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

Math 9, Lesson 13, Fall 2019, 12/08/2019

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We review Angles, Polygons, Congruence, and Similarity.

Homework:

#5 – #20 from the 4 pages below:

Page1Page2Page3Page4

Answers for last week’s problems: Answers1, Answers2

Math 9, Lesson 12, Fall 2019, 11/24/2020

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We review Set Language and Matrices.

A set is a well-defined collection of distinct objects. We talk about how to describe a set, the concept of an element, a subset, when two sets are equal. We also talk about the universal set, the empty set, the complement set for a set, the set union and intersection operations.

We talk about the Venn diagram to represent sets.

We also go over some more practice with matrices.

Homework: From the three pages below: #1 – #5, #11 – #14, #15 – #17

Page 1Page 2Page 3, Page 4

Answers to last week’s homework:

Answers page

Math 9, Lesson 11, Fall 2019, 11/17/2019

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We spend more time on matrix multiplication by doing more practice questions.

Homework:

Workbook Page 23, #14 – #16, #20, #22 – #24. Please use Lesson 10’s homework pages for the questions.

Answers to last week’s homework:

Answers page

Math 9, Lesson 10, Fall 2019, 11/10/2019

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We study multiplication of a matrix by a scalar and multiplication of two matrices.

A matrix can be multiplied by a real number (usually called a scalar). If k is a scalar, then the scalar multiplication of a matrix A by k, denoted by kA, is obtained by multiplying every element of A by k.

Matrices multiplication is defined as follows:

If A is a matrix of order m x n and B a matrix of order n x p, then the product AB is a matrix of order m x p whose element at the ith row and jth column is the sum of the products of the corresponding elements in the ith row of A and jth column of B.

If the column number of A is not equal to the row number of B, then AB is undefined.

We introduce Identity Matrix of order n, which has 1 on its major diagonal line and 0 anywhere else..

Homework:

Workbook Page 21, #7, #10 – #12, #18, #19. Please use last lesson’s homework pages for the questions.

Answers to last week’s homework:

Answers page1, answers page2

Math 9, Lesson 9, Fall 2019, 11/03/2019

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We start a new topic today. We study matrices.

In real life, we often use tables to help organize data. If we abstract the concept by extracting the data from a table and arrange them in a rows and columns with brackets, we call this rectangular array of numbers a matrix. The numbers in a matrix are called entries or elements. An element is identified by its row and column positions in the matrix. If a matrix has m rows and n columns, we say that the order of this matrix is m x n. A matrix having the same number of rows and columns is called a square matrix. For a square matrix, we can simply say its order with the number of rows.

We usually use capital letters to represent matrices.

Two matrices A and B are equal, written as A = B, if they have the same order and their corresponding elements are equal.

We then discuss the addition and subtraction of two same-order matrices.

If A and B are two matrices of the same order, then sum A+B is the matrix obtained by adding the corresponding elements in A and B.

Similarly, we define subtraction of two same-order matrices.

We talk about zero matrix where all elements are zero. It is often represented  as O.

Homework:

Page 1Page 2Page 3Page 4Page 5Page 6Page 7Page 8 (please keep these pages, we will need them for the next two lessons)

Workbook Page 19, #1 – #6, #12, #14, #16

Math9, Lesson 8, Fall 2019, 10/27/2019

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We have our midterm exam today.