Complete the following questions for our class tomorrow. We’ll have a short (1 question) quiz on this material tomorrow. Remember, if you get stuck, just post a comment below!
Exercise Set 3G.1 questions 1–3
Exercise Set 3G.2 questions 1, 4, 5
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?
\[\arctan\left(\frac{1}{2}\right)-\arctan\left(\frac{1}{3}\right) = \arctan(a), a \in \mathbb{Q}^+\]
- Find the value of \(a\).
- 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.
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!)
11 SL Exponential Equations
Complete the following questions before our class on Thursday.
Exercise Set 3E questions 1gk, 2aeino, 3a, 4ae, and 5ef.
11 SL Exponents Continued
Complete the following questions for our next lesson.
Exercise Set 3D.1 questions 2adgjk
Exercise Set 3D.2 questions 1ade, 2adg, 3ade, 4aef, 5adg
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
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
12 SL Explorations
At this point you should have created (and shared with me) a Google Doc that indicates your exploration’s
- Title
- Aim
- Rationale
- Area of Mathematics Involved
Your completed draft should be in by the end of the day on Friday next week (October 20th).
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
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