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.

We’ll have a test on the material from Chapter 1 of the textbook on Friday, September 29th.

In order to prepare for this test, have a look at the questions below, as well as the sample questions document on the SL Resources page.

Review Set 1A—complete any 8 questions
Review Set 1B—complete any 8 questions
Review Set 1C—complete any 8 questions

12 SL Derivatives of Logarithmic and Trigonometric Functions

We’ve now covered the derivatives of logarithmic and trigonometric functions, and the questions below involve applications of those derivative results.

For logarithmic functions, you may find it easier to simplify some expressions using the properties of logarithms before you try to differentiate. See the list of properties of logarithms at the bottom of page 376, and you can see an example of how these can simplify your calculations in Example 12 on page 377.

Exercise 15F 1ghk, 2adeh, 3abegi, 5
Exercise 15G 1adgh (see page 379 for more about the derivative of $$\tan x$$, 2adgk, 3bek, 4b

12 SL Derivatives Test [updated]

To give you all more time to prepare, our test on derivatives (Chapters 14 and 15) will be during class on Monday, October 2nd.

To help you prepare, Mr. Prior has shared the following document with plenty of practice questions. (Note that we won’t cover some of this material until next week.) Try some of those questions, and I’ll make the solutions available here next week.

Update: Solutions to Mr. Prior’s questions can be found here.

12 SL Exponential Functions and the Quotient Rule

Complete the following questions before our next lesson.

Exercise 15D (the quotient rule) questions 1abf, 2ad, and 4.
Exercise 15E (the derivative of the exponential function) questions 1ijno, 2acg, 3a, and 5.

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.”

Make sure you complete the questions here before our next lesson.

Once you’ve completed those questions, work on the following questions.

Exercise 1F question 15
Review Set 1A questions 1, 2b, 4, 6, 7, 9, 11–13

Make sure you complete at least up to question 6 in Review Set 1A before our next class.

11 HL The Binomial Theorem

Complete the following questions before tomorrow’s class.

Exercise 8G questions 1, 2, 3, 4, 6ab, 10, 15

12 SL The Chain Rule

Complete the following questions for our next class.

Exercise 15B.2 questions 1ad, 2abcdfi, 3acef, 4, 5