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

Answers to last week’s homework: answers

We review Angles, Polygons, Congruence, and Similarity.

Homework:

#5 – #20 from the 4 pages below:

Page1, Page2, Page3, Page4

Answers for last week’s problems: Answers1, Answers2

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 1, Page 2, Page 3, Page 4

Answers to last week’s homework:

Answers page

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

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

Answers to the last week’s homework:

Answers