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.
We start the new chapter on vectors.
While a scalor is a quantity that has only magnitude, a vector is a quantity that has both magnitude and direction. We usually use directed line segment to represent a vector. The direction of the line segment, indicated by an arrow, represents the direction of the vector, and the length of the line segment represents the magnitude of the vector.
Two vectors are equal if they have equal magnitude and are in the same direction.
For vector additions, we study the triangle law and parallelogram law of vector additions.
Homework:
Page 1, Page 2, Page 3, Page 4
Workbook P 31, #1, #2, #3, #4, #5, #12, #15.
Answers to last week’s homework: Answers
We study circles, ellipses, and hyperbolas.
A circle is a locus of points in a plane that are a fixed distance from a given point in that plane. The fixed distance is the radius of the circle and the given point is the center.
An ellipse is defined geometrically as: for a given two points F1 and F2 in a plane, for any positive constant k greater than the distance F1F2, the locus of all points P in the plane such that PF1 + PF2 = k.
A hyperbola is defined as: for a given two points F1 and F2 in a plane, for any positive contstant k, the locus of all points P in the plane such that |PF1 – PF2| = k.
We study the common properties of these three kinds.
This is our first lesson for Algebra 2. Students got their textbooks.
Today We study parabolas, with its relationship to quadratic functions.
Three parents came to the class, with two stayed through the class. I welcome the input from the students and the parents.
Parents: please talk to your kid to get his feedback. Examine your kid’s notebook to see how much exercise he/she did in the class.
We started with talking about the geometric definition of a parabola, its basic properties and how to find the function based on the information about vertex, focus, directrix, etc. We did this by looking at a number of problems. Students then got time to work on some problems. We then talked about those problems and solved them in the class.
After the break, we looked at using parabola to solve problems. Again, we looked a few problems before the students worked on a few more. We then talked about those.
Lastly we looked at one of the major applications of parabola: finding the minimum and maximum values of quadratic functions. Again, we studied a few examples, having students work on a few more. We finished after going over those problems again.
This is a pretty fast paced class and I want to make sure that students feel OK. As I told students, they should have notebooks with them, not just note pad. They should get into a habit of taking notes in the class.
Again, please provide your feedback.
Students will bring home their final exam papers. I have uploaded answers for the exam here.
Apart from going over some exam questions, we review the properties of circles.
In the symmetry properties category, we have the following:
In the category of angle properties, we have:
Homework:
Page 0, Page 1, Page 2, Page 3
#2, #4, #6, #8, #10, #12, #14, #16, #18
