Below is a question that you should complete for tomorrow.
Find the area enclosed between the graphs of the functions \(f(x)=x^3-3x^2+2x+2\) and \(g(x)=-x^3+4x^2-4x+3\).
Composites and Inverse Functions Test
On Wednesday, September 28th we’ll have our first HL test on composite and inverse functions.
The following list of questions should be completed as part of your review of this material, and we can discuss any problem you may be having in class before the test.
Pages 85–89 questions 1 to 4, 9 to 11, 15 to 22
Composite and Inverse Functions
Complete the following questions for Sunday, the 18th of September.
Composite Functions
Pages 60–61 questions 1, 2, 5, 6, 9, 10, 12, 17, 19, 24, 25
Inverse Functions
Pages 68–69 questions 15, 16, 17, 24, 30, 31, 34, 35, 36, 37, 38
Applications of Derivatives
Complete the following questions for Sunday, the 18 of September.
Pages 751–752 questions 1–6, 8, 14
Indefinite Integrals
Complete the following questions on indefinite integrals for tomorrow’s lesson.
Page 780 questions 1, 3, 7, 8, 9, 10, 12, 13, 14
12 HL Composite Functions Homework
Let \(f(x)=x^2\) and \(g(x)=x-1\).
- Find the range of \(f\) and \(g\), assuming the domain for both is \(\mathbb{R}\).
- Find the range of \(f\) and \(g\), assuming the domain for both is \([-2,\infty[\).
- Find the value of each of the functions below when \(x=4\).
a) \(f\circ g\)
b) \(g\circ f\) - Find the range of each of the functions in Question 3.
Finding Derivatives
Here are a few questions to look at that involve applications of the new techniques and results (the chain rule, the product rule, and derivatives of exponential functions) we’re recently covered.
Make sure to start these before our next lesson, and aim to have them completed by Monday.
Pages 715–716 questions 3, 7, 9, 11
Pages 728 questions 1 a b e h i, 4, 6, 9, 10
The Chain Rule
Attached is a set of questions that you can use to practice the chain rule. We can look at the answers in our lesson tomorrow.
Welcome Back!
Welcome back for Year 13, and our second year of Mathematics HL!
This year we’ll be in Mathematics 12, in the Mathematics Corridor (formerly the English Corridor—our room was formerly Ms Donnelly’s room), and our first lesson will be Sunday, Lesson 5.
Ready?
Review: The Derivative Part 3 + Assignment
Attached below are the final review notes for the summer.
Derivatives Review Notes (Complete)
Again, this document contains all prior review notes, so you won’t need to refer to the earlier versions when working through this material.
The newly added sections focus on using the graph of the derivative (and the second derivative) to discover features of the graph of the original function, as in applications of Calculus it’s often the case that we understand more about the derivative than we do about the original function.
Also included below is your assignment, due on the 29th of August (your second day back). I’ve marked the last two questions (4 and 5) with a star, as they are optional (though I would strongly encourage you to do those as well). As always, post any questions below!