Homework Due Tuesday, 27/11/12

Ex. 14.1:

#9, 12, & 14

Ex. 14.2:

#7, 8 & 9

Homework Due Thursday, 22/11/12

Ex. 14.1:

#6

Homework Due Wednesday, 21/11/12

Ex. 14.1

#10

Ex. 14.2

#6

Binomial Theorem

Folks, after today's class you should try and reflect on the discovery, discussion and video that we saw. In fact, you can watch the video again if you'd like to refresh your memory. For those of you who were not in class, you can view the video by clicking on the link below but before you see the video look at the results of the expansions we did at the end of class on Wednesday and see if you can find any patterns, especially with the coefficients of the terms.

Binomial Theorem Uncovered!

[When you click on the link, it'll most likely open a new tab and automatically download the video on your computer. For some of you, it may load in the web-browser itself.]

Once you've thought about it and watched the video again, you should proceed to do the reading and look at the kinds of expansions that were being attempted in Newton's time and how he approached it. In addition, you'll get some great background on Newton and why he is revered as such a genius. 

Note: The video you saw, or will see, is by James Stanton from his website called Thinking Mathematics and you can view many other videos on various topics in the subject. Unfortunately, these days Youtube is down in Pakistan and you will not be able to see any of his videos through official channels. This is why I have made it available for downloading/viewing through the blog. 

Homework Due Tuesday, 06/11/12

Page 307, Ex. 13.3

#1, 2, 3, 4, 5, 6 & 7

Note: Finish Ex. 13.2 in your class work journals and then do the above in your homework journals. Also, don't forget, in Combinations the order doesn't matter. 

Quiz 2 Solutions

You can download the solutions PDF by clicking here. Please remember that it is better to try and attempt the questions yourself first, make any corrections that you can on your own and then check the solutions for help. 

Homework Due Wednesday, 17/10/12

Page 188-189, Ex. 8.1:

7h, 8, 9 & 10. 

Homework Due Tuesday, 16/10/12

Page 187-188, Ex. 8.1:

# 3, 4, 5, 6, 7 a-b-c-d

Work in your graph books for the graphing questions and your homework journals for question 7. 

Homework Due Thursday, 11/10/12

Page 187, Ex. 8.1:

# 2

To be done in your graph books. 

Choose your scale wisely.

Homework Due Tuesday, 09/10/12

Page 256, Ex. 10.3:

# 3 g-i, 6, 8 & 10

Page 259, Ex. 10.4:

# 8

Page 275, Ex. 11.2:

# 6 e, 7 d, & 13

Page 284, Ex. 12.1:

# 3 b-c, & 4 c

Homework Due Thursday, 04/10/12

Page 223-224, Ex. 9.4:

#5, 6, 7, 11 & 12.

Homework Due Tuesday, 25/09/12

Page 284, Ex. 12.1:

# 5, 6, 7 a-c-d-e-g-i-j, & 8.

[Please note that in some questions in the exercise above, you will find that now and then they have inserted an angle in degrees (the symbol gives it away) and so be sure to change the calculator modes accordingly. Especially one of the questions where they have written an angle as Pi degrees. They are trying  to trick you into thinking that it is a radian measure because of the Pi symbol except right after they give degree symbol. When there is no symbol then you should always assume the angle to be in radians.]

Page 290, Ex. 12.2:

# 12, 13 &15.

Homework Due 11/09/12

So folks, we should keep in mind one of the discoveries from today's class (and please do test this for yourself) that if the period of the function changes, then one can add and subtract the value of the period from the angles we get as a result of our calculations. Do the following for homework and don't forget to do some questions from the miscellaneous exercises of chapter 10 and 11.

Page 275, Ex. 11.2:

7, 8, 9 & 14 

Homework Due Wednesday, 5/09/12

Page 275, Ex. 11.2:

#4, 5 & 6 a-d-g-l

Homework Due Tuesday, 04/09/12

Page 275, Ex. 11.2

#10 a-c-d, 11, & 12.

 You are not required to do these on graph paper. Just make good legible sketches. For question 11, part (c), you may have to make a table of values for tan 3x, just like we did in class and then figure out the period for the tangent function when it undergoes a horizontal stretch or compression. It does not quite work the same way as the sine and cosine periods.

Homework Due 28/08/12

Page 268-269, Ex. 11.1:

# 8 - 27

{Some of these can be challenging, but do the best you can and attempt all of them.There are cases such as question 25 where you will need to remember the two other identities we derived based on the pythagorean identity.}

Homework Due 22/08/2012

Page 256-257, Ex. 10.3:

#1, 3 a-b-c-d-h, 4 a-b-e, 7, & 9

[In question 3, when they say "state the corresponding range of y, they mean the range of the outputs or the interval between the minimum and maximum values. Also, for question 7, you may want to draw accurate sketches on graph paper as you will have to rely on those sketches for what is being asked.]

Page 258, Ex. 10.4:

#2, 3, 4, 6 & 7.

