Complete the following for our next lesson.
Exercise 16D.1 questions 2cf, 3efh, 9
Exercise 16D.2 questions 1, 2
Review Set 16C question 13
11 HL Trigonometric Equations and Identities Test
On Friday, November 24th we’ll have a test on trigonometric equations and identities (this includes all of the material we’ve covered on trigonometry, but does not include the sine and cosine rules, which will come on the next test).
To prepare for this test, I suggest you look at the review sets in Chapters 10, 12, and 13, and also have a look at Chapter 7 in the Pearson textbook.
12 SL Stationary Points
In class we defined a stationary point, and noted that a stationary point may be a local maximum or a local minimum. There is, however, a third option, as illustrated by the function \(f(x)=x^3\) when \(x=0\). While the function does have a stationary point at \(x=0\), it is neither a local maximum, nor a local minimum, instead, it’s called a point of inflection.
Read Section 16C, then try questions 1 and 2ac in Exercise 16C before our class on Wednesday.
11 HL The Ambiguous Case
After having solved The Ambiguous Case, try the following questions tonight.
Exercise Set 11C.2, questions 1, 3, 5, and 9
11 SL Laws of Logarithms
Use the laws of logarithms to answer the following questions for the start of our next class on Thursday.
Exercise 4C.1 questions 1adghko, 2adg, 3ad, 4de, 5ad, 6abde, 7c Exercise 4C.2 questions 1aef, 2ace, 4abd
Exercise 4D.1 questions 1, 2, 4, 6abef
Exercise 4D.2 questions 1abhk, 2ae, 4ab, 5b
11 SL Logarithms
Complete the following questions for our next class.
Exercise 4A questions 1, 2, 6
Exercise 4B questions 1ade, 2adgh, 3abjmqrs, 4, 5, 6acdfgmn
11 HL The Sine Rule
Complete the following questions for next class.
Exercise 11A questions 2, 3, 7, 9, 10, 11
Exercise 11C.1 questions 1, 2
11 HL Trigonometric Identities and Equations Continued
Below is the list of questions we began in class today. Aim to finish up to the end of 13E before our lesson on Thursday.
Exercise 13A.2 questions 3cd
Exercise 13B question 5
Exercise 13C.2 questions 2h, 3c
Exercise 13D question 12
Exercise 13E questions 3ab, 5ab, 26, 27
Exercise 13F questions 3ac, 4ab
Exercise 13G question 5
12 SL Derivatives, Tangents and Normals
After today’s review of techniques for differentiation, try the questions listed below before our next class.
We’ve already seen how to find the equation of the tangent line to a curve that passes through a given point, and finding a normal through a given point on a curve is essentially the same. A normal is a line that is perpendicular to a tangent, and you will recall that if one line has slope \(m\), any line perpendicular to it will have slope \(-\frac{1}{m}\). For example, the equation of the line tangent to the function \(f(x)=x^2\) that passes through the point \((1,1)\) has slope \(2\) (found by taking the derivative), and so has equation \(y=2x-1\). Similarly, the normal to the function \(f(x)=x^2\) that passes through the point \((1,1)\) has equation \(y=-\frac{1}{2}x-1\).
Complete 16A questions 1acf, 2cd, and 4
11 SL Modelling with Exponential Functions
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