We study Fieta’s Formulae, which examines the relationships between the roots of a polynomial and its coefficients. We talk about using roots to make equations.
This concludes Chapter 8. Next week we will start a new chapter on factoring multi-variables polynomials.
We start a new chapter, which is also about polynomial roots. But now we move on to study irrational roots and nonreal roots. Important things to know is that irrational roots and nonreal roots come in pairs: if a polynomial with rational coefficients has an irrational root, then is radical conjugate is also a root; if a polynomial with real coefficients has a nonreal root, then its conjugate is also a root of the polynomial.
We wrap up Chapter 7 by studying graphing and Fundamental Theorem of Algebra, as well as talking about algebraic applications of the Fundamental Theorem.
We will start a new chapter next time.
We continue Chapter 7 on polynomial roots. we study rational roots and bounds.
We move on to the chapter about mathematics in practical situations, and today we study profit, loss, simple interest, and compound interest. These topics are not new for most students.
Profit is achieved when the selling price is bigger than the cost price. The difference is the profit. Profit over the cost defines the profit percentage.
When the selling price is lower than the cost, you have a loss, which is defined as the difference between the cost and the selling price. The loss over the cost defines the cost percentage.
Banking usually deals with interest. The original amount you deposit into a bank account is called the principal. The interest is calculated based on an interest rate, which usually is given as an annual percentage.
In simple interest calculation, the interest calculation is based solely on the principal. So interest $I earned on the principal $P at the interest rate of i% annually for a period of n years is given by:
I = P x i% x n
In compound interest calculation, interest is calculated on prior interest accumulated over a period of time. Suppose an initial principal $P is invested at i% per period with compound interest for n periods, let An be the amount after n periods, then:
An = P(1 + i%)^n
Homework:
Workbook Page 41, #1 – #4, #13 – #16.
We have our midterm exam today. I will email parents the graded exam back. I will also post the answers to the exam later as well.
There will be no school next Sunday on 4/16.
There will be school on 4/23 as a snow makeup day. We will start a new chapter. There will be a substitute teacher for that day, as I planned my China trip long time ago.
We have a review lesson today to go over what we have learned so far this semester. We will have our midterm exam next Sunday.
No specific homework, but students should look at the homework so far to prepare themselves.
Answers to last week’s homework: answers
We start a new chapter (Chapter 7) on polynomial roots. We will spend the next several lessons to go over Chapter 7 and 8, both are about polynomial roots, from finding the integer roots, to rational roots, to irrational roots, finally to nonreal roots.
Today we talk about Factor Theorem and finding integer roots.
We review measuration, with the focus on:
Homework: from Page1, Page2, Page3:
#5- #18
Answers to last week’s homework: answers1, answers2
