We have our Fall semester final exam today. I will have the test results ready for students next Sunday.
Next Sunday will be the first class for 2017 Spring semester.
We have our Fall semester final exam today. I will have the test results ready for students next Sunday.
Next Sunday will be the first class for 2017 Spring semester.
We review what we have learned this semester in preparation for the final exam for next Sunday.
In this semester so far we have learned matrix and matrix multiplications, along with going over old content of equations, inequalities, set languages, angles, polygons, congruence, and similarities.
We will have the final exam next Sunday 1/22/2017.
There is no specific homework today. Students should go over their past homework questions.
Answers for last week’s homework: Answers
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, Page 4
Answers to last week’s homework: Please see Lesson 11’s answer pages.
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.
Answers to last week’s homework: Please see Lesson 11’s answer pages.
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 have mid term exam today. I will have the test results ready next week.
We have a review lesson today to go over what we have learned so far this semester, as we will have our midterm exam next week.
No specific homework today, but students should go over their class notes as well as their homework so far to prepare for the exam. As I told students, if they have had no problem with their homework, then they will be fine with the exam.
Good luck.
Answers to last week’s homework
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