## NCLS Math 7A, Lesson 7, 10/28/2012

Weidong Posted in Fall 2012, Homework, Teaching info
Comments Off on NCLS Math 7A, Lesson 7, 10/28/2012

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.

## How to work with your blog site

Comments Off on How to work with your blog site

## Math 7A, Lesson 6, 10/21/2012

Weidong Posted in Fall 2012, Homework, Teaching info
Comments Off on Math 7A, Lesson 6, 10/21/2012

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

## Math 7A, Lesson 5, 10/14/2012

Weidong Posted in Teaching info
Comments Off on Math 7A, Lesson 5, 10/14/2012

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