Category: Mathematics

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11 HL Inverse Trigonometric Functions and Equations

Complete the following exercises before our next class (after the break).

Exercise Set 13A.3 questions 6bdij and 12

Also, have a look at the question below (which was discussed in class). It was mentioned in class that a solution can be found (to both parts!) without a calculator. Can you figure it out over the break?

\[\arctan\left(\frac{1}{2}\right)-\arctan\left(\frac{1}{3}\right) = \arctan(a), a \in \mathbb{Q}^+\]

  1. Find the value of \(a\).
  2. Hence, or otherwise, solve the equation \(\arcsin (x)=\arctan(a)\).

I’ll post a hint in the comments below [update: one error in that comment has been corrected, and the hint has been extended]—you may find it useful.

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11 SL Exponential Functions

In class we looked at functions of the form \(f(x)=a\cdot b^x+d\), and we had a brief discussion of the effect of the values of \(a, b,\) and \(c\) on the graph of the function. Below, you’ll extend this treatment to understand the effect of the values of  \(a, b, c,\) and \(d\) on the graph of functions of the form \(f(x)=a\cdot b^{x-c}+d\).

Read through Investigation 1 on page 95 of the textbook, and use graphing software (I suggest either GeoGebra or Desmos) to explore the effects of various values on the graph of each function. As discussed in class, using sliders can make it easier to see the effect of each, and you can see an example of this below. (But it’s more fun to try to make your own version of this!)

Once you’ve completed your investigation, complete questions 4 and 5 from Exercise 3F. (Record your answers in your notebook, and then bring your notebook to class!)

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11 SL Exponents

Remember to complete the following questions for our lesson tomorrow.

Exercise Set 3A questions 3 and 4
Exercise Set 3B questions 3–5
Exercise Set 3C questions 3, 5

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11 HL Modelling with Trigonometric Functions

In our last class we looked at how we could transform the sine and cosine functions to model periodic behaviour. The questions posted during class are listed below. Try to get through to the end of Section 12D, and we’ll continue with these questions during our next lesson.

Exercise 12C questions 1, 3
Exercise 12D questions 2–4
Exercise 12E question 1
Exercise 12F questions 1, 3, 5, 6def, 8

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12 SL Explorations

At this point you should have created (and shared with me) a Google Doc that indicates your exploration’s

  1. Title
  2. Aim
  3. Rationale
  4. Area of Mathematics Involved

Your completed draft should be in by the end of the day on Friday next week (October 20th).

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11 SL Functions Test

We’ll have our functions test on Thursday, the 19th of October.

In order to prepare for this test, have a look at the questions below. We’ll be spending part of Tuesday’s lesson looking at inverse functions and working on these questions, but it’s a good idea to start these early so you can ask questions if you get stuck.

Review Set 2A questions 1–3, 7, 10, 11
Review Set 2B questions 4, 6, 7
Review Set 2C questions 4, 10, 12

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11 HL Trigonometry and the Unit Circle

Complete the following exercises before our next class (you may find 5a and 6a useful when answering the other parts of those questions, but if you can answer b, c, and d without doing part a, that’s fine too).

Exercise 10C questions 4, 5bcd, 6bcd, 7, 10c

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11 SL Rational Functions

Your homework for tonight involves work with sign diagrams and rational functions.

Read through Example 9 on sign diagrams on page 68, and see if you can answer the assigned parts of question 2 and 3 (see below) without graphing the given function.

Also read through the textbook section on rational functions (2F), paying particular attention to the discussion of asymptotes. Note that the textbook’s definition of a rational function is actually more limited that the (correct) definition we’ve used, which is how they avoid talking about polynomials in this section.

Complete all of the section 2E questions listed below, and as many of the questions below from 2F as you are able.

Exercise 2E questions 1fhk, 2adg, 3agh
Exercise 2F questions 1bc, 2ab