Mathematics 10, 2007/2008

 Marilake Education Centre, Agincourt C.I. and Sir John A. MacDonald C.I.

"Teachers open the door, but you must enter by yourself."
(Chinese proverb)

Teacher Contact Information

Mr. Hin Lun Lee -- Agincourt C.I. -- E-mail: hinlunlee@gmail.com -- Facebook: Click Here
Miss Jean Meng -- Sir John A. MacDonald C.I. (2nd Semester) -- E-mail: a_ajean@hotmail.com
Mr. George Tai  -- Sir John A. MacDonald C.I. (1st Semester) -- E-mail: cslr134@hotmail.com

Feel free to e-mail your teacher if you have questions or problems throughout the course.

Section Information and Course Rules is available here. A general information handout with all basic course information is available here (in PDF).

Links to Other Marilake Courses / Other Interesting Links

Pictures from award presentation last school year (2006/07) - http://marilake.spaces.live.com/photos/

Advertisement for Marilake (mostly in Chinese) (Feel free to print it out and pass it to your friends!) -- Click here (in PDF) 

Perfect gifts for your math-loving friends - Click here

Mathematics 9 (to review background material that you need in this course) - http://www.xanga.com/teacherwebsite

Mathematics 11 (to preview what you will learn next year) - http://termei.freeservers.com

Creative Writing Level 2 - http://www.edu.yorku.ca/~Karrie_Cheung/0389DEDE-000F4CB5

Course Announcements

June 13 -- Please note that the last few homework assignments have been revised since we (the instructors) first received them in August 2007.  As a result, the solutions need to be re-written.  We will post the solutions once they have been re-written.  This can take a couple of weeks.  Please be patient!

See you all tomorrow.

June 13 -- For Agincourt students only:

Class pictures taken last week can be downloaded by visiting the link in the course calendar below under week 31.

I would like to offer my congratulations to the following trophy winners.  You will get your trophy from Principal Chow tomorrow during class time.

9 am - Oscar Chan (1st), Vincent Luong (2nd)

10 am - Keith Tong (1st), Joyce Cheung (2nd)

12 noon - Elliott Tin (1st), Alfred Sze (2nd)

2 pm - Amanda AuYeung (1st)

3 pm - Jimmy Fang (1st)

Please note that the number of winners is determined by the class size.  This is why there are more winners in some classes than others.

May 30 -- Those of you who have not written the final exam should e-mail your instructor if you haven't already made arrangements for making up the exam.  Your exam papers will be returned to you in two weeks.

All exam papers have been graded for those of you who wrote the exam in Agincourt C.I. last Saturday.  The following is a histogram of the marks:

The overall average is 56.61%.  The 9 am class has a class average of 61.55%, 10 am - 55%, 12 noon - 53.41%, 2 pm - 47.58%, and 3 pm - 64.38%. 

Most students passed the exam.  Congratulations!

We will discuss more about these results tomorrow in class.  See you then.

Click here for older announcements.

File Download

  • The class notes are only provided as reference and for those students missing the class. Please take notes in class diligently. The lessons / black board notes will likely be more detailed than the notes posted here.
  • Homework assignment solutions are posted here as well.
  • All posted files require a password which is different every week. Your teachers will announce them in class.
  • If your teacher forgets to announce a password or you forget the password for certain week(s), please e-mail your teacher with your name, section code, and the week(s) desired and ask to have the password(s) e-mailed to you.
  • All files in the same week will have the same password. For example, the assignment solution and notes for week 2 will have the same password.
  • All posted materials are in PDF format. Please download Adobe Acrobat Reader if you don't have it installed on your computer already.  You can download it for free from: http://www.adobe.com/products/acrobat/readstep2.html
  • Please e-mail your teacher if you find error(s) in the posted material.
  • Although the notes and homework solutions may sometimes be posted before a class, DO NOT DOWNLOAD THE FILES YET as they may be updated before the class. You may download the files after the class.

Week Unit Number Class Date Class Notes / Homework Hints / Homework Solutions
2007
1

1

September 8

Class Notes, Homework Solutions

2

2

September 15

Class Notes, Homework Solutions

3

3

September 22

Class Notes, Homework Solutions

4

4

September 29

Class Notes, Hints for Question 6, Homework Solutions

Question: How do I find the equation in 4b and 4d?

Answer: You use the chart at the bottom of page N3. Look at the chart. What is the y value and first difference for x = 1. Once you have these two expressions, equate them to the y and first difference for x = 1 in your question. You now have equations (1) and (2).

What is the value of a then? From the chart on page N3, the 2nd difference is always equal to 2a, so you can equate 2a to the constant 2nd difference in your question. With the value of a, you can substitute this value in equations (1) and (2). At that point, you have two equations with two unknowns. You should know what to do from that point on.

After you have found a, b, and c, you can write out the equation.

This is just similar to question 3 in the class practice problems on page N4. Please make sure you understand that example.

