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 last week’s homework: Answers

Note, there is no school next Sunday on 11/27. Have a nice Thanksgiving Holiday!

We went over the midterm exam first, then did a review on equations and inequalities.

We looked at linear equations, system of linear equations, quadratic equations, rational equations, and linear inequalities.

For homework, use the sheets below:

#2 – #18.

Page 1, Page 2, Page 3

Two events are called to be independent events if the occurrence or non-occurrence of one event does not affect the probability of the other event.

If A and B are independent events, the probability of both events A and B occurring is the product of their individual probabilities:

P(A and B) = P(A) * P(B)

With this, we can simplify tree diagrams when dealing with problems with multiple same items by simply marking their probabilities.

When two (or more) events are dependent to each other, we cannot use the product rule, but we can still use the tree diagrams to help us finding probabilities.

Homework:

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

Workbook Page 12, #6 – #10, #16 – #20.

Answers to last week’s homework

Answers1    Answers2

[We have a substitute teacher as I am out of the country for two weeks (this Sunday and next Sunday). I will keep posting the teaching info as well as the homework here.]

We start a new subject on probability. Students should have learned some basic concepts before about simple probability, the concept of a sample space with events consisting of some outcomes. In this chapter ,we study probabilities with multiple stages.

When a random experiment involves two stages, we can use a rectangular grid, called a probability diagram, to represent the sample space to help us find probabilities.

If a random experiment has two or more stages, we can use a tree diagram to represent the process, which should help us see all the possible outcomes and figure out the outcomes associated with a particular event.

We then talk about mutually exclusive events. In a sample space, two events are mutually exclusive if they cannot occur at the same time. If A and B are two mutually exclusive events, the the probability of A or B occurring is: P(A or B) = P(A) + P(B).

Homework:

Print these pages: Page 1, Page 2

Workbook Page 11, #1 – #5, #21.

Answers to last week’s homework

Answers

Today we review functions and graphs. We look at linear functions, quadratic functions, functions in the form of y = ax^n, where n = -2, -1, 0, 1, 2, and 3,  exponential functions y = ka^x, a > 0, and how to estimate the gradients of curves by drawing tangents.

Students should have learned these topics before and this is a review lesson to refresh their memories.

There is no school next Sunday on 10/9/2016, sathe school observes Columbus Day.

I will be out of the country for two weeks so I will miss the class for the Sunday of 10/16 and 10/23. There will be a substitute teacher covering for me and I will continue post the class info as well as homework here.

Homework: #1 – #12 from the pages below:

Page 1, Page 2, Page 3

Answers for last week’s homework

Answers

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 1, Page 2, Page 3, Page 4

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

Answers to last week’s homework:

Answers

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.

Answers to last week’s homework:

Answers

We have our first class today.

First thing first, each student should prepare two notebooks, one for taking the notes in the classroom, and one for doing the homework.

For this year, while we learn new material, we will also spend time reviewing what we have learned in the past. The review sessions will be mixed with the new lessons.

Today we review the topics of Algebraic Manipulation And Formulae. You can find the corresponding material in your Workbook on Page 72.

For homework, please download the following 4 pages and do the following: #3, #4, #5, #6, #7, #9, #11, #13, #14, #15, #18, #19, #20.

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