Dr. McDonald's Mathematics Course Blog
We’ll have our first test on the Calculus Option topics on Sunday, March 6th.
This test will cover material that includes differential equations, important theorems and definitions in Calculus (Rolle’s Theorem, the Mean Value Theorem, continuity and differentiability, etc.), and l’Hôpital’s Rule.
Update: The following questions will be useful.
page 1471–1474 questions 1, 4, 10, 16, 19, 22–27
page 1436 questions 9, 17
page 1354 questions 4, 6, 14, 15
Complete the questions on this PDF file for the beginning of class on Wednesday, March 2nd.
You should now have received an email with a list of questions. Complete questions 4, 7, and 14 for tomorrow’s class.
Update: note that there’s an error in question 14: \(y(2)\), rather than \(y(3)\), should appear in part c).
We’ll have a test on logarithms on Thursday, February 25th.
The following questions will be useful for revision, and we can discuss any difficulties with these in class on Wednesday.
Page 243–245 questions 2, 4, 7, 8, 14, 16–19, 21–25
Complete the following question for tomorrow’s lesson.
If you can earn 5% interest compounded quarterly, how long will it take for your investment to double in value? Find an exact expression for your answer, with time measured in years.
[Note that \(\ln 2\) is an exact expression, and may appear in a correct solution to this question.]Complete page 1470 questions 25 and 27. You will find it helpful to simplify expressions as much as possible in your intermediate steps.
Complete the following questions for our next lesson. These are all relatively short, so you should be able to complete all questions for our lesson on Monday.
Pages 232–233 questions 3, 5, 12, 15, 18, 20, 21, 26, 31, 33, 44, 47, 48, 54, 56, 57, 60, 61, 63, 67, 69, 71, 72–77, 79, 80, 84
We’ll have a test on mathematical induction and the Binomial Theorem on Monday, February 8th.
To prepare for the test, complete p. 203–205 questions 20, 22, 24, 28, 26, 45, 47
We will discuss these questions in Thursday’s lesson.
Here’s a short homework assignment on proof by indication, to be collected on Wednesday, February 3rd.
Show that \(6^n+4\) is divisible by \(10\) for all \(n \in \mathbb{Z}^+\).
Update: You can download the template from class here.