Question: What does question 7b mean in the week 4 homework?

Answer: The question is "At what point does the company break even?". "Break even" means the company does not make any profit ($0 profit). In other words, the question can be read as, "How many units must the company produce and sell to result in $0 profit?"

Question: I am not sure what question 7c is asking for.

Answer: The question is basically asking you how many units (x) must be sold to make the maximum possible profit (y). You basically need to tell me what the x and y values are that will give you the maximum possible y.

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-

October 6

No class -- Happy Thanksgiving!

5

5

October 13

Class Notes, Homework Solutions

Question: For the Quadratics II homework, for question 1, do we sketch both the new graphs from the original y=x^2?

Answer: You need to sketch all four graphs in part (b) using the graph of y=x^2 (which you also need to sketch as well) using the transformation method I described in the last class. Be sure to label each graph you are drawing. I strongly recommend that you use colour pencils for this one and label the graphs.

Question: For question number 5, what do you mean by the maximum or minimum value?

Answer: By that I mean, "What is the maximum or minimum value of y?"

If a > 0, than the curve opens up and you have a minimum value (recall the range is y >= something). That "something" is your minimum value.

If a < 0, than the curve opens down and you have a maximum value (recall the range is y <= something). That "something" is your maximum value.

Question: For stretching by factor of |a| , for example if i needed to stretch by factor of 2, the point (3,10) would be (6,10) or (5,10)?

Answer: Note:

1) You can only stretch from y=x^2 to y = |a| x^2

2) When you stretch, you multiply the y values by |a|. Let say a = -2 or 2. Therefore, (1,1) becomes (1,2), (2,4) becomes (2,8), (3,9) becomes (3,18).

If a = 0.1, (1,1) becomes (1, 0.1), (2,4) becomes (2,0.4), (3,9) becomes (3,0.9).

The examples you provided are not from y = x^2 and hence it confuses me. If you still don't understand, please let me know.

Question: I don't understand how I'm suppose to get the vertex in question 7C. I know the Y value is -3 but how am I suppuse to get the X value?

Answer: Actually, you made a mistake here.

If the vertex lies on the x-axis, it means the vertex's y value is 0.

Since the vertex always lies on the axis of symmetry, the x value is -3.

Question: I'm also not sure how to do question #10.

Answer: Your final answer is in the form of y = a(x-2)^2 + k. You need to substitute in the points (0, 17) and (2,5) into the equation. You then have 17 = a(0-2)^2 + k and 5 = a(2-2)^2 + k. You now have two equations and two unknowns. You should know what to do.

After that, you know the values of a and k, you can then write out the entire equation in the form of y = a(x-2)^2 + k.
6

6

October 20

Class Notes, Hints for Question 6, Homework Solutions

Test 1 notice is handed out.

Question: I don't understand the section "Check by formulas" in each part of question 2. What are we suppose to do there?

Answer: For each part in question 2, I want you do apply completing the square technique to find out the axis of symmetry, vertex, and maximum or minimum value (be sure to indiciate whether it is a maximum or minimum).

After you have done that, there are formulas at the bottom of page N2 that allow you how to find the three things directly. I have also derived the formulas in class. You can use these formulas to check whether you have done completing the square properly (and you can go back and fix your completing the square section if you did not do it properly). This is what I asked by "Check by formulas".

7

-

October 27

Course Review and Preparation for Test 1

Test 1 Review Exercise Solutions

8

-

November 3

Test 1 is being held in class. Good luck!

Test 1 covers units #1-6.

Test 1 Solutions and Marking Scheme

9

7

November 10

Class Notes, Homework Solutions

10

8

November 17

Class Notes, Homework Solutions

11

9

November 24

Class Notes, Homework Solutions

Question: Hi sir, I'm stuck on homework problem #3b. Can you help me out?

Answer: You can find the definition of median here:
http://en.wikipedia.org/wiki/Median_%28geometry%29

After reading the article, you know that S is the midpoint of QR, so find it!

The hint says to find the slopes of PS and QR, so find them!  Once you have found their product, you will know what is angle PSR.  If you still don't know after finding the product, read the notes again.  Let me know if you are still not sure.

Question: Can you help me out with question 9(b)i)?  Can't we just use the line segment formula?

Answer: You are suppose to use the distance from a point to a line formula in 9)b)ii).

In 9)b)i), you know the formula to find the area of a triangle is 0.5 X (base) X (height or altitude).  Therefore, the area of the triangle is 0.5 X PQ X QR.  Since the area formula 0.5 X (base) X (height or altitude) does not specify which side of the triangle has to be the base, if PR is treated as the base, then the length of the altitude drawn from Q to PR is the height.  Therefore, the area is also 0.5 X (PR) X (altitude from Q).  Put them together, you have 0.5 X PQ X QR = 0.5 X PR X (altitude from Q).  After you have found PR, you can substitute these values into this formula to find the length of the altitude from Q.  

You will get the same answer as in 9)b)ii), but this is just another way of looking at the same problem.

