Category: Mathematics

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12 HL Integration by Parts

Complete the following two questions for next class (Friday).

  1. Find \(\int x \sin x \; dx\), and verify that your answer is correct.
  2. Find \(\int x^2 \sin x \; dx\), and verify that your answer is correct.
[spoiler title=’Hint for question 2′ style=’blue’ collapse_link=’true’]You may find it helpful to use integration by parts twice.[/spoiler]
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11 SL Quadratics: Intersecting Quadratics

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

Exercise 1E questions 1abd, 2, 3

A harder question that you might also try is question 4. If you do try this question tonight, you’ll probably find that Example 24 in the textbook is helpful.

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11 SL Polynomials Challenge

The questions below are optional, but if you can answer them correctly, please do show your solutions to Dr. McDonald! (Also, the equations won’t show up correctly in an email, so click to see these questions on the website if you’ve received an email notice for this post.)

Consider the quadratic equation \(ax^2+bx+c=0\), with \(a\neq 0\) for questions 1 and 2.

  1. Complete the square to find another expression for the left side of the equation.
  2. Use your answer from question 1 to isolate \(x\). What is the name of the formula you’ve just derived?
  3. Consider the quadratic function \(f(x)=3x^2+kx-4\), where \(k\) is some constant real number. Explain how you know that, no matter the value of \(k\), the graph of \(f\) will always have two \(x\)-intercepts.
  4. Consider the quadratic function \(f(x)=x^2+kx-(k+8)\), where \(k\) is some constant real number. For which value of \(k\) will the \(x\)-intercepts of the graph of \(f\) be closest together?
  5. Are there any quadratic functions that can’t be represented in factored form? Are there any quadratic functions that can’t be represented in vertex form? Explain your answers.
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11 SL Quadratics Test

We’ll have a test on Quadratics (corresponding to the material in Chapter 1 of our textbook) on Thursday, September 27th.

In order to prepare for this test, have a look at the questions below from the textbook, as well as the sample questions document on the SL Resources page.

Review Set 1A—complete any 8 questions
Review Set 1B—complete any 8 questions
Review Set 1C—complete any 8 questions