Category: 11 HL Homework

Complete the questions on this document before the beginning of class on Monday, April 10th.

For this assignment, you should submit your work electronically as a PDF file.

Now that we’ve looked at the unit circle definitions of the trigonometric functions, complete the following questions.

Complete the following questions for our next lesson.

Pages 286–288, questions 1, 2, 3, 8, 10, 12, 25, 28, 29, 34, 35, 38, 40

Here’s a short homework assignment on proof by indication, to be collected on Monday, February 6th.

Show that \(6^n+4\) is divisible by \(10\) for all \(n \in \mathbb{Z}^+\).

You can download the template from class here.

Find the simplified expansion of \((a+b)^7\). You can use any method you prefer, but the Binomial Theorem may save you some work!

Complete the following questions during the break. Remember, if you get stuck you can leave a comment below. If you see a question in the comments and you have a suggestion to make, post that too!

Pages 172–173 questions 1, 2, 3, 11, 12, and 20

Additionally, see if you can complete all of the question below.

Consider the series shown here.

\[\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\cdots\]

 

1. Find the formula for \(S_n\)
2. Write down the value of
   1. \(S_3\)
   2. \(S_{10}\)
   3. \(S_{100}\)
3. What do you notice happening to the value of \(S_n\) as \(n\) increases? Can you use the formula for \(S_n\) to explain why this is happening?

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 \(\displaystyle{\frac{x+1}{x-4}\leq \frac{1}{x-2}}\).

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!

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 \(p\).