Complete the following questions before our next class.
Exercise 3C.1 questions 2–4 and 5acegi
Exercise 3C.2 questions 1–3
9 Extended: Further Expansion
During class on Monday, April 8th, you should read the examples in Section 3B of the textbook, then complete the questions listed below.
Exercise 3B questions 1–4
11 SL Transformations of Trigonometric Functions
You should have the following questions completed by the end of class on Monday, April 8th. (In order to complete these, you may also find it helpful to read the textbook material in Sections B to F in the textbook.) Yes, there are lots of questions, but you’ve got lots of time!
One formula that you should have in your notes (this was discussed in our last class), is the formula to find the value of \(b\) that will change the period (of either \(f(x)=\sin (bx)\) or \(f(x)=\cos (bx)\)) to a desired value. That formula is given below.
\[b=\frac{2\pi}{\text{period}}\]
Questions
Exercise 10B.1 questions 1–4
Exercise 10B.2 questions 1–3, 4acegi
Exercise 10C questions 3–5
Exercise 10D questions 1adgi, 2, 3, 4
Exercise 10E questions 1–3
Exercise 10F questions 1, 2c, 3, 4ce, 4, 6ace, 7, 8
9 Extended: Algebraic Expansion
Complete the following questions before our next class.
Exercise 3A.1 questions 1–9 (3 each)
Exercise 3A.2 questions 1–3 (3 each)
Exercise 3A.3 questions 1–2 (3 each)
Exercise 3A.4 questions 1–2 (3 each)
12 HL The Ratio Test
Complete the following questions before our next class.
Use the ratio test to determine the convergence or divergence of the following series.
- \[\sum_{n=1}^\infty \frac{n^3 3^{n+1}}{4^n}\]
- \[\sum_{n=1}^\infty \frac{n^{10}}{10^n}\]
- \[\sum_{n=1}^\infty \frac{n^n}{n!}\]
From the Haese book, complete Exercise K.3 question 1.
12 SL Conditional Probability
Complete the following questions before our next class.
Exercise 22I questions 9, 12
Exercise 22J question 4
(Also, make sure you’ve completed the questions that were assigned over the break, see here.)
11 SL Periodic Functions
In class today we saw that the graph of the sine function will be periodic (though we didn’t introduce that term). Read Section 10A to find the definition of a periodic function, then complete the question below.
Exercise 10A question 1
12 HL The Comparison Test(s)
Complete the following questions (from the Haese book) before tomorrow’s class.
Exercise K.1 questions 1acd, 3, 4bcef, 5
12 SL Venn Diagrams and Laws of Probability
Read sections H, I, and J in Chapter 22, then complete the following questions before our next class.
Exercise 22G questions 1, 3, 5, 6, 10
Exercise 22H.1 questions 6, 7, 8
Exercise 22I questions 1–5, 7
Exercise 22J questions 1–3
12 HL Sequences and Convergence
Complete the following questions before our next class.
(From the Haese book)
Exercise B.1 questions 3 and 5
(Read Section J, then complete )
Exercise J.1 questions 1bdf, 2acdf, 3
Exercise J.2 questions 1, 2, 3
Pay particular attention to questions 1 and 2 in J.2, which makes use of two (often useful) algebraic methods for showing that a sequence is monotonically increasing/decreasing: a sequence is decreasing if either \(u_{n+1}-u_n <0\), or \(\frac{u_{n+1}}{u_n} <1\) for all \(n\), and with inequalities reversed either method establishes that the sequence is increasing.