Math 9, Lesson 2, Spring 2019, 2/10/2019

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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 uu – 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 0a + (-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 1Page 2Page 3Page 4Page 5

Workbook Page 33, #6, #7, #10, #11, #14 – #18, #20, #21.

Math 9, Spring 2019, Lesson 1, 2/3/2019

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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 1Page 2Page 3Page 4

Workbook P 31, #1, #2, #3, #4, #5, #12, #15.

AoPS Algebra 2B, Lesson 16, Fall 2018, 1/27/2019

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We  wrap up this semester (and this school year) by going over some more problems with floor functions, as well as talking about recursive sequences.

Math 9, Lesson 16, Fall 2018, 1/27/2019

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Today we have our final exam. I will email the test result to each family soon.

Next week we will start Spring 2019 semester and teach the 2nd half of Math 9.

 

Math 9, Lesson 15, Fall 2018, 1/13/2019

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This is a review lesson. We will have our final exam next Sunday.

Students should review what we have learned this semesters by going over their homework.

AoPS Algebra 2B, Lesson 15, Fall 2018, 1/13/2019

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We study absolute function graphs and floor functions.

Math 9, Lesson 14, Fall 2018, 1/6/2019

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We review the properties of circles.

In the symmetry properties category, we have the following:

  • Equal chords are  equidistant from the center;
  • The perpendicular bisector of a chord passes through the center;
  • Tangents from an external point are equal in length;
  • The line joining an external point to the center bisects the angle between the tangents

In the category of angle properties, we have:

  • Angle in a semicircle is a right angle;
  • Angle between tangents and radius is a right angle;
  • Angle at the center is twice the angle at the circumference;
  • Angle in the same segment are equal;
  • Angle in opposite segments are supplementary.

Homework:

Page 0Page 1Page 2Page 3

#2, #4, #6, #8, #10, #12, #14, #16, #18

AoPS Algebra 2B, Lesson 14, Fall 2018, 1/6/2019

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We study piecewise defined functions and absolute functions.

AoPS Algebra 2B, Lesson 13, Fall 2018, 12/16/2018

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We study even and odd functions, as well as monotonic functions. We finished Chapter 15.

Math 9, Lesson 13, Fall 2018, 12/16/2018

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We review Angles, Polygons, Congruence, and Similarity.

We won’t have school until 1/7/2018. Have a wonderful holiday season!

 

Homework:

#5 – #20 from the 4 pages below:

Page1Page2Page3Page4