12 HL: Further Functions

Complete the questions below for Friday, October 24th. Any questions you don’t complete should be completed over the break.

(green textbook)
Exercise 6A questions 1, 2, 3, 6, 7, 8
Read Section 6B, then complete Exercise 6B questions 1, 2, 4
Exercise 6C questions 5a and 5b (for ii and iv only)
Exercise 6D.1 questions 1, 2be, 3
Exercise 6D.2 questions 1, 2

12 HL: Transformations of Functions

Complete the following questions (from the blue textbook) for Monday, October 20th.

Exercise 16A questions 1, 2, 4, 7a, 8, 9, 11, 12
Exercise 16B questions 1, 2, 3, 7, 8, 13, 16, 17
Exercise 16C questions 1, 2, 3, 7, 9, 11
Exercise 16D questions 3, 5, 7, 8, 10, 12

12 HL: Inverse Functions

Complete the following questions for Tuesday, October 14th. We haven’t yet looked at graphs of functions and their inverses, and we also haven’t discussed the conditions required for a function to have an inverse (Do all functions have inverses?). If you want to look into those features of inverse functions, you can do some reading in Section 15F of our (blue) textbook.

Exercise 15F questions 2, 4, 17, 18

12HL: Functions Review

Complete the following questions (from the blue textbook) before the end of the week (but ideally ASAP).

Exercise 15A questions 1a, 3, 5
Exercise 15B — just read this section (and do a couple of questions to check your understanding)
Exercise 15C questions 3ade, 4
Exercise 15E questions 1, 3, 6, 14

12 HL: Permutations and Combinations

Complete the following questions before class on Friday, October 3rd.

Exercise 7A questions 2, 3, 4
Exercise 7B questions 1cd, 2
Exercise 7C questions 2adeh, 3be, 5abe, 6bfe
Exercise 7D.1 questions 1, 3, 6, 7, 10, 12, 18
Exercise 7D.2 questions 3, 5
Exercise 7E 1, 2, 6, 7, 8, 9, 11, 14, 20, 24

12 HL: Polynomials and Complex Numbers Test

On Thursday, October 2nd we’ll have a test on all the material we’ve covered on polynomials and complex numbers, corresponding to Chapter 4 and Chapter 5 (Sections A to I) of the green textbook. Note that this is a no calculator test.

12 HL: Intro to Complex Numbers

You may want to get a start on the next set of homework questions (which will be due Wednesday, September 17th).

Exercise 4A questions 2, 3, 4adb
Exercise 4B questions 1, 3
Exercise 4C questions 1, 7, 8
Exercise 4D questions 1, 3, 5, 6
Exercise 4E questions 1–6, 8*

*This last question is quite challenging.

Also, see if you can complete the proof that, for \(z_1, z_2 \in \mathbb{C}\), \((z_1 + z_2)^* =z_1^*+z_2^* \).