Math 9, Lesson 4, Spring 2017, 3/12/2017

Weidong Posted in Homework, Math 9, Spring 2017, Teaching info，
12 March 2017
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We continue our study of vectors.

We can simplify the position of a point P on a plane by the vector OP where O is a reference point on the plane. The vector OP is called the position vector of P with respect to the reference point O. That is, every point on the plane can be represented by its position vector wrt the reference point O.

Then vector PQ = vector OQ – vector OP.

Furthermore, when we look at the coordinate plane for a point P (x, y), we can use its coordinates x and y to represent its position vector with respect to the origin O. We introduce column vector notation. A column vector is like a special form of a matrix (2 rows, 1 column). All matrix operations apply to column vectors.

We can apply what we have learned about vectors to help us solve geometry problems.

Notice when vector AB = vector DC, it means line AB is parallel to line DC and AB = DC.

Homework: Page 1, Page 2, Page 3, Page 4, Page 5, Page 6

Workbook Page 33: # 8, #9, #13, #19 – #26

Answers to last week’s homework: answers

 

Math 9, Lesson 3, Spring 2017, 3/5/2017

Weidong Posted in Homework, Math 9, Spring 2017, Teaching info，
05 March 2017
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For a given vector a, a vector which has the same magnitude but in the opposite direction of a is called the negative of vector a , and is denoted by –a.

The subtraction of a vector v from a vector u can be denoted as adding the vector –v to u: u – v = u + (-v).

A vector with the same initial point and the terminal point has zero magnitude. It is called a zero vector, or a null vector, and is denoted by 0. a + (-a) = a  – a = 0.

When a vector a is multiplied by a constant k, the product ka is called a scalar multiplication of a and is defined as follows:

* If k > 0, ka is a vector with magnitude k|a| and in the same direction as a;

* If k < 0, ka is a vector with magnitude -k|a| and in the opposite direction of a;

* If k = 0, ka is a zero vector 0.

Homework: Page 1, Page 2, Page 3, Page 4, Page 5

Workbook Page 33, #6, #7, #10, #11, #14 – #18, #20, #21.

Answers to last week’s homework: answers

Math 9, Lesson 2, Spring 2017, 2/5/2017

Weidong Posted in Homework, Math 9, Spring 2017, Teaching info，
05 February 2017
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We start the new chapter on vectors.

While a scalor is a quantity that has only magnitude, a vector is a quantity that has both magnitude and direction. We usually use directed line segment to represent a vector. The direction of the line segment, indicated by an arrow, represents the direction of the vector, and the length of the line segment represents the magnitude of the vector.

Two vectors are equal if they have equal magnitude and are in the same direction.

For vector additions, we study the triangle law and parallelogram law of vector additions.

Homework:

Page 1, Page 2, Page 3, Page 4

Workbook P 31, #1, #2, #3, #4, #5, #12, #15.

Answers to last week’s homework: Answers

Math 9, Lesson 1, Spring 2017, 1/29/2017

Weidong Posted in Homework, Spring 2017, Teaching info，
29 January 2017
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Students will bring home their final exam papers. I have uploaded answers for the exam here.

Apart from going over some exam questions, 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

Math 9, Lesson 14, Fall 2016, 1/8/2017

Weidong Posted in Fall 2016, Homework, Teaching info，
08 January 2017
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We review Angles, Polygons, Congruence, and Similarity.

Homework:

#5 – #20 from the 4 pages below:

Page1, Page2, Page3, Page4

Answers to last lesson’s homework: Answer1

Math 9, Lesson 13, Fall Semester, 12/18/2016

Weidong Posted in Fall 2016, Homework, Teaching info，
18 December 2016
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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 1, Page 2, Page 3, Page 4

Answers to last week’s homework: Please see Lesson 11’s answer pages.

 

Math 9, Lesson 12, Fall 2016, 12/11/2016

Weidong Posted in Fall 2016, Homework, Teaching info，
11 December 2016
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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.

Answers to last week’s homework: Please see Lesson 11’s answer pages.

 

Math 9, Lesson 10, Fall Semester 2016, 11/20/2016

Weidong Posted in Fall 2016, Homework, Teaching info，
20 November 2016
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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 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!

Math 9, Lesson 9, Fall 2016, 11/13/2016

Weidong Posted in Fall 2016, Homework, Teaching info，
13 November 2016
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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

Math 9, Lesson 6, Fall Semester 2016, 10/23/2016

Weidong Posted in Fall 2016, Homework, Teaching info，
23 October 2016
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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

 

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