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.
12 HL Slope Fields and Euler’s Method
Complete the following questions before our next class.
(from the Haese book)
Exercise M questions 1, 5, 7, 8
(from the Pearson book)
pages 1467–1469 questions 14, 29, 30, 33
11 SL: Trigonometry Part 3: Finding Angles
Complete the following questions before our next class (Period 2 on the first day back after the break!).
Exercise 8D.1 questions 4–5
Exercise 8E questions 3–5 (do question 5 without using a calculator—find the reference angles)
12 SL Introduction to Probability
Complete the following questions before our next class.
Exercise 22B questions 1, 2c, 3
Exercise 22C.1 questions 1, 2, 3, 6
Exercise 22F questions 1–3