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 SL Composite Functions
We’ve now discussed domain and range and had an introduction to composite functions. I suggest that you read pages 64–65, and then complete the questions below before our next class on Tuesday.
Exercise 2C questions 1–3, 4aceik
Exercise 2D questions 3, 5–7
12 SL Explorations
We’re now beginning work on the SL Mathematical Exploration. A number of resources (a student guide, the marking criteria, and some additional notes on the criteria) are available for download from the SL Resources page, along with some sample explorations that we’ll be looking at in our next class.
Important Dates
October 20th: First Draft Due
November 2nd: Final Draft Due
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 SL Quadratics Test
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.