Winter 2012 Math 12 Home Page
Class 22, Th., Mar. 15, 2012
We reviewed. Here's the list of study guide subjects:
1 question from Ch. 1: Exponential and linear functions; for example: find the exponential and linear functions through two given points.
3 questions from Ch. 2: Rate of change / Derivatives (algebraic/data/geometric) /2nd derivative / Marginal revenue and marginal profit
5 questions from Ch. 3: Differentiation / polynomials / exponential and logarithmic functions / chain rule / product and quotient rules / sines and cosines
3 questions from Ch. 4: Max and min / inflection points / applications / elasticity / logistic functions
3 questions from Ch. 5: Definition of integral / area under curve / applications / fundamental theorem
2 questions from Ch. 6: Average value / surplus / present and future value / relative rates of change
4 questions from Ch. 7: Antiderivatives / substitution / fundamental theorem / graphical analysis
2 questions from Ch. 9: Partial derivatives / compute from a table / contour diagrams / algebraic calculation
1 questions from Ch. 10: Differential equations / logistic functions as solutions of certain differential equations
Homework from chapters 7, 9.1-9.3, and 10.1-10.2 will be checked during the exam on Tuesday.
Class 21, Tue., Mar. 20, 2012
Oral reports on essays.
Class 20, Th., Mar. 15, 2012
We went over sections in chapters 7 and 9
Class 19, Tue., Mar. 13, 2012
We went over sections 10.1 and 10.2
Class 18, Thu., Mar. 8, 2012
We went over sections 9.3 and 9.4.
Do homework for sections 9.1-9.4
Class 17, Tue., Mar. 6, 2012
We went over finding antiderivatives and sections 9.1 and 9.2.
Homework chapter 8, 9, and 10 (you are only responsible for sections we cover in class):
Ch. 10.1: # 1, 2, 4, 5, 11, 8, 9, 12, 14
Ch. 10.2: # 1? 3, 5, 6, 10, 11, 16, 21, 22
Ch. 10.3: # 1, 2, 3, 4, 6, 8, 9, 14, 15
Ch. 10.4: # 1, 2, 3, 4, 6, 8, 9, 14, 15
Ch. 10.5: # 2, 3, 7, 12, 13, 17, 18, 21, 22
Ch. 10.6: # 1? 3, 6, 7, 8, 10? 13
Ch. 10.7: # 1, 2, 5, 7, 8, 11, 12, 13, 14, 15
Ch. 9.1: # 1, 2, 4, 9, 11
Ch. 9.2: # 2, 4, 6, 7, 14, 21, 22, 28, 29, 33
Ch. 9.3: # 5, 6, 8, 10? 13, 16
Ch. 9.4: # 3, 6, 7, 15, 16, 19, 20, 22, 23, 36
Ch. 9.5: # 2, 4, 6, 10, 14, 15, 18, 20
Ch. 9.6: # 1, 8, 11, 28, 29, 33
Ch. 8.1: # 1? 6, 8, 9, 12, 13, 16
Ch. 8.2: # 1, 4, 7? 9, 12, 14, 15, 17, 18
Ch. 8.3: # 2? 4, 6, 8, 10
Class 16, Thu., Mar. 1, 2012
We started chapter 7
Ch. 7.1: # 1, 4, 10, 13, 14, 19, 20, 24, 25, 31, 32, 37, 40, 45, 46, 52, 58
Ch. 7.2: # 1, 2, 3, 6? 40 multiples of three, 41, 42
Ch. 7.3: # 3? 20 multiples of three, 23, 24, 28, 31, 33? 36, 38, 39, 43, 45
Ch. 7.4: # 2, 3, 6, 9, 10, 15, 18, 19, 24? 27
Class 15, Tue., Feb. 28, 2012
Ch. 6 Homework:
Ch. 6.1: # 1, 2, 3, 7, 8, 11, 12, 20, 22
Ch. 6.2: # 1, 2, 3, 5, 10, 11, 12
Ch. 6.3: # 2, 4? 6, 12, 15, 16
Ch. 6.4: # 1, 2, 5, 6, 14, 17
Class 14, Th., Feb. 23, 2012
We had exam 2.
Class 13, Tue., Feb. 21, 2012
We went over section 5.3, but mostly reviewed material from chapters 3 and 4.
Exam 2 is on Thursday, Feb. 23. It will cover material from chapter 3.3 to 5.2.
Homework for chapter 4 is due Thursday after the exam.
Here are a few more things to know for exam 2:
In an applied problem, what is the practical meaning of the derivative of a function?
In an applied problem, can you name the units of the derivative?
What is the practical meaning of an inflection point of a function?
Given a table of values of a function, or of the derivative of a function, can you find maxes and mins?
What are the relationships between revenue, cost, profit, marginal revenue, marginal cost, and marginal profit?
What is the relationship between average cost and marginal cost?
What is the relationship between elasticity and demand?
How does an integral give area under a curve?
Class 12, Thu., Feb. 16, 2012
We went over sections 5.1, 5.2, and part of 5.3.
We also spent a good amount of time on elasticity.
Do homework through 5.2.