12

10

December 1

Class Notes, Homework Solutions

13

11

December 8

Class Notes, Homework Solutions

Mid-term Examination notice is handed out.

14

-

December 15

Course Review and Preparation for Mid-term Examination

Notes from Review Class at Agincourt

Review Exercise Solutions (as handed out in class)

Please note that there is an error in this solution set for question 14 (b).  You can download the revised solution for that question here.

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-

December 22

No class -- Merry Christmas!

-

-

December 29 No class
2008
-

-

January 5 No class -- Happy new year!
15

-

January 12

Mid-term Examination is being held in class. Good luck!

Mid-term Examination covers units #1-11 (everything up to and including week 13).

Midterm Examination Solutions

16

12

January 19

Class Notes, Homework Solutions

17

13

January 26

Class Notes, Homework Solutions

18

14

February 2

Class Notes, Homework Solutions

-

-

February 9

No class -- Kung Hei Fat Choi -- Happy Chinese new year!

Today is the third day of the year of the Rat.

19

15

February 16

Class Notes, Homework Solutions

20

16

February 23

Hint on the Homework Assignment: For question 3 in the homework, all angles in the question are in radian. In general, if you see an angle WITHOUT the small circle in superscript (which represents degree), you should treat the angle in radian measure.

Class Notes, Homework Solutions

Test 2 notice is handed out.

21

-

March 1

Course Review and Preparation for Test 2

Review Exercise Solutions (as handed out in class)

-

-

March 8

Class cancelled due to snow storm.

As a result:

  • There will be no class on March 8.
  • In addition, there will be no classes on March 15 (March Break) and March 22 (Easter). (unchanged)
  • Test 2 will now be held after March Break and Easter, on March 29.  You will now have THREE extra weeks to study for this test so you better do well on it! :-)
  • Everything (except for early bird deadline for pre-registration next year) will be postponed by one week.  The school year will now be extended by one more week.  The last class will now be on June 14, 2008.
  • If you previously could not write the test on March 8 and made an arrangement with the instructor to write the test, these arrangements are now VOID because you cannot write the test before the actual test date.  You are now expected to write your test on March 29 in class.  If you have problems with that, please contact your instructor by e-mail as soon as possible.
  • If you cannot write your test on March 29, please contact your instructor by e-mail as soon as possible.
  • The school office at 3030 Midland Avenue will be open on March 11 and 12 (11 am - 6:30 pm), and then it will be closed for the holiday until March 24.  Regular office hours will resume from March 25 onwards (Tuesdays to Fridays 11am - 6:30pm).
  • Enjoy your March Break, Easter holiday and happy studying!
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-

March 15

No class -- Enjoy your March Break!

-

-

March 22

No class -- Happy Easter!

22

March 29

Test 2 is being held in class. Good luck!

Test 2 covers units #12-16.

Test 2 Solutions

23

17

April 5

Class Notes, Homework Solutions

24

18

April 12

Class Notes, Homework Solutions

25

19

April 19

Class Notes, Homework Solutions

Deadline for Early Bird Pre-registration Discounts

26

20

April 26

Class Notes, Homework Solutions

27

21

May 3

Class Notes, Homework Solutions

Final Examination notice is handed out.

28

-

May 10

Course Review and Preparation for Final Examination

Review Exercises Solutions (as handed out in class)

-

-

May 17

No class -- Victoria Day

29

-

May 24

Final Examination is being held in class. Good luck!

Final Examination covers units #1-21.

Final Examination Solutions

30

22

May 31

Class Notes, Homework Solutions

31

23

June 7

Class Notes, Homework Solutions

  • (For Agincourt students only) Class pictures were taken on this day -- click here to access the pictures
  • A stamped, self-addressed envelope must be handed in to your instructor by today if you are not attending the last class.  There should be sufficient postage to enable us to send you your marked homework assignment(s), handout package(s), and your report card.
  • (For Agincourt students only) To give your instructor sufficient time to prepare your report cards, unless permission is given by the instructor, all homework assignments up to and including homework 30 must be handed in by today to receive credit.  All homework assignments up to and including homework 30 received after June 7 without the instructor's permission will not be marked and will receive a mark of zero.
  • (For MacDonald students only) Awards / trophies distributed -- see http://marilake.spaces.live.com/photos/ for the pictures
32

24

June 14

Class Notes, Homework Solutions

Last Class -- Report Cards Distributed

(For Agincourt students only) Awards / trophies distributed -- see http://marilake.spaces.live.com/photos/ for the pictures

For pictures of award winners who take Math 10 in Agincourt, click here!

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-

June 21

No class -- Enjoy your summer!

If ANOTHER class is cancelled in this school year due to whatever reason, this day will be used for the make up class.

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June 28 No class -- Enjoy your summer!

Math is Beautiful!

1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321


1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 +10= 1111111111


9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888

Brilliant, isn't it?

And look at this symmetry:

1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111= 12345678987654321