Note: In many of the questions you will be required to apply what you already know in new situations. Do not forget the basics and in any circumstance, try something before coming on to the blog and asking a question. 

Homework Due 07/08/12

Folks, as I had instructed you in class. You will be graphing the sine, cosine and tangent functions by make a table of values with 15 degree increments for the inputs from -360 degrees to positive 360 degrees and then plotting them on the sheets I provided you in class. As some of you astutely pointed out that even with 30 degrees for one square we are two boxes short on each end. So, please take our rulers and pencils and extend the grid by two boxes before proceeding.

Also, write down any observations you have of the graphs you plot.

Note on the tangent graph :
This graph should leave you a little anxious as something will happen in its output values that you would not anticipate until you actually plot the graph. Do write down any special observation you have of this graph.

Classwork Continued...

You will continue the class work in your CW notebooks.

Page 248, Ex. 10.2, 

#12 a-b-e-f-g-h-j, 13, & 14.

Summer Work

Okay folks, below are the exercises you have to complete over the summer, in addition to your exam corrections. You can do these questions on separate sheets of paper or in your H.W. journals. You will submit this work to me in our first class in August. You can use the blog post to discuss questions with me or with each other. Some of the questions will challenge and stretch your understanding. For many of you this is a great opportunity to learn and catch up with the rest of the class. Please don't try and do it all at the last minute!

Page 171-175, Misc. Ex 7.:

# 4, 5, 6, 10, 15, 24, 26, 29, 30 & 31

Page 80 - 81, Misc. Ex.4:

# 1, 2, 3, 4, 5, 6, 9, 15, 16, 17, 18, 21 & 24

Page 95 - 97, Misc. Ex.5:

# 1, 2, 6, 7, 8, 10, 11, 14, 16, 17, 18, 20 & 24

Page 57 - 60, Misc. Ex. 3:

# 3, 5, 6, 10, 13, 14, 16, 19, 23, 24 & 28

[For question 28, you can use the software Graphmatica, which is 

a graphing software that you can download from http://graphmatica.com/]

Page 34, Ex. 2.2:

# 13 - 16 

[Again, for question 16 , you can use Graphmatica]

Page 240-241, Ex. 10.1:

# 1-11 (all questions)

[In these question when they say basic angle they mean the angle 

the star makes with the horizon line, no matter what quadrant it is in.]

Page 247-248, Ex. 10.2:

# 1-11

Homework due Tuesday, 17/04/12

Folks, the following homework should basically be done without a calculator. You're going to be expected to use your understanding of logarithms and manipulate the expressions in order to find what is being asked.

Page 52, Ex. 3.5

#6; 7[b , c], 8 [b , c , f], 9 [a , e],

10 [d , e], 12, 13 [a , c] , 14 [a , c].

Page 55, Ex. 3.6

# 1, 5, 9, 11 (b), 12, 13 & 14.

Project #2: Geometric Solution of the Sine of 36 Degrees

Folks you have the worksheet which was given to you on Saturday. You can work together on this but make sure that you understand what you are doing. Please do not copy from each others' work. The worksheet can also be downloaded by clicking here. You can use this post to discuss your progress on the solution.

The first question in the assignment has to do with the interior angles of regular polygons. Click below for an activity that you can do to make sense of why the interior angles of a pentagon are each 108 degrees.

Interior Angle Activity

Homework due Friday, 06/04/12

Page 47, Ex. 3.4

# 2, 4, 5, 8, 9, 16, and 17

Homework due Monday, 02/04/12

 Page 45, Ex. 3.3

# 1 - 4

Homework due Monday, 26/03/12

Page 39, Ex. 3.1

# 5 and 6.

You can read Example 3 on page 37-38 of your 

textbook for help in understanding how to 

simplify expressions in question 6 of Ex. 3.1. 

Page 41-42, Ex. 3.2

# 1 [b, c, d, f, g, k, l], 2, 3b, 5, 6 and 7d.

Take-Home Test due Monday, 19/03/12

Folks, this is the post for the take-home test discussions. Ask your questions, but be careful about not disclosing too much of what you've done. If you happen to lose your copy of the test, then you can download it from the link below. Remember, you are to do the test on separate sheets of paper, not on the question sheet itself.


http://dl.dropbox.com/u/13710778/Test%205%20-take%20home.pdf

Do not start the test on the weekend, you will needlessly suffer!!!

Homework due Monday 12/03/12

Page 92, Ex. 5.4

#1, 2, 3 a -e - f, 4, 6 and 8. 

Page 96, Misc. Ex

# 21

Note: In this homework you will be required to think broadly about the techniques you will use to solve these questions. Remember that the techniques of factoring you use with quadratic expressions can also extend to certain other functions of higher degree (as we've seen in class as well). The questions will require you to apply all the techniques you have learned in various ways.

