Complete the following questions for the start of our lesson tomorrow.
Pages 879–881 questions 5a–d, 6a–c, 8, 9bc, 13, 14, 15
Roots of Complex Numbers
Below is a GeoGebra applet that will allow to you find the \(n^{\textrm{th}}\) roots of a complex number \(G\), for a value of \(n\) from 1 to 5. (Note that it does take some time to load.)
Probability and Complex Numbers Test
Our next test (on Wednesday, November 30th) will be a mix of questions on the topics of probability and complex numbers.
In preparing for the test, the following questions will be useful.
Pages 562–570 questions 1, 3, 14, 18, 24, 34, 42, 43
Pages 459-460 questions 1, 3, 4, 10, 11, 14, 15, 17, 24
Polynomials Test
We’ve now covered all the material that will appear on our next test, to be held on Monday, November 28th.
The following questions from our textbook will help you prepare for the test.
Page 150 questions 11–21, 28
Inequalities
Here’s a question to consider tonight. This question can be answer in much the same way as the inequalities we considered in class today (there is one minor difference—see if you can figure this out!).
Solve the inequality \(\displaystyle{\frac{x+1}{x-4}\leq \frac{1}{x-2}}\).
Exploration Information
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.