Complete the questions in the PDF file attached before next class. (Questions 1 b) and 3 a) are challenge questions, but you might be able to figure these out using the material we’ve covered in the past few lessons… see the hint below.)

## 11 HL: Vector Equations of Lines in 3D

Complete the following questions before our next class.

Exercise 13A questions 4, 5ac, 6ab

Also, (as a challenge question) can you answer question 2 from class? Both questions are shown below.

- Find the vector equation of the line passing through \(A(1,-1,4)\) and \(B(3,3,-1)\).
- Find the distance of the point \(A(1,2,3)\) to the line given by

\[\vec{r}=\begin{bmatrix}4\\2\\1\end{bmatrix}+\lambda \begin{bmatrix}4\\1\\-1\end{bmatrix}\]

## 12 SL: Antiderivatives

As I’m away on Monday, you’ll want to get a head start on *antiderivatives*, which are, in some sense, the opposite of *derivatives*. For example, if the derivative of \(x^2\) is \(2x\), then the antiderivative of \(2x\) is \(x^2+c\), where \(c\) is *the constant of integration.*

Read Section 18B, 18D, and 18E.1 (paying particular attention to the examples), and complete the following questions.

Exercise 18B questions 1–3

Exercise 18D questions 1–9, 11, 12

Exercise 18E.1 questions 1–3

Aim to complete most, if not all, of these questions before our next class.

## 12 SL: Derivatives of Trigonometric Functions

Complete the following questions before our next class.

Exercise 15G questions 1defghi, 2defjkl, 3abcghi, 4

## 12 SL: Distance From a Point to a Line

Complete the following questions before our next class.

Exercise 13E questions 1, 2, 5, 6, 7

## 9 Extended: Graphs of Quadratic Functions Part 2

Complete Investigation 1 on pages 374–375 of the textbook. You can skip parts of questions that mention vectors (so, you can skip parts of questions that show vector notation, like \(\begin{pmatrix}\ldots\\ \ldots \end{pmatrix}\), which we haven’t covered).

## 12 HL Homogeneous Differential Equations

Complete the question we had started in class, and then complete the textbook questions listed below (all questions are from the Calculus Option chapter in the Pearson book).

\[\text{Solve }\frac{dy}{dx}=\frac{x^2+3y^2}{xy}\text{, for }x,y>0.\]

Complete p. 1470 questions 24, 25 and 27.

## 12 HL Improper Integrals and The Integral Comparison Test

Complete the following questions before our next class.

Exercise I.1 (from the Haese book), questions 1, 3, 5b, 6, 7

## 9 Extended: General Form Equation of a Line

If we are given a point on a line, and the slope of that line, we already know how to find the equation of that line in slope-intercept form. How can we find the *general form* equation of that same line?

In one sense it’s very easy, we can just move the *x*-term to the same side as the *y*-term. For example, the line with slope-intercept form \[\begin{align}y&=3x+1 \quad\textrm{can also be written as}\\y-3x&=1\end{align}\]

which is in general form.

There is, however, another easy way to find either the general form equation of a line that you may also want to use. If you want to learn that method, have a look at page 174 in our textbook. You can use any method you like!

Complete the following questions before our next class.

Exercise 9E.1 questions 1–3, 4ef, 5, and 7 (if you want a challenge, try 11 as well!).