We review measuration, with the focus on:
Homework: from Page1, Page2, Page3:
#5- #18
Answers to last week’s homework: answers1, answers2
We review Pythagoras’ Theorem and basic trigonometry. We talk about the Sine Rule and Cosine Rule and how to use them to help solve some geometry problems.
We talk about terminologies like Angel of Elevation, Angle of Depression, the Bearing.
For homework, download: Page 1, Page 2, Page 3
#4 – #17.
Answers to last week’s homework: answers1, answers2
We start the new chapter (Ch. 6) on Polynomial Division.
We go over polynomial review, talk about long division and start talking about synthetic division, which is a quicker and more compact way of dividing a binomial in the form of x-a.
We continue our study of vectors.
We can simplify the position of a point P on a plane by the vector OP where O is a reference point on the plane. The vector OP is called the position vector of P with respect to the reference point O. That is, every point on the plane can be represented by its position vector wrt the reference point O.
Then vector PQ = vector OQ – vector OP.
Furthermore, when we look at the coordinate plane for a point P (x, y), we can use its coordinates x and y to represent its position vector with respect to the origin O. We introduce column vector notation. A column vector is like a special form of a matrix (2 rows, 1 column). All matrix operations apply to column vectors.
We can apply what we have learned about vectors to help us solve geometry problems.
Notice when vector AB = vector DC, it means line AB is parallel to line DC and AB = DC.
Homework: Page 1, Page 2, Page 3, Page 4, Page 5, Page 6
Workbook Page 33: # 8, #9, #13, #19 – #26
Answers to last week’s homework: answers
We continue to study complex numbers and graphing in the complex plane. We finish this chapter today.
With the extra time, we review parabolas, circles, ellipses, and hyperbolas and do some more exercises to refresh students memory.
For a given vector a, a vector which has the same magnitude but in the opposite direction of a is called the negative of vector a , and is denoted by –a.
The subtraction of a vector v from a vector u can be denoted as adding the vector –v to u: u – v = u + (-v).
A vector with the same initial point and the terminal point has zero magnitude. It is called a zero vector, or a null vector, and is denoted by 0. a + (-a) = a – a = 0.
When a vector a is multiplied by a constant k, the product ka is called a scalar multiplication of a and is defined as follows:
* If k > 0, ka is a vector with magnitude k|a| and in the same direction as a;
* If k < 0, ka is a vector with magnitude -k|a| and in the opposite direction of a;
* If k = 0, ka is a zero vector 0.
Homework: Page 1, Page 2, Page 3, Page 4, Page 5
Workbook Page 33, #6, #7, #10, #11, #14 – #18, #20, #21.
Answers to last week’s homework: answers
From the evaluation tests, I see that most of the students do not know about complex numbers, so I decided to add this chapter into this semester. We will spend the next two lessons on complex numbers.
We covered 2/3 of Complex Number chapter. We will finish it next lesson, plus we should have some extra time which I will use to go over some Hyperbola content again.
