n | + qmx
—————————————-
pqx^2 + mn | (pn + qm)x
With this skill, we looked at solving quadratic equations where we factor first.
Note, we have not got into the general solution of a quadratic equation yet.
Homework:
Page 19 18 a c e g i k m o, 19 b d f h j l n, 20 a ii, f ii, g ii, i ii, j ii, k ii
We started with solving simple linear equations, then we talked about linear equations with all letters, with some representing constants and one as unknown to be solved.
From there, we talked about transformation of formulae, where from one given formulae, we can rewrite it to make any variable as the subject of the formulae, or, in other words, expressing this variable in terms of the rest.
For example, given 1/u + 1/v = 1/f, we can ask to express v in terms of u and f, or make u the subject, or rewrite it in the form of f = …..
This is is help students get to know better about algebra where we can generalize everything in a linear equation.
We started to talk about quadratic equation where there is one variable whose highest power is 2. For example, x^2 + 3x -5 = 0. Its general form is ax^2 + bx + c = 0, where a, b, c are constants and a <> 0.
For now, we look at a quadratic equation in factored form: (ax+p)(bx+q) = 0. Since we know for P x Q = 0, either P= 0 or Q=0, we do the same: either ax+p = 0 or bx+q = 0. So we have two solutions: x = – p/a or x = – q/b.
Next time, we will talk about quadratic factorization and solving word problem with quadratic equations.
Homework:
Page 17: 3a, 3b, 4a, 4b, 5a, 5c, 5e, 5g
Page 18: 7a, 7b, 10a, 10b, 14a, 14b
Page 19: 18b, 18h, 18i, 20 j i, 20 l i
We talked fractional equations and word problems with fractional equations.
Any equation involving any fraction, either x (unknown) either in enumerator or denominator, is called a fractional equation.
We studied fractional equations with x in enumerators, and we studied equations with x in denominators. When x is in denominators, one important step is to check the answer to make sure that it does not make any denominator zero and throw away any answer that does.
For word problems, it is important to come up with the right equation with the given information.
Homework is as follows:
Page 9: 49 a c d e g i k m n o, 52 a, 53, 54, 55, 56
Note, someone left an umbrella in the classroom. I have it.
We covered the following today:
The factorization refers to the process to find the common factors among all terms to make up an expression in product. For example, 3x + 6 = 3(x+2). For simple ones, every term has the common factor to take out. For some others, we talk about doing factorization with grouping, by looking at 2 terms as a group.
Like any fraction number being referred as real number, fractions involving algebraic expressions are called algebraic fractions or rational expression. For example, (x-1) / (x+1).
Like real number addition and subtraction, to add or subtract two algebraic fractions, we need to first find the LCM, Least Common Multiple for the denominator, then simplify.
And, multiplication and division of algebraic fractions work the same way as real numbers. For multiplications, you multiply the denominators and enumerators separately and then simply. For division, you flip the denominator to change it to multiplication.
Homework is as follows:
Page 8: 11, 13, 15, 17, 19, 21, 23, 25, 27, 29,31, 33, 35, 37
Page 9: 50 a, 50b, 50c, 51a, 51b, 51c
We covered the following material today:
To represent a number, scientists use the form of A * 10^n where 1 <= A < 10, n is an integer. This is called scientific notation or standard form. The key point is, A must be smalled than 10.
We talked about how to convert from a decimal form to the standard form, and vice versa. We talked about how to perform addition, subtraction, multiplication, and division with two numbers in standard form.
For special algebraic rules, we established the following three rules:
For expanding products, the key point we went over is the distributive law, using which one should be able to expanding products in any form.
For homework, it is on the Workbook:
http://blog.newtonchineseschool.org/wangweidong/files/2012/09/HW_L2_P4.pdf
http://blog.newtonchineseschool.org/wangweidong/files/2012/09/HW_L2_P5.pd
fhttp://blog.newtonchineseschool.org/wangweidong/files/2012/09/HW_L2_P6.pd
fhttp://blog.newtonchineseschool.org/wangweidong/files/2012/09/HW_L2_P7.pdf
We covered the material about Exponents. The following are the important rules and defintions to memorize:
With the above rules and defintions, we can simply expressions. We did several in-class exercises and the homework will be mostly about simplying expressions.
We also talked about exponents with variables, whose operation is no different, exception we use variables, like x, y, a, b, c, etc., to represent the things in the operation. Same rules and definitions apply.
For homework, it is on the workbook:
Since the school ran out of the Workbook today, and some students who just paid today did not get the workbook, so for today, I will scan the pages for the homework:
http://blog.newtonchineseschool.org/wangweidong/files/2012/09/HW_1_1.pdf
(fixed!) http://blog.newtonchineseschool.org/wangweidong/files/2012/09/HW_1_2.pdf
Also, some parents asked about where to get the textbook. Here is a link where you can buy:
http://www.singaporemath.com/New_Elem_Math_Textbk_2_p/nemt2.htm
The last one is about 10% cheaper compared to the singaporemath site.
The school starts this coming Sunday. The classroom is 325. For each paid student, you will get a workbook.
Please visit my blog site at blog.newtonchineseschool.org/wangweidong for more information about this class, the textbook information, the teaching plan, etc.
I see most of the students have taken NCLS Math 6, which is the prerequisite for this class. This is good. I am also aware that last year’s Math 6 did not finish all the content in the syllabus. School is discussing what to do at this time.
For those new students, you are required to go over the page for “New Student“, which contains helpful information for you to decide if you are ready for the class, including a placement test.
Remember, sending a student too early for a class does not do any good. The last thing you want is to make your kid hate Math and lose interest!
For all students, go over the “New Student” section as well, as it also contains information about homework, classroom rules, classroom expectation, etc.
I will start using my blog site exclusively for the communication with you guys, so get into a habit to check it often.
Once again, welcome to my class.
