Math 9, Lesson 10, Fall 2017, 11/19/2017

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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.

Math 9, Lesson 9, Fall 2017, 11/12/2017

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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

Algebra 2, Lesson 9, Fall 2017, 11/12/2017

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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.

 

Math 9, Lesson 8, Fall 2017, 11/5/2017

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

Good luck.

 

Algebra 2, Lesson 8, Fall 2017, 11/5/2017

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

 

Math 9, Lesson 7, Fall 2017, 10/29/2017

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We have a review lesson today to go over what we have learned this semester so far: probabilities, complex numbers, and standard deviation.

We will have our midterm exam next week. There is no specific homework today, but students should go over their class notes and homework to prepare for the test.

 

Algebra 2, Lesson 7, Fall 2017, 10/29/2017

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

 

Math 9, Lesson 6, Fall 2017, 10/22/2017

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We continue study of standard deviation. We first review the formula for ungrouped data and grouped data.

We apply the standard deviation to help analyze two data sets. While means can give us the picture of average, standard deviation helps us to determine how consistent the data are. For example, if we look at two sets of data representing two basketball players’ scores, the lower the standard deviation, the more consistent the player is.

Homework:

Print these pages: Page 1Page 2Page 3Page 4

Workbook Page 2, #7, 8, 9, 10, 12, 14, 16.

Algebra 2, Lesson 6, Fall 2017, 10/22/2017

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We start a new chapter on Exponents and Logarithms.

Today we cover Exponential Functions Basics and Introduction to Logarithms.

 

Math 9, Lesson 5, Fall 2017, 10/15/2017

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We study standard deviation. In statistics, we have learned using mean to find the average, and we have learned to use range and interquartile range to see the spread of the data. But both range and interquartile range are not very good as the tool to represent the spread of the data.

A better way is the measure called standard deviation:

Standard Deviation SD = sqrt(sum of (Xi – AvgX)^2/N)

where N is the total number of data, AvgX is the mean of the data. Xi – AvgX is called the deviation of Xi from the mean AvgX for each i = 1, 2, …, N

For a set of grouped data in the form of a frequency table, we have

Mean AvgX = sum of fx / sum of f

where x is the class mark of each class and f is the frequency of the corresponding class.

Standard Deviation SD = sqrt(sum of f(Xi – AvgX)^2 / sum of f)

[Sorry, I can’t type using the summation notation sigma, which is what we learn in the class. This will simplify the writing.]

Here is a written proof of going from the definition to a formulae often used:

sqrt(∑(Xi – AvgX)^2 / N) = ∑Xi^2 / N – (∑Xi / N)^2

I showed the proof in the classroom, but students may not get it.

Homework:

Page 1  and Page 2: #1, #2, #3, #4, #5, #6.