### 12 HL: Calculus: Reviewing the Basics

Complete the following questions before the start of class on Tuesday, August 25th.

Complete:

• Review Set 16A (all questions)
For question 6 you can use the rule that $\textrm{If } f(x)=x^n, n\neq 0, n\in \mathbb{R}\textrm{, then }f'(x)=nx^{n-1}$ rather than using first principles. (Also, remember that “from first principles” is the way that some textbooks will indicate that they want you to start from the definition.)
• Exercise 17A questions 2, 3, 6, 7cdef, 8, 11

(If you finish this and want to work ahead, continue reading Chapter 17.)

### 11 HL: The Definition of the Derivative

Complete the following questions (and any others you haven’t finished) before class on Tuesday.

Exercise 16A.1 question 2
Exercise 16A.2 questions 1 and 3 (read, but don’t complete, question 4)
Exercise 16C question 3ab
Exercise 16D question 3
Exercise 16E questions 2 and 7

### 11 HL: Introduction to Derivatives

Using the method presented in class, calculate the derivative of $$f(x)=x^2$$ at the point $$x = 5$$.

Bonus (as suggested by Amin): Using that same method, can you find an expression equal to the derivative of $$f(x)=x^2$$ at the point $$x=a$$?

### 11 HL: Limits at Infinity

Complete the following questions before our next class. Before completing these questions, make sure you read section 15C in the textbook.

Exercise 15C questions 2ade, 4, 5

### 11 HL: Limits and Continuity

Complete the following questions before our next class. You’ll find it helpful to read textbook sections 15B and 15E.

Exercise 15B questions 2, 4, 5, 6, 8
Exercise 15E questions 1, 2, 4abde, 5a

### 11 HL: Introduction to Limits

Read sections 15A (along with the example) and complete the following questions before our next class.

Exercise 15A questions 1–5, 6abef

### 11 HL: Roots of Arbitrary Complex Numbers

Here I’ve attached the entire PDF presentation from today’s class. I suggest you read through that presentation and complete the questions on page 5 and 6 (page 5 contains the questions you’ve already worked on in class, so those may already be finished!).

If you want to finish complex numbers completely, read the final two slides, and give the questions from the textbook a try. (This would be a great way to review your understanding of complex numbers before the end-of-year exam!)

Update: Here’s a GeoGebra applet that will let you view the roots of an arbitrary complex number.

### 11 HL: End-of-Year Exam

#### When and where is the exam?

The exam is at your place, on Friday, May 29th, starting at 8:30 am, and will be 2 hours long.

#### What will the exam be like?

• The exam will be out of approximately 100 marks.
• An (approved) calculator is required.
• Have a blue or black pen, pencils, an eraser, and a ruler.
• The IB Mathematics HL Formula Booklet (this may be provided).

#### How much is the exam worth?

The final grade in Grade 11 Higher Level Mathematics Analysis and Approaches is based on the IB level bands. Your exam result will be one (among many) components of your end-of-year course grade.

#### What will be on the exam?

The exam will be based on all of the course material that we’ve covered up to this point. Using the IB topic numbering (note that some topics have not yet been covered), this includes:

• Topic 1 – Number & Algebra (exponents, logarithms, sequences and series, complex numbers, polynomials, the binomial theorem, proofs by induction, contradiction, and counterexample, systems of equations, etc.)
• Topic 2 – Functions and equations (transformations, composition, inverse functions, quadratics, rational functions, exponential functions, inequalities, etc.)
• Topic 3 – Geometry and trigonometry (unit circle definitions, radian measure, identities, inverse and reciprocal functions, vector equations of lines and planes, magnitude, dot and cross products, etc.)

#### How should I study for the Math 11 HL exam?

• Do as many practice problems as you can, the more practice the better. Review question sets have been distributed, and these should be your principal resource when preparing for the exam. Also make use of the relevant end-of-chapter Review Set questions, and other resources that are made available.
• Check your answers as you go along. Get help if you have any questions! I’m happy to meet with you should you have any questions, just send me an email (or ask in class), and we’ll arrange a time to meet.
• Review your notes and tests, and make sure you’re familiar with the relevant terminology.

### 11 HL: Roots of Unity

Complete the questions in the file linked here. The second file here is more challenging (in parts), but you should try that one as well! There’s a hint for question 3 below.

Hint
For question 3, a proof by contradiction might be a good way to proceed!

### 11 HL: De Moivre’s Theorem

Complete the following questions before our next class.

Exercise 14F questions 2ce, 3bde, 4, 6, 8, 11