## 11 SL Arithmetic Sequences

Complete the following questions before our next class. (We’ve talked about arithmetic and geometric sequences, but for this set of questions you’ll see that the focus is on arithmetic sequences.)

Exercise 6A questions 1ac, 2bc, 3
Exercise 6B questions 1, 2, 3bc, 4bc
Exercise 6C.1 questions 1, 2bc, 3, 4, 6, 7bce, 9a, 10, 11
Exercise 6C.2 questions 1, 2

## 9 Extended: Equations of Lines

If we plot all the points that satisfy the equation y = mx + c, we’ll see that we get a line with slope m and y-intercept c. This form of the equation of the line (we’ll see another next class) is called the point-slope form equation of a line.

Now that we’re familiar with this type of equation, we can find the equation of a line with a given slope that passes through a given point.

For example, if I want to find the equation of a line with slope –2 that passes through the point A(1, 2), we know the equation will have the form y = –2x + c, but we still need to find the y-intercept (in other words, we still need to find the value of c). Here we can use the fact that the point A(1, 2) should be on our line. Since A is on our line, we should have \begin{align}2&=-2(1)+c\quad \text{ and so}\\ 4&=c\end{align}

But this means we’ve just found the “right” value for c! Now we now know that the equation for the line with slope –2, and passing through A(1, 2), is y = –2x + 4. (You can check this using GeoGebra.)

Complete the questions below before our next class.

1. Find the equation of the line with slope –1, passing through the point (1, 4).
2. Find the equation of the line with slope –1, passing through the point (2, 0).
3. Find the equation of the line that passes through (1, 3) and (2, –1).
4. Find the equation of a line perpendicular to the line you found in question 3, which also passes through the point (1, 3).

## 12 SL More Integration

Complete the following questions before our next class.

Exercise 18E.1 questions 1–3

(For some of these, a little algebraic manipulation before integrating will be a big help!)

## 12 HL The Poisson Distribution

Complete the following questions before our next class.

Exercise 25G questions 2, 4, 5, 8, 10

## 12 SL Indefinite Integrals

Complete the following questions before our next class (tomorrow).

Exercise 18B questions 1–3
Exercise 18D questions 1–12

## 9 Extended: Collinear Points

Complete the following questions before our next class.

Exercise 9D.2 questions 1–3

## 11 SL Transformations Review

Complete the following questions before our next class.

Review Set 5A questions 3, 5, 6cd, and 7

## 9 Extended: Parallel and Perpendicular Lines

Now that we’ve got a definition of the slope of a line (or a line segment), we can now give easy definitions of what it means for two lines to be parallel or perpendicular.

Complete the following questions before our next class.

Exercise 9D.1 questions 1–4, 6, 10

## What is a Voronoi Tessellation?

Here is a link to an interesting article from Scientific American about something called a Voronoi tessellation. What is a Voronoi tessellation? A giraffe might be able to answer that question for you…

## 11 SL Reflections

Complete the following questions before our next class.

Exercise 5E questions 1, 3–8