Dr. McDonald's Mathematics Course Blog
On Monday, October 24th, we’ll have a test on further integration methods (integration by parts and integration by substitution, there will be no questions on solids of revolution).
The following questions will be useful in preparing for the test (all taken from the Cambridge book, Chapter 19).
Page 644 questions 3–7
Page 648 questions 6, 7, 8
Pages 653–654 questions 1, 3, 5–9
Page 658 questions 2 and 3
Here’s the function that was introduced at the end of the last lesson.
\[f(x) = \frac{5x-6}{x+2}\]
Can you determine the \(x\)-axis intercepts and any asymptotes for the graph of \(y=f(x)\)?
We’ll discuss this question in today’s lesson.
Today we saw how to use a definite integral to calculate the volume of a solid of revolution. (Some textbooks will refer to this as finding a “volume of revolution.”)
The solid we studied today is shown below, and the equation used to generate this solid was \(y=\cos x +2\), with \(x\) running from 0 to 5. Can you use your knowledge of solids of revolution to derive the formulas for
On Tuesday, October 18th we’ll have a test on transformations of functions.
The following questions will be useful in preparing for the test.
Pages 84–85 questions 1, 2, 4, 19
Pages 86–89 questions 5, 6, 13, 14, 23
Update: Not that calculators will not be permitted for this test.
On Sunday, October 16th we’ll have a test on differentiation and integration (not including integration by parts and integration by substitution).
The following questions will be useful in preparing for the test.
(Pearson Textbook)
Pages 751–752—pick any two questions that you have not yet completed
Pages 759–760 2, 3, 13
Pages 762–770 questions 1, 2, 5, 9, 15, 26, 36, 40, 52, 60
Pages 846–853 questions 1, 3, 7, 11 (a and b only), 16
As discussed on Thursday, try the following questions this weekend. Some may not be as difficult as they first appear, and others…
Complete pages 780–781 questions 26, 28, 33, 45, and 49.
If you’re interested in (what may be) a challenge, also try questions 43, 48, and 50.
Below is a question that you should complete for tomorrow.
Find the area enclosed between the graphs of the functions \(f(x)=x^3-3x^2+2x+2\) and \(g(x)=-x^3+4x^2-4x+3\).
On Wednesday, September 28th we’ll have our first HL test on composite and inverse functions.
The following list of questions should be completed as part of your review of this material, and we can discuss any problem you may be having in class before the test.
Pages 85–89 questions 1 to 4, 9 to 11, 15 to 22
Complete the following questions for Sunday, the 18th of September.
Composite Functions
Pages 60–61 questions 1, 2, 5, 6, 9, 10, 12, 17, 19, 24, 25
Inverse Functions
Pages 68–69 questions 15, 16, 17, 24, 30, 31, 34, 35, 36, 37, 38
Complete the following questions for Sunday, the 18 of September.
Pages 751–752 questions 1–6, 8, 14