Attached are the slides used in part of today’s lesson, which contain a few notes on the exploration (most of which come directly from IB documentation).
You can find the slides here.
Factors, Roots, and the Fundamental Theorem of Algebra
We’ve now covered a number of important theorems concerning polynomials. For our next lesson complete the questions below.
Complete pages 124–125, questions 6, 11, 18, 22, 24, 26, 27, 32, 33, 34
In addition to these questions, if you’re ready for a challenge, try to answer any of the questions shown in the Polynomials Super Challenge. These are not assigned as homework, but if you can correctly complete question 1 you’ll get 1 bonus mark on our next test, and if you can correctly complete question 2 you’ll get 2 bonus marks on our next test. You have until the date of our next test to complete any of these challenge questions. Good luck!
Working with the Factor Theorem
Below is the question we considered at the end of our lesson today. Complete this question for our next lesson.
Let \(p(x)=2x^3+ax^2-29x+60\). The polynomial \(p\) is divisible by \((x-3)\).
a) Find \(a\).
b) \(-4\) is also a zero of \(p\). Find the third zero of \(p\).
The Remainder Theorem
Complete the following questions for tomorrow’s lesson.
Page 125 questions 28 and 29
Quadratics + Rational Functions Homework Assignment
Complete the questions in the file attached here and submit your work electronically (as a PDF).
Your file should be received before the beginning of our lesson on Sunday, November 13th. Note that the two bonus questions are optional, but I would encourage everyone to try at least one!
As always, you can write any questions you have about the assignment below in the comments section.
Quadratics + Even and Odd Functions
For tomorrow’s lesson complete the following questions.
Pages 110–112 questions 28, 30, 31, 43
Also, see if you can answer the following question: Is the sum of two odd functions always an even function? (And similarly, is the sum of two odd functions always an odd function?)
Probability Homework Assignment
Complete the assignment attached below for Wednesday, November 9th.
More Probability
Here are a few questions that will involve all of the material that we’ve covered so far. Complete these before our next lesson on Thursday.
Page 548–552 questions 6, 12, 13, 14, 16, 18, 20, 25
Conditional Probability
Here are a couple of questions to look at before our next lesson.
Page 533–535 question 5, 14, 15, 26
Page 548–549 questions 5, 8, 9
Quadratic Functions Homework
Complete the following question for our next lesson on Tuesday. Remember, you can leave a comment below if you run in to any trouble with these!
Consider the quadratic function \(f(x) = 2x^2 + 4x -16\).
- Express \(f\) in factored form.
- Express \(f\) in vertex form.
- Describe a sequence of transformations that would produce the graph of \(y = f(x)\), starting from the graph of \(y = x^2\).
- Describe a sequence of transformations different from your answer to c) that would also produce the graph of \(y = f(x)\), starting from the graph of \(y = x^2\).