Resources (Updated 6/9)
Blank Copies of Old Tests (solutions can be found on the corresponding page of this website)
Updated to Include This Semester's Exams & Quizzes
Announcements (Updated 6/9)
The Final Exam will be Thursday 6/12 from 10:50 AM to 12:35 PM (Periods 3 & 4) in Room 616.
Solutions for Exam 3 are posted below.
There will not be a Quiz on Friday 6/6.
If you are one of the two people who still have not presented a Homework Problem, you must see me on Wednesday 6/4 to pre-approve your presentation, which will then be on Friday 6/6. If you do not pre-aprove your presentation on Wednesday 6/4, you will not be able to present a problem, and your maximum Homework grade will be 5 out of 10%.
Exam Corrections for Exam 3
You have an opportunity to increase your Exam 3 score, by an unspecified amount, to be determined solely at my discretion. You must follow the below instructions precisely, or your Exam Corrections will not be accepted or graded.
1) Download a blank copy of Exam 3.
2) Redo the entire Exam in pencil. Your work must be presentation quality: neat, organized, complete, thoughtful, include explanations where appropriate, conveyed with proper mathematical notation, and correct.
3) If necessary, you may use the textbook and any notes in your own handwriting to help you do the Exam Corrections. All other resources, including the use of humans and/or the internet are prohibited. By handing in the Exam Corrections, you are attesting that you have neither given nor received help, nor used any prohibited resources, and you agree that, if it is determined otherwise, this will constitute a violation of BHSECQ's Academic Honesty Policy, and will be dealt with accordingly.
4) You must hand in your original Exam, as well as the Exam Corrections. The original and corrected versions should be stapled or attached by paper clip, with the Exam Corrections on top.
5) Exam Corrections (with the original Exam attached) are due at the beginning of class on Friday 6/6. No late Exam Corrections will be accepted.
6) You may not receive your Exam Corrections (with the original Exam attached) back before the Final Exam, so please make a photocopy if you need them to study for the Final Exam.
An opportunity to make up points on Exam 3 will be posted by 5 PM on Tuesday 6/3 and will be due in class on Friday 6/6.
IF YOU ARE ONE OF THE 4 PEOPLE WHO HAVE STILL NOT PRESENTED A HOMEWORK PROBLEM, PLEASE SEE ME MONDAY 6/2 BEFORE CLASS!
Tentative Exam Dates
Exam 3: Thursday 5/29 (Note Change!)
Final Exam: Thursday 6/12
As noted in class, you may present homework problems in pairs, but both students must materially participate in the presentation. Trig Graphