Precalculus
Welcome to Precalculus class! Calculus is the study of change; it's a way to quantify change both in space and in time. The word "calculus" comes from a Latin word for a type of small stone used for counting in the ancient world.
Precalculus is what we need to do so that the image to the right isn't your life. Come to class on time. Do all of your work. Ask intelligent questions. Give me a reason to give you a good grade. |
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The image to the left is a link to the course syllabus. Read this thoroughly. It has information about course content, the kind of work we will do, what is expected of you, assessments, availability of extra help, the breakdown of grading, PBAs, and other useful things.
If you have any questions, let me know.
This is what your homework should look like. The goal is clarity so (a) you can use your work later on for studying purposes and (b) your work is clear enough to earn credit. The characteristics of a successful homework assignment are:
* Showing your work is necessary because (a) I need to see what you thought about the problem and (b) you need to see what process you used later on when you are reviewing the material.
- You include first and last name, the assignment title, the date and your Band.
- You write the prompt or problem before beginning work. (This is not necessary for word problems; do not write out word problems.) In the sample, this is the "1. 270 degrees".
- You show your work.*
- Your final answer is rounded to the hundredths.
- You box or circle your answer.
- You skip a line between problems.
- You use a ruler for all diagrams and graphs.
- Your work is done in pencil.
- Your work is generally neat and legible.
* Showing your work is necessary because (a) I need to see what you thought about the problem and (b) you need to see what process you used later on when you are reviewing the material.
Class Calendar and Announcements
Office Hours will be held E2, C2 and C3 in room 508. If there is not enough space in that room, I will post where we have gone. If you come to room 508 and I am not there, please check that room.
If you can't come to those times, please make an appointment. Please bring questions with you and ready to go. "I'm stuck," isn't a question. "I tried this and I got lost at this step," is much better.
Office Hours will be held E2, C2 and C3 in room 508. If there is not enough space in that room, I will post where we have gone. If you come to room 508 and I am not there, please check that room.
If you can't come to those times, please make an appointment. Please bring questions with you and ready to go. "I'm stuck," isn't a question. "I tried this and I got lost at this step," is much better.
Assignments
Week 18 (6/13)
You must bring your textbook to the exam on Friday (or bring it in on Tuesday or Weds if you come to study session). You may sit for the exam on Friday without your textbook in, but the score will not be entered until you turn it in. Please bring in your textbook.
Week 17 (6/6 - 6/10)
Day 1: 11.04 p. 643 #35, 37, 39, 41, 42, pp. 653-654 # 27, 28, 29, 31, (ignore eccentricity for the following): 37, 39, 41, 43
The key to 11.03 is here. For #2 on the first page on the left, the (x...) and (y...) terms in the answer should both be squared.
The key to some of the evens from 11.02 is here.
Day 2: 11.05 p. 665 #7-10, graphing: #13, 17, 19, 21, 25
A Band: You have an extra day this week. Please work on 11.05 above to practice hyperbolas. To use your time tomorrow with no school, please work toward finishing your review assignment.
D Band: Please work on your review assignment. After Wednesday, you don't have class until Monday.
During PBA week, the classroom will be open for more practice during the following times:
Your exam is Friday morning (6/17) in the gym at 9AM. Please arrive by 8:45.
Week 16 (5/31 - 6/3)
Day 1: Complete Log and Expo practice from class.
Day 2: Complete 11.01 to practice circles here. Also, you should write a list of expected topics for the semester exam. This is second semester only.
Day 3 (weekend assignment): Practice with circles and ellipses: 11.02 pp. 643 # 29, 31, 35, 37; p. 653 # 9-12, 13-18 (ignore eccentricity).
Week 15 (5/23 - 5/27)
Day 1: Complete the first two pages of 9.11 Limits Summary Assignment posted here. (A band got it in class.)
Day 2: Complete the second two pages of 9.11 Limits Summary Assignment. The key for assignment 9.10 from the book is here.
Day 3: Opportunity on Day 4. Answer Key for 9.12 is here.
Day 4:
Week 14 (5/16 - 5/20)
Day 1: Finish 9.06 from class. Then 9.07 p. 768 #51-56. Graph each function and evaluate the limits as specified. Answer key is here.
Day 2: Please see the key for 9.07 above. Then, 9.08 Look at p. 768 #61-64. The instructions say to graph those functions using a graphing calculator or a website. Try to do it by hand. The x-values you should use are unit circle values (pi/2, pi, 3pi/2, etc.) Before you graph, think about the shapes. As x increases in size (absolute value), what would be happening to the coefficient? What does that mean about the overall value of the function? Do your best to graph them along with the lines y=x and y=-x. Graph each of the four separately.
Day 3: 9.09 pp. 786-787 #5-12, 13-30
Day 4 (weekend assignment): 9.10 p. 767 #23-32. Some of them might just work outright if you evaluate for the specified x value. You should always plug in and test first. Not all of these are strictly a "Multiply by the conjugate," situation. For example, in #27 you should multiply the function by (x+1)/(x+1) to clear the denominator in the numerator. You must multiply by something over itself so that it's a 1, though. Don't forget that. Have fun.
Week 13 (5/9 - 5/13)
Day 1: 9.01 Use the four functions on page 757 #7-10 as graphing prompts. Graph each one on its own coordinate plane.
Day 2: 9.02 p. 757 # 8, 9; p 759 # 53-62. Also, graph each of #59 and #60 in their own coordinate planes.
Day 3: 9.04 p. 767 # 5-8 (for the second part of the prompt, the book is asking for the simplified function), # 9-20
Day 4: 9.05 (weekend assignment): p. 758 #33-40; p. 767 #21, 22; p. 768 #72
Also, please bring 9.03 with you (finished) to class on Monday.
Week 12
Day 1: Complete your PBA.
Day 2: Finish the assignment from class and 8.13 here.
Day 3: Complete 8.11 from class. Answer key is here. SOMEbody made a mistake on the graph for w(x), so here is the corrected one.
Day 4: Complete 8.12 from class. Answer key is here. Opportunity is Monday.
Week 11
Day 1: Based on the recent opportunity, we need to fix our equation solving. Please complete 8.04 here.
Day 2: Complete 8.06 here.
Day 3: Complete 8.08 here. Key is here.
Day 4: Complete 8.09 as distributed in class. Please bring it with you on Monday. If you need it, the file is here.
Week 10
Day 1: See 8.01 here. The answer key is here.
Day 2: See 8.02 here. The answer key is here.
Weekend assignment: 8.03 pp. 147-148 #1-3, 5 using the tables, 11-16, 37-44 "finding zeroes" means finding the x-intercept. In addition, find the y-intercepts too.
Week 9 (4/4 - 4/8)
Day 1: 7.12 p. 217, 218 #31-36, 59-64, 94, 96, 98-100
Day 2: 7.13 p. 217, 218 #43-46, 65-68, 71-72, 77-78, 101-106
Day 3: 7.14 is here. This is a long assignment. Use it as practice and have it completed by the date of the opportunity (Monday 4/11).
Day 4: We have an opportunity on Monday. Be prepared to hand in 7.12, 7.13, 7.14, and 7.15.
Here is a challenge problem. You won't be able to do this until after you have 7.15 from class on Day 4 this week. Good luck.
Week 8 (3/28 - 4/1)
Day 1: Complete PBA V here.
Day 2: The only thing tonight is 7.09 from class so you might use some time to get a good start on your project.
Day 3: 7.10 p. 217 #1-6, 7, 9, 11, 13, 23-30
Day 4: 7.11 p. 217-218 #37-40, 47-52, 55-58, 91, 93, 95, 97
PBA Check in #1 (pages 1-3) is Tuesday, April 5th.
Answer Key for 7.09 is here.
Week 7 (3/21 - 3/25)
Day 1: Complete PBA Annuities II.
Day 2: You have a lot of work ahead of you. We will add a few problems tomorrow working toward our goal of becoming fluent with the Present Value and Future Value of an Annuity formulas forwards and backwards. You will get some more practice problems on Day 3 in class, but not four more pages.I suggest doing at least three pages of "PBA - Annuities III" tonight. It's okay to leave some for tomorrow in class. We will review answers to that assignment and the previous one in class on Day 3.
Day 3: Enjoy your weekend.
Week 6 (3/14 - 3/18)
Day 1: 7.07 p. 200 # 55-60, 61-66; p. 207 #13-20
Day 2: 7.08 p. 207-208, #21-24, 37-44, 47-58, 69-78
Day 3: Start thinking about a budget as an adult. What will you spend your money on? How much will you spend each month? Come up with a list of at least ten categories and what you think you will spend in each of those categories per month in your 20s. What will change in your 30s? Write this down in a place in your notes. You will need it for your semester project.
Day 4: Complete this assignment to take the next step for the project.
Week 5 3/7 - 3/11
Day 1: Complete 7.02 here to get some help with the idea of compounding and debt.
Day 2: Complete 7.04 here.
Day 3: 7.05 pp. 189-190 #9-12, please graph as follows: graph #9 and 11 together, 10 and 12 together. Include 3 (x,y) points per graph for x=-1, x=0 and x=1; #29-32; complete the table for #57, 58 (two tables total, one for each problem); and write functions for #69 and graph each one by plotting points for f(0), f(10) and f(20). You should have three points per graph for a total of three graphs. Label all 9 points. Do this graph well as if it was going to be hung on the wall, fourth grade-style.
Day 4: 7.06 pp. 199-200 #7-22, 45-50, 51-54
Week 4 2/29 - 3/4
Day 1: 6.11 pp. 38, 39 # 60-62 (graphing), and do # 65-72 but don't use a graphing calculator; and #79-82. Also, make good use of the answer keys to check your work to other assignments.
Day 2: Opportunity tomorrow.
Day 3: Complete 6.12 here. Also, be prepared to turn in 6.09, 6.10 and 6.11 on Day 4 of this week.
Day 4: 7.01 p. 189 #5-8, 17-20, 21-26
(Partial) Answer Keys are here:
6.09
6.10
Week 3 2/22 - 2/26
Day 1: 6.07 p. 25 #39-44, 61-64
Day 2: 6.08 can be found here.
Day 3: Click here for 6.09
Day 4:
Week 2 2/8 - 2/12
Day 1: 6.04 p. 47 #10, 15, 16, 21, 22, 51, 53, 55, 57 [for the prompts in the 50s, ignore instruction (d)]. Also, these three prompts on the same paper.
Day 2: 6.05 p. 68 #39-44, 59-64, 81-86 Also, finish the work on the last page of this document.
Day 3 (weekend assignment): Please complete 6.06 you received in class.
Week 1 2/2 - 2/5
A Band
2/2 - See the post for D Band below
2/3 - 6.02 p. 56-57 # 19, 20, 23, 25, 27, 28, 41-44 (there are 3 parts to each of these last four)
2/5 (weekend assignment) -
D Band
2/2 - Welcome back! Good to see you all today. We are going to make a slight change to the numbering of the assignments in class. Winston Churchill said, “To improve is to change. To be perfect is to change often.” Goodbye to C2.03 and H 4.01. Tonight’s assignment is 6.01 here.
2/3 - See 6.02 above.
2/4 (weekend assignment) - Please read page 60 and the top of page 63. Then do 6.03 pp. 67 # 1-3, 11-18, 20-23, For #25-30, show that the functions are inverses algebraically by substituting and either getting x or not.
Week 18 (6/13)
You must bring your textbook to the exam on Friday (or bring it in on Tuesday or Weds if you come to study session). You may sit for the exam on Friday without your textbook in, but the score will not be entered until you turn it in. Please bring in your textbook.
Week 17 (6/6 - 6/10)
Day 1: 11.04 p. 643 #35, 37, 39, 41, 42, pp. 653-654 # 27, 28, 29, 31, (ignore eccentricity for the following): 37, 39, 41, 43
The key to 11.03 is here. For #2 on the first page on the left, the (x...) and (y...) terms in the answer should both be squared.
The key to some of the evens from 11.02 is here.
Day 2: 11.05 p. 665 #7-10, graphing: #13, 17, 19, 21, 25
A Band: You have an extra day this week. Please work on 11.05 above to practice hyperbolas. To use your time tomorrow with no school, please work toward finishing your review assignment.
D Band: Please work on your review assignment. After Wednesday, you don't have class until Monday.
During PBA week, the classroom will be open for more practice during the following times:
- Tuesday 6/14: 10:30 AM - noon
- Wednesday 6/15: noon - 1:30 PM
Your exam is Friday morning (6/17) in the gym at 9AM. Please arrive by 8:45.
Week 16 (5/31 - 6/3)
Day 1: Complete Log and Expo practice from class.
Day 2: Complete 11.01 to practice circles here. Also, you should write a list of expected topics for the semester exam. This is second semester only.
Day 3 (weekend assignment): Practice with circles and ellipses: 11.02 pp. 643 # 29, 31, 35, 37; p. 653 # 9-12, 13-18 (ignore eccentricity).
Week 15 (5/23 - 5/27)
Day 1: Complete the first two pages of 9.11 Limits Summary Assignment posted here. (A band got it in class.)
Day 2: Complete the second two pages of 9.11 Limits Summary Assignment. The key for assignment 9.10 from the book is here.
Day 3: Opportunity on Day 4. Answer Key for 9.12 is here.
Day 4:
Week 14 (5/16 - 5/20)
Day 1: Finish 9.06 from class. Then 9.07 p. 768 #51-56. Graph each function and evaluate the limits as specified. Answer key is here.
Day 2: Please see the key for 9.07 above. Then, 9.08 Look at p. 768 #61-64. The instructions say to graph those functions using a graphing calculator or a website. Try to do it by hand. The x-values you should use are unit circle values (pi/2, pi, 3pi/2, etc.) Before you graph, think about the shapes. As x increases in size (absolute value), what would be happening to the coefficient? What does that mean about the overall value of the function? Do your best to graph them along with the lines y=x and y=-x. Graph each of the four separately.
Day 3: 9.09 pp. 786-787 #5-12, 13-30
Day 4 (weekend assignment): 9.10 p. 767 #23-32. Some of them might just work outright if you evaluate for the specified x value. You should always plug in and test first. Not all of these are strictly a "Multiply by the conjugate," situation. For example, in #27 you should multiply the function by (x+1)/(x+1) to clear the denominator in the numerator. You must multiply by something over itself so that it's a 1, though. Don't forget that. Have fun.
Week 13 (5/9 - 5/13)
Day 1: 9.01 Use the four functions on page 757 #7-10 as graphing prompts. Graph each one on its own coordinate plane.
Day 2: 9.02 p. 757 # 8, 9; p 759 # 53-62. Also, graph each of #59 and #60 in their own coordinate planes.
Day 3: 9.04 p. 767 # 5-8 (for the second part of the prompt, the book is asking for the simplified function), # 9-20
Day 4: 9.05 (weekend assignment): p. 758 #33-40; p. 767 #21, 22; p. 768 #72
Also, please bring 9.03 with you (finished) to class on Monday.
Week 12
Day 1: Complete your PBA.
Day 2: Finish the assignment from class and 8.13 here.
Day 3: Complete 8.11 from class. Answer key is here. SOMEbody made a mistake on the graph for w(x), so here is the corrected one.
Day 4: Complete 8.12 from class. Answer key is here. Opportunity is Monday.
Week 11
Day 1: Based on the recent opportunity, we need to fix our equation solving. Please complete 8.04 here.
Day 2: Complete 8.06 here.
Day 3: Complete 8.08 here. Key is here.
Day 4: Complete 8.09 as distributed in class. Please bring it with you on Monday. If you need it, the file is here.
Week 10
Day 1: See 8.01 here. The answer key is here.
Day 2: See 8.02 here. The answer key is here.
Weekend assignment: 8.03 pp. 147-148 #1-3, 5 using the tables, 11-16, 37-44 "finding zeroes" means finding the x-intercept. In addition, find the y-intercepts too.
Week 9 (4/4 - 4/8)
Day 1: 7.12 p. 217, 218 #31-36, 59-64, 94, 96, 98-100
Day 2: 7.13 p. 217, 218 #43-46, 65-68, 71-72, 77-78, 101-106
Day 3: 7.14 is here. This is a long assignment. Use it as practice and have it completed by the date of the opportunity (Monday 4/11).
Day 4: We have an opportunity on Monday. Be prepared to hand in 7.12, 7.13, 7.14, and 7.15.
Here is a challenge problem. You won't be able to do this until after you have 7.15 from class on Day 4 this week. Good luck.
