Schedule for Math 12- Week of March 24-28, 2009

Tuesday: review questions for logs, new word problems sheet, introduction to laws of logarithms

Wednesday: review homework questions for law of logarithms, word problems

Thursday: Exam review

Friday: Exam review, word problems due

Reminder: Math 12 Quiz on Wednesday, March 11, 2009

This is just a reminder that there is a math 12 quiz on Wednesday. This quiz will only include quadratic word problems. You will not need to be responsible for the quadratic equation.

Math- Factoring Homework Reminder, February 19, 2009

Just a reminder to Math 12 students that the factoring practice problems are due in class tomorrow. You may complete 10-15 questions, depending on how much practice you feel you need. If you complete 10 problems but only 4 are correct, you will be required to complete more.

Question 12 and 14 are also due in class tomorrow (page 94-97).

Math: Page 12-14 and Power Sequences Homework Hints, February 15, 2009

Question: “On question 38 on the pg 12-14 assignment, it asks about diagonals and gives a bunch of pictures to start of the sequence. It asks how many diagonals a term with twenty sides would have. What confuses me is that I am not sure what exactly constitutes a diagonal in the first couple terms of the sequence.”

Response: For question 38, they are asking you to write a sequence to show the relationship between the number of points and the number of lines connecting the points. n represents the number of dots and tn represents the number of lines. So:

For n=1, there are no lines, tn = 0
For n=2, there is 1 line, tn = 1
For n=3, there are 3 lines, tn=3

And so forth. Write your values of tn in a sequence as so: {0, 1, 3, …tn}

In question 39, n represents the number of sides (the lines around the outside) and the sequence is the number of diagonals that cut through the middle of your shape.

So,
n= 3 is the triangle with tn= 0 (there are no lines cutting through the middle)
n=4 is the next shape (square) with tn=2 (there are two lines that criss cross)
n= 5 has tn=5
and so forth.

Question: On question 41, I am confused because I do not understand how to begin the question. Is the first term T0? As in T0, T0.2, T0.4? If so, is N the height in metres or the seconds?

Response: For Question 41, the terms tn are in the {} brackets. n= 0, 0.2, 0.4, 0.6, 0.8 and 1. n represents the number of seconds that has passed since the frisbee was thrown. The terms are tn ={2.00, 3.12, ….6.00}. These terms represent the height of the frisbee from the ground.

Question: What are we suppose to do for the last page of the Power Sequences homework?

Response: The last page of the homework asks you to analyze the sequence and provide information on them.

For example, with #2, the sequence is {-1, -6, -15, -28, -45, -66…}

– what are the next 2 terms? To figure this out, you will need to figure out what kind of function would produce this. What is the D1 difference? What is the D2 difference? Where is there a common difference? If this is a linear sequence, you would find your common difference in D1. If it is a quadratic sequence, you would find your common difference in D2, etc.

– once you have figured out what type of sequence you have, you can work backwards from the D1 or D2 common differences to figure out what the next two terms are. This will require you to do some problem solving. If the common difference is 4 in D1, what would your next term be? If your common difference is something in D2, you need to figure out what the difference in terms would be in D1 before you can apply it to the sequence.

– Power? This question basically asks if this is a type of function you’ve seen before. If there are no common differences, then it is not a power function.

– Level of common difference? That is just asking if your common difference is in D1, D2, etc.

– Common Difference? That is asking what the difference actually is

Going back to #2:
My D1 is equal to: {-6-(-1), -15-(-6), -28-(-15)…}
My D2 is equal to: {-4, -4, -4, -4…}

So my common difference is -4 and it is at the second level. It is a power sequence. It is a quadratic sequence because the common difference is at D2.

To figure out the next two terms, I need to look at the last two terms given and the common difference. The D1 difference between -45 and -66 is -21. I know that the D2 difference is -4, which tells me that each term in D1 is -4 of the one before it. So, the next D1 difference would be -25 and then -29. Knowing the next two D1 differences, I can just subtract -25 from the last term in the sequence (-66-25=-91) and thn -29 from -91 (-120).

So, the sequence is {-1, -6, -15, -28, -45, -66, -91, -120}

Quadratic Equation

For those who forgot…

Mathematics- Quadratic Number Patterns, Thursday February 12, 2009

In today’s class, we reviewed the results of Investigation 2 from the text. We were dealing primarily with functions such as

These are quadratic functions, which take on the expanded form ofA quadratic sequence is a sequence with terms generated by a quadratic function.

Quadratic functions have common differences in D2. The common difference is twice the size of the coefficient a.

For homework, please complete page 9-11 question 22, 23, 26, 28 and 29.

Math 12- Wednesday, February 11, 2009

Today in math we started Investigation 2 in our texts. This investigation asked you several questions that are meant to help you discover the pattern for quadratic functions. Just as a clarification for some aspects of the exercise:

• Alice and Beatrice never eat at the same fast food outlet. If there were 10 outlets in total, Alice has 1o choices but Beatrice, who chooses second, only has 9 (she does not go to the same one as Alice).
• The investigation wants you to figure out how many different ways Alice and Beatrice could purchase food from outlets. They want you to figure out how many combinations you could have if there were 2 outlets in total, 3 outlets, 4 outlets, 5 outlets, etc. One way to solve for this is by setting up a table:
• The also want you to solve for the sequences of differences (D1 and D2). Refer to the definitions in your book to find D1 and D2.

For homework, please complete questions 17-21 that follow Investigation 2 for tomorrow.

Math 12- Tuesday, February 10, 2009

So far in mathematics 12, we have completed Investigation 1 and questions 1, 2, 5 and 6 in the text. This investigation asks you to explore nmber patterns and to develop sequences. We can find the sequence of differences by subtracting adjacent terms and use this difference to identify linear or other types of functions.

Some patterns that you may have noticed include:

• the common difference of your sequence is equal to the slope when you graph the data (if the common difference is 6, your equation may look like tn=6n)
• the first sequence of difference resulted in a common difference (the difference between the terms were the same) –> this tells us it is a linear function
• if you find the common difference between each term, you can then just figure out what constant needs to be added each time to find your equation y=mx+b

Some of the terms that we reviewed included:

• independent variable: is “manipulated” and can cause change in something else (ex. increasing the hours you work will change the amount that you are paid) – graphed on the x axis
• dependent variable: is dependent on something; changes in relationship to something (ex. the wage you are paid changes/depends on the hours you work)- graphed on the y axis
• domain: refers to the possible x values for your function
• range: refers to the possible y values for your function

For homework, page 4-6 questions #8, 10, 13, 14 and 15 were assigned. The due date for this homework is in class tomorrow (Wednesday).

Grade 12 Mathematics Syllabus

Grade 12 Mathematics is divided into 5 units:

• Quadratics
• Exponential Growth
• Probability
• Circle Geometry
• Rate of Change

The breakdown of your final grade is as follows:
25% Term One Grade (50% Term One Course Work, 50% Midterm Exam)
25% Term Two Course Work
50% Final Exam (40% Written Exam, 10% Oral Exam)

Availability
Mondays 2:50-4:00PM
Tuesdays 12:00-12:30PM
Friday 12:00-12:30PM

Classroom Expectations

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Submissions: Homework assignments, whether they are to be submitted or not, are due the next school day in class. All work is expected to be submitted on time and as complete as possible. There will be random homework checks throughout the semester. Late assignments must still be completed for feedback but will receive a mark of zero.

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