Math 9, Lesson 12, Fall 2018, 12/09/2018

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

Page 1Page 2Page 3

AoPS Algebra 2B, Lesson 12, Fall 2018, 12/09/2018

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We start a new chapter on special classes of functions. Today we study rational functions, which are any function that can be expressed as one polynomial divided by another. We then talk about rational function equations and inequalities.

Math 9, Lesson 11, Fall 2018, 12/02/2018

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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.

AoPS Algebra 2B, Lesson 11, Fall 2018, 12/02/2018

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We wrap up Chapter 14 by studying radical conjugates and doing more exercises.

Math 9, Lesson 10, Fall 2018, 11/18/2018

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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.

AoPS Algebra 2B, Lesson 10, Fall 2018, 11/18/2018

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We start a new chapter today about radicals, or roots.

We explore some common methods for dealing with expressions with radicals.

 

AoPS Algebra 2B, Lesson 9, Fall 2018, 11/11/2018

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We finish up the chapter on logarithms by studying advanced log to exponent exchange and by introducing natural logarithms.

 

AoPS Algebra 2B, Lesson 8, Fall 2018, 11/4/2018

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We continue the study of logarithm. Today we go over logarithmic identities.

Math 9, Lesson 8, Fall 2018, 11/4/2018,

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

Good luck.

Math 9, Lesson 9, Fall 2018, 11/11/2018

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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