## 11 HL Vectors Test

We’ll have our test on all the vectors material on Tuesday, February 13th.

The best resource to use in preparing for the test is the set of questions that has been distributed to you via email. If you have any questions about the solutions, we can discuss some of these in our classes leading up towards the test.

## 11 SL Transformations, Sequences and Series Test

On Monday, February 5th, we’ll have a test on transformations, sequences, and series (Chapters 5 and 6).

Two resources have been added to the SL Resources page: one contains sample test questions, and the other contains the mark scheme for the solutions. Those questions will be a useful resource when you’re preparing for the test.

## 12 SL Integration by Substitution

Complete the following before our next lesson.

Exercise 18G questions 1, 2cd, 3ac, 4bd, 5b

## 11 HL Lines and Planes

Complete the following questions before our next class.

Exercise 15H.2 questions 1fg, 2
Exercise 15I 9, 10, 11a, 12, 13

## 11 SL Geometric Series

Complete the following questions before our class next week.

Exercise 6G.1 questions 1ac, 2acd, 3, 4ab, 6

## 11 HL Lines in 3D

Consider the three lines defined below.

$L_1: \vec{r}=\begin{bmatrix}1\\2\\3\end{bmatrix}+\lambda \begin{bmatrix}1\\-3\\-4\end{bmatrix}$

$L_2: \vec{r}=\begin{bmatrix}-2\\-3\\0\end{bmatrix}+\lambda \begin{bmatrix}4\\4\\0\end{bmatrix}$

$L_3: \vec{r}=\begin{bmatrix}2\\-5\\-3\end{bmatrix}+\lambda \begin{bmatrix}0\\2\\1\end{bmatrix}$

Show that $$L_1$$ and $$L_2$$ are skew lines, then find the point of intersection of $$L_1$$ and $$L_3$$.

## 11 SL Arithmetic Series

Complete the following questions before our next class.

Exercise 6F 1ad, 2ac, 3ac, 6

If you’re up for a challenge, also try questions 10 and 11.

## $$\LaTeX$$ and Selected Topics in Mathematics

If you’re unfamiliar with  $$\LaTeX$$, it’s the system I use to create the slides and tests in our courses. It’s also used to enter mathematical expressions on this site (and many others).

By request I’ll be running some tutorials in $$\LaTeX$$ on Mondays after school (usually these will be held in my classroom, but for the first week it’ll be in 122). It would be useful to know if you’re writing a math-heavy extended essay (in mathematics or one of the sciences, for example), and would also be useful for your mathematical exploration.

After we’ve finished looking at  $$\LaTeX$$, we can look at some additional topics in mathematics, with topics selected based on interest (these could include things that typically fall outside the scope of the IB Mathematics courses, like linear algebra, logic, set theory, abstract algebra, or analysis).

If you’re interested in getting started with  $$\LaTeX$$, I recommend that you install a full version of  $$\LaTeX$$ on your computer—I’ve added instructions for installation here.

## 11 HL Planes

Here are a couple of short questions to look at before our next lesson.

1. Verify that the points $$A(1,2,3)$$, $$B(-2,0,0)$$, and $$C(3,-2,-1)$$ are not collinear.
2. Find the vector equation of the plane that contains all three points from question 1.
3. Find the Cartesian equation of the plane you determined in question 2.