Our next class is the test, so you should have the questions below completed for our lesson on Thursday next week.
Exercise 10A 1abcdghim, 2abc, 3abcdfgh, 4abc
Exercise 10B 1, 5, 7, 8, 10, 13
11 HL Induction (Continued)
Work on the following questions for tomorrow’s class. You don’t need to complete all of these, but try to complete at least one from each section.
Exercise 9B.2 1d, 2b, 6, 10, 11, 12B
Exercise 9B.3 2ab, 3
Also, make sure you see the updated test information here.
Challenge Question: Prove that an arithmetic sequence with first term \(a_1\) and common difference \(d\) is such that
\[S_n=\frac{n}{2}\left(2a_1+(n-1)d\right)\]
11 HL Induction
Complete the following questions for our next class.
Exercise 9B.1 questions 2b and 3b
Here is a template you can use for proof by induction. (Note that the template is set up for a proof that involves a claim concerning all natural numbers. If the claim concerns, for example, all positive integers, you need to adjust the base case and other remarks accordingly.)
11 HL Induction and the Binomial Theorem Test [Updated]
On Tuesday, October 12th [note the revised date + content] we’ll have a test on induction and the binomial theorem (including combinations and permutations). Graphing calculators will be required for this test.
In order to prepare for this test, have a look at the questions listed below.
Review Set 8A (all)
Review Set 8B 2, 8–10
Review Set 8C 1, 2, 7–10
Review Set 9A 1–7
Review Set 9B 2
Review Set 9C 1, 2, 5, 7
You may also find some of the additional resources on the HL Resources page useful.
11 HL The Binomial Theorem and Philosophy
After trying question Exercise 8G question 14, have a look at the quotation from Wittgenstein’s Tractatus Logico-Philosophicus.
With regard to the existence of \(n\) atomic facts there are \(K_n=\sum_{r=0}^n \left(\begin{array}{c}n\\r\end{array}\right)\) possibilities.
Show that Wittgenstein could equally have written “…there are \(K_n=2^n\) possibilities.”
11 HL The Binomial Theorem
Complete the following questions before tomorrow’s class.
Exercise 8G questions 1, 2, 3, 4, 6ab, 10, 15
11 HL Combinations and Permutations
Here is a (fairly long!) list of questions to work on before our next class.
You don’t need to complete all of these (we’ll continue with this material next class), but make sure you try at least one question from each section.
8A 2, 3, 6
8B 2
8C.1 3, 5ag
8C.2 2
8D 3, 5, 10
8E 3, 4, 9, 10
11 HL Polynomials Test
On Friday, September 22nd, we’ll have a test on polynomials (and complex numbers). As with all tests, some questions will require familiarity with past course material, and you may want to review your notes on transformations.
In order to prepare for the test, the exercises listed below would be a good start. Note that you may find additional questions in the materials available on the HL Resources page.
Review Set 6A questions 3–5, 9, 11–13, 16, and 17.
11 HL Working with Polynomials
Complete the following questions for our next lesson.
Exercise 6F.3, question 1ace, 2ace, 3acg, and 7.
11 HL Challenge
Have a look at the questions in the PDF file here, and try to complete both questions before our next class. (Note that this is an optional homework assignment, so while I would encourage you all to try the questions, you need not complete them both.)
In addition to the mathematical content, your emphasis should also be on clarity of communication.