Homework due Friday, 09/03/2012

Page 84, Ex 5.1

# 1, 3, 5, 10 and 12

Proving the Remainder Theorem

Okay folks, it's time that you put your thinking caps on. We observed some interesting results in class today when it came to dividing polynomial functions by expressions that were not generated by the roots of the functions. To prove these results to be true for every case, we will have to remember a few things about division, and especially about remainders.

When dividing a number, say 79, by another number, say 7, we get a remainder of  2. If I were to write this statement differently then I could say that 79 = (7)(11) + 2  (you should try out and verify what I am saying here).

Now see if this same kind of statement works for an actual example of a polynomial that is divided by an expression that is not a factor. You can use the two examples from class and try and write the statement I showed you but instead using the polynomials.

After this the work gets interesting and tricky. Try and write a similar statement for a random polynomial f(x) being divided by (x-a) and you can call the remainder r. bring to class anything and everything that occurs to you


NOTE: The class work that you have to complete are questions 1 and 2 from page 90 of your text book.

Homework due Friday, 17/02/12

Page 76, Ex. 4.3

#1 (b),1 (d),1 (e),1 (j), 3, 5, and 9.

 

Remember that a solution set is the same thing as saying the value(s) of x (or whatever input variable) that satisfy something. Please don't try to do these algebraically; visualize the function by first making the inequality a roots argument and then see what values satisfy the statement. For sketching the function you have options:

1. Find roots and see if the function is opening up or down.

OR

2. Convert to a form where the transformations are easy to see and then sketch it (you may still need to find roots for the solution set to the inequality).

Either way, roots are important!

Homework due Monday, 13/02/12

Page 74-75, Ex. 4.2

#10, 12, 14, 18 and 19

Remember, the first 3 questions are along the same lines as the previous ones you have done for homework. However, 18 and 19 deal with the intersections of linear and quadratic functions. Now, here's a clue: You will be making use of the discriminant in these questions as well.

Homework due Friday, 10/02/12

Page 74, Ex. 4.2

# 5, 7 and 9.

Homework due Monday, 06/02/12

Page 67, Ex. 4.1
#14

Page 73-74, Ex. 4.2

#1, 2, 3 and 4

Remember, when they are talking about the "nature" of the roots, they mean whether there is one real root, two real roots or no real roots. The discriminant helps you determine exactly this when the function is in standard form. You should certainly post your queries about the homework on the blog. Some of you may be wondering why they are using the word "real" to describe the roots every time. Do you remember that we learned about the Real numbers? Think about it and we can discuss this further in class.

Also, don't forget that your test on quadratics is on Tuesday, 7th February, 2012.

Homework due Friday, 03/02/12

Page 67, Ex. 4.1

# 9 and 7 (in that order)

Homework due Tuesday, 31/01/12

Page 67, Ex. 4.1

# 8 and 10

Homework due Monday, 30/01/12

We are now ready to tackle the problems from the textbook. Your homework is:

Page 67, Ex 4.1

#2, 3, 4, 5, 6 and 11

Homework due Friday, 27/01/12

The homework worksheet, if forgotten or misplaced, can be downloaded by clicking here. To download the file you can right-click and click on "save link as".

Solution to Q. 2 of the Last Homework Assignment

We had neglected to discuss how you approached question 2 of the Homework due 20th January, 2012. Below is the solution. I chose factorization because as it was simpler that way, but completing the square could also have been used.

 

Term Project due 02/03/2012

The project assignment sheet can be viewed by clicking on the image below. If you would like to download it then right-click and go to "save link as" and then save the pdf file on your computer.

You can use this post to discuss your approach. 

Homework due Friday, 20/01/12

Your homework is the worksheet I gave you in class. If you have misplaced it then you can download the pdf from the link below. (If by just clicking on the link the pdf does not open in your browser window, then you can right-click on the link and click "save link as" to download the file onto your system.)

http://dl.dropbox.com/u/13710778/Homework%2016-01-12.pdf

I look forward to discussions about this homework as well!

Homework due Monday, 16/01/12

Below are the steps we discussed in class, in case some of you had trouble copying them down:

1. Rearrange the equation in a way that it becomes an argument of finding missing length on a diagram that has a square and a rectangle joined together to form a bigger rectangle whose total area is a given number.

2. After drawing the diagram next to the equation, cut the rectangular portion of the diagram in half and relocate it to the bottom of the square portion.

3. Add the missing piece to the diagram such that a square is completed and add the area of that missing piece to both sides of the algebraic equation.

4. Now you can just factor the left side of your equation (the one with variables in it) and simplify the right side of your equation (the numerical side) and continue to solve for x as you saw in class.

I will post answers to the problems on the weekend so that you can try and check your work before Monday. Please don't take too many short cuts and always draw the diagram or you will needlessly suffer with inaccurate results. You should use the blog to post questions and share your thoughts with each other.

Homework due Tuesday, 10/01/12

Happy New Year Everyone! The blog is back in action once again.
Below is your homework for Tuesday.