Here are the chapter 5 homework problems:
Ch. 5.1: # 2, 4, 6, 10, 11, 14, 16
Ch. 5.2: # 2, 3, 5, 6, 8, 12, 14, 17, 20
Ch. 5.3: # 3, 4-7, 8, 11, 12, 15, 16, 17, 18, 26, 27
Ch. 5.4: # 2, 4, 6, 7, 10, 12, 13, 19, 20, 29
Ch. 5.5: # 1-4, 8, 9, 11, 13
Class 11, Tue., Feb. 14, 2012
We went over sections 4.6 on elasticity and 4.7 on logistic functions.
Class 10, Thu., Feb. 9, 2012
We went over sections 4.4 and 4.5
Do homework through 4.5.
Class 9, Tue., Feb. 7, 2012
We went over sections 4.1, 4.2, and 4.3.
Here are the Chapter 4 homework problems:
Ch. 4.1: # 2, 4, 6, 10, 14, 15, 19, 22, 24, 27
Ch. 4.2: 3, 4, 6, 9, 13, 18, 24, 25, 26, 28, 31
Ch. 4.3: 4, 5, 6, 10, 14, 18, 22, 24, 29, 30, 37, 44, 46, 50
Ch. 4.4: 1, 2, 5, 6, 8, 14, 22, 24
Ch. 4.5: 1, 2, 4, 5, 8, 10, 14
Ch. 4.6: 1, 2, 3, 4, 8 10, 12, 14, 18
Ch. 4.7: 1, 4, 5, 6, 8, 10, 15
Ch. 4.8: 1, 2, 3, 7, 10, 12
Class 8, Thu., Feb. 2, 2012
We went over sections 3.4 and 3.5; chapter 3 homework will be due next Thursday.
We also went over the exam.
Here's a trick allowing you to do that puzzling problem from class, which involved finding the derivative of y = f(x) ^ g(x):
First take the natural log of both sides: ln y = (g(x)) (ln f(x)).
Then take the derivative of both sides: y'/y = d/dx [g(x) ln f(x)].
To find the right hand side you need to use the product rule: y'/y = g(x) (1/f(x)) + g'(x) ln f(x)
Then multiply both sides by y to get y':
y' =
y [g(x) (1/f(x)) + g'(x) ln f(x)] = f(x) ^ g(x) [g(x) (1/f(x)) + g'(x) ln f(x)]
Complicated, but you can see where the sum comes from; there are easier ways, but involving more complex math.
Class 7, Tue., Jan. 31, 2012
We had exam 1, and briefly went over material from chapter 3.4 on the product rule. We will finish chapter 3 on Thursday, and Chapter 3 homework will be due next Tuesday.
Class 6, Thu., Jan. 26, 2012
We went over problem 2 chapters and material from chapters 3.3 and 3.4.
Exam 1 will cover material through chapter 3.2 (not 3.3). It is on Tuesday, and it is open book, open notes, calculator allowed, but computers or cell phones are not allowed.
Chapter 2 homework is due following the exam on Tuesday.
Class 5, Tue., Jan. 24, 2012
We went over sections 2.5, 3.1, and 3.2.
Do homework though section 3.2.
Chapter 2 homework will be due next Tuesday, Jan. 31.
Homework for chapter 3:
Ch. 3.1: # 1, 7, 8, 24, 25, 30, 39, 41, 43, 47, 49, 51, 53, 55
Ch. 3.2: # 3, 13, 15, 21, 23, 24, 27, 29, 31
Ch. 3.3: # 1, 5, 9, 16, 25, 31, 36, 39, 40, 42, 44, 49, 53
Ch. 3.4: # 3, 4, 5, 8, 19, 34, 35, 40, 41, 44
Ch. 3.5: # 1, 2, 8, 14, 21, 24, 25, 26
Class 4, Thu., Jan. 19, 2012
We went over ch. 1 homework and ch. 2.3 and 2.4.
Do homework through the end of 2.4
Turn in ch. 1 homework on Tuesday, Jan. 24
Class 3, Tue., Jan. 17, 2012
We went over homework and sections 2.1, 2.2, and began 2.3.
Complete the chapter 1 review odd problems by Thursday, and turn in on Thursday.
Homework for chapter 2:
Ch. 2.1: # 1, 3, 4, 6, 7, 11? 13, 15, 17, 18, 24
Ch. 2.2: # 3, 6, 9-12, 13, 15, 17, 28, 29
Ch. 2.3: # 1, 7-10, 17, 19, 36
Ch. 2.4: # 2, 6, 8-13, 19, 21, 22, 24
Ch. 2.5: # 2, 6, 8, 10, 14, 15
Class 2, Th. Jan. 14, 2012
We went over material from most of chapter 1.
Complete the pretest at the end of the book and turn it in on Tuesday.
Complete the chapter 1 review odd problems by Thursday, and turn in on Thursday.
Class 1, Tu. Jan. 12, 2012
We went over linear and exponential functions, which are the major emphasis of chapter 1.
Homework: the odd problems in the chapter review on page 71.
Please take the Pretest on page 474 at the end of the book. This will give you a sense of what you have to work on in the way of review.
Read ahead chapters 1.1 and 1.2.