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.

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 0, Page 1, Page 2, Page 3

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

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:

Page1, Page2, Page3, Page4

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 page2 below: #1 – #5, #11 – #14, #15 – #17

Page 1, Page 2, Page 3

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.

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.

We have our midterm exam today. I will send the test paper to parents afterwards.

Good luck.

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

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