Week 8 (3/28 - 4/1)
Day 1: Complete PBA V here.
Day 2: The only thing tonight is 7.09 from class so you might use some time to get a good start on your project.
Day 3: 7.10 p. 217 #1-6, 7, 9, 11, 13, 23-30
Day 4: 7.11 p. 217-218 #37-40, 47-52, 55-58, 91, 93, 95, 97
PBA Check in #1 (pages 1-3) is Tuesday, April 5th.
Answer Key for 7.09 is here.
Week 7 (3/21 - 3/25)
Day 1: Complete PBA Annuities II.
Day 2: You have a lot of work ahead of you. We will add a few problems tomorrow working toward our goal of becoming fluent with the Present Value and Future Value of an Annuity formulas forwards and backwards. You will get some more practice problems on Day 3 in class, but not four more pages.I suggest doing at least three pages of "PBA - Annuities III" tonight. It's okay to leave some for tomorrow in class. We will review answers to that assignment and the previous one in class on Day 3.
Day 3: Enjoy your weekend.
Week 6 (3/14 - 3/18)
Day 1: 7.07 p. 200 # 55-60, 61-66; p. 207 #13-20
Day 2: 7.08 p. 207-208, #21-24, 37-44, 47-58, 69-78
Day 3: Start thinking about a budget as an adult. What will you spend your money on? How much will you spend each month? Come up with a list of at least ten categories and what you think you will spend in each of those categories per month in your 20s. What will change in your 30s? Write this down in a place in your notes. You will need it for your semester project.
Day 4: Complete this assignment to take the next step for the project.
Week 5 3/7 - 3/11
Day 1: Complete 7.02 here to get some help with the idea of compounding and debt.
Day 2: Complete 7.04 here.
Day 3: 7.05 pp. 189-190 #9-12, please graph as follows: graph #9 and 11 together, 10 and 12 together. Include 3 (x,y) points per graph for x=-1, x=0 and x=1; #29-32; complete the table for #57, 58 (two tables total, one for each problem); and write functions for #69 and graph each one by plotting points for f(0), f(10) and f(20). You should have three points per graph for a total of three graphs. Label all 9 points. Do this graph well as if it was going to be hung on the wall, fourth grade-style.
Day 4: 7.06 pp. 199-200 #7-22, 45-50, 51-54
Week 4 2/29 - 3/4
Day 1: 6.11 pp. 38, 39 # 60-62 (graphing), and do # 65-72 but don't use a graphing calculator; and #79-82. Also, make good use of the answer keys to check your work to other assignments.
Day 2: Opportunity tomorrow.
Day 3: Complete 6.12 here. Also, be prepared to turn in 6.09, 6.10 and 6.11 on Day 4 of this week.
Day 4: 7.01 p. 189 #5-8, 17-20, 21-26
(Partial) Answer Keys are here:
6.09
6.10
Week 3 2/22 - 2/26
Day 1: 6.07 p. 25 #39-44, 61-64
Day 2: 6.08 can be found here.
Day 3: Click here for 6.09
Day 4:
Week 2 2/8 - 2/12
Day 1: 6.04 p. 47 #10, 15, 16, 21, 22, 51, 53, 55, 57 [for the prompts in the 50s, ignore instruction (d)]. Also, these three prompts on the same paper.
Day 2: 6.05 p. 68 #39-44, 59-64, 81-86 Also, finish the work on the last page of this document.
Day 3 (weekend assignment): Please complete 6.06 you received in class.
Week 1 2/2 - 2/5
A Band
2/2 - See the post for D Band below
2/3 - 6.02 p. 56-57 # 19, 20, 23, 25, 27, 28, 41-44 (there are 3 parts to each of these last four)
2/5 (weekend assignment) -
D Band
2/2 - Welcome back! Good to see you all today. We are going to make a slight change to the numbering of the assignments in class. Winston Churchill said, “To improve is to change. To be perfect is to change often.” Goodbye to C2.03 and H 4.01. Tonight’s assignment is 6.01 here.
2/3 - See 6.02 above.
2/4 (weekend assignment) - Please read page 60 and the top of page 63. Then do 6.03 pp. 67 # 1-3, 11-18, 20-23, For #25-30, show that the functions are inverses algebraically by substituting and either getting x or not.
