Category: 11 Mathematics HL

Posted on

11 HL Implicit Differentiation

Complete the following questions before our next lesson. Remember, you can use GeoGebra or Desmos to check your answers!

Exercise 18E questions 1dgij, 2bcf, 3
Exercise 18F question 9

Posted on

11 HL Math End-of-Year Exam

When and where is the exam?

  • The exam is on Tuesday, June 5, starting at 8:30 am, and will be 2.5 hours long.
  • All exams are written in the field house.

What will the exam be like?

  • The exam will be out of approximately 120 marks.
  • TI-83/84 calculators are allowed, but memories must be cleared of all non-approved apps. The TI-89 calculator may NOT be used.
  • Bring your own blue or black pen, pencils (2), eraser, ruler, and calculator. Please note that no sharing of materials will be allowed during the exam.
  • The IB Mathematics HL Formula Booklet will be provided.
  • Do NOT bring any notes or books into the exam.

How much is the exam worth?
The final grade in Grade 11 Higher Level Mathematics is based on the IB level bands. Your exam result will be a key component of your final mark as it will provide a good picture of the level of your knowledge in each of the topics covered this year.

What will be on the exam?
The exam will be based on Chapters 1–18* of your textbook. These chapters cover five topics of the course:

  • Topic 1 – Algebra (exponents, logarithms, sequences and series, complex numbers, polynomials, the binomial theorem, proof by induction, etc.)
  • Topic 2 – Functions and equations (transformations, composition, inverse functions, quadratics, rational functions, inequalities, etc.)
  • Topic 3 – Circular functions and trigonometry (unit circle definitions, radian measure, identities, inverse and reciprocal functions, etc.)
  • Topic 4 – Vectors (vector equations of lines and planes, magnitude, dot and cross products, etc.)
  • Topic 6 – Calculus* (limits and derivatives, rules for differentiation, tangent lines and derivatives, etc.)

How should I study for the Math 11 HL exam?

  • Do as many practice problems as you can, the more practice the better. A review question set will be distributed, and this should be your principal resource when preparing for the exam. Also make use of the relevant end-of-chapter Review Set questions, and any other resources that are made available.
  • Check your answers as you go along. Get help if you have any questions.
  • Review your notes, tests and any terms/rules that will be needed for the exam.
  • Math help will be available every day (before and after school, or by appointment) in room 0181 until the exam.

*Subject to some adjustment based on the material we cover leading up to the exam.

Posted on

11 HL The Product Rule

Complete the following questions before our next class.

Exercise 18C questions 3bcd, 4
Exercise 18H (here you can use the results we derived in class) questions 1dfg, 2ahj, 3a

Posted on

11 HL Working with Derivatives

Following on from our discussion from class, complete the following question.

Let \(f(x)=\frac{1}{3}x^3-2x^2\). Find the coordinates of the local maximum and the local minimum of \(f\).

Are you interested in seeing something else that’s sort of neat? Read on.

We’ll eventually be discussing something called the second derivative. Once you’ve found the derivative of a given function, you can then go on to find the derivative of that derivative. For example, if \(f(x)=2x^5\), then \(f'(x)=10x^4\). The second derivative is represented as \(f^{\prime \prime}(x)\); in this case, we have \(f^{\prime \prime}(x)=40x^3\).

Find the second derivative of the function \(f(x)=\frac{1}{3}x^3-2x^2\), then solve the equation \(f^{\prime \prime}(x)=0\). On the graph of \(f\), plot the point on \(f\) whose \(x\)-coordinate is the solution you found to \(f^{\prime \prime}(x)=0\). What do you notice about the location of this point?