11 SL Trigonometric Models Review

We’ve now finished the chapter on modelling with trigonometric functions, and the questions listed below will help you review this material. We’ll begin our next class with a discussion of the solutions, then we’ll begin looking at the next (and final) chapter on trigonometry.

Review Set 10A questions 3–6
Review Set 10B questions 2–5
Review Set 10C questions 3 and 6

11 SL Modelling with Trigonometric Functions Part 2

Now that we’ve built our London Eye model, we can use the same technique (applying our knowledge of transformations) to model other situations that involve periodic behaviour (and to answer more general questions about transformations involving trigonometric functions).

Read the (brief) section at the top of page 242 about the “general” sine function, then get a good start on the following questions before our next class (tomorrow).

Exercise 10B.1 questions 3 and 4
Exercise 10C questions 4 and 5 (for more of a challenge, try question 1)
Exercise 10F question 1

11 SL Modelling with Trigonometric Functions

Now that we’ve learned about the graphs of trigonometric functions, we can apply our understanding of transformations of functions to transform trigonometric functions (particularly sine and cosine) to model period behaviour, like the tides, temperature, etc.

Try to complete the following questions before our next lesson (I suggest leaving the horizontal stretch until the end).

The London Eye is 15 m off the ground, and has a diameter of 120 m. The London Eye completes one revolution every 30 minutes.

  1. Develop a function to model the height of a passenger on the London Eye t minutes after boarding a capsule.
  2. How far above ground would passengers in a capsule be after
    a. 10 minutes have passed?
    b. 25 minutes have passed?

12 SL The Normal Distribution Part 1

We’ll be finishing the course material over our next two classes, but we’ll also spend some time working thought normal distribution problems in our (long) class tomorrow.

So, while you’ll have some time to work on the questions below in class tomorrow, the more of these you can complete in advance, the more time you’ll have to focus on other questions involving the new material we cover tomorrow.

Exercise 24A questions 4, 6, 8
Exercise 24B questions 1, 2, 3, 4, 7

11 SL The Cosine Rule

Complete the following questions before tomorrow’s class.

Exercise 9B questions 1a, 2, 5, 9
Exercise 9D questions 1, 5, 6, 9, 13, 16

12 SL The Binomial Distribution

Complete the following questions before our next class.

Exercise 23A questions 3ac and 4a
Exercise 23D.2 questions 1, 2a, 4a

(We’ll continue with this material in our next class, and in particular we’ll look at the easy way to answer binomial distribution questions using our calculators.)