Math 9, Lesson 7, Spring 2020, 4/5/2020

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We have a review class today. We will have our midterm exam next time.

Note, there is no school on 4/12, so the midterm exam will be on 4/19.

Here are the answers for last week’s homework.

Math 9, Lesson 6, Spring 2020, 3/29/2020

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We focus on speed-time graphs, how to read a speed-time graph, how to calculate the distance, how to draw a distance-time graph from a speed-graph, etc.

We will have a review class next time. We will have our mid exam on 4/12.

Here are some more homework:

Page 3Page 4Page 7Page 8Page 9Page 10Page 11

#8-#10, #18, #19, #20, #22, #23, #24, #25.

Last week homework answers.

Math 9, Lesson 5, Spring 2020, 3/22/2020

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We study distance-time graphs.

With a distance-time graph, we can calculate speed.

Homework:

Page 1Page 2Page 3Page 4Page 6Page 7

From the workbook, Page 50: #5- #7, #15 – #17.

Complete answers for the last week’s homework

Math 9, Lesson 4, Spring 2020, 3/15/2020

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We go over the application of vectors, particularly in geometry.

Notice when vector AB = vector DC, it means line AB is parallel to line DC and AB = DC.

If you have not done your homework last week because you have some questions on certain problems, please do them now:

Homework: Page 1Page 2Page 3Page 4Page 5Page 6

Workbook Page 33: # 8, #9, #13, #19 – #26

Answers to last homework: answers, answers1

Math 9, Lesson 3, Spring 2020, 3/8/2020

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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 1Page 2Page 3Page 4Page 5Page 6

Workbook Page 33: # 8, #9, #13, #19 – #26

Answers to last homework: answers

Math 9, Lesson 2, Spring 2020, 3/1/2020

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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.

Answers to last homework: answers

Math 9, Lesson 1, Spring 2020, 1/19/2020

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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.

Math 9, Lesson 16, Fall 2019, 1/12/2020

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We have our final exam today. I will email the graded test result to each family.

Math 9, Lesson 15, Fall 2019, 1/5/2020

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We have a review lesson today. We will have our Fall Semester final exam next week.

Answers to last lessons homework: answers

Math 9, Lesson 14, Fall 2019, 12/15/2019

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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

Answers to last week’s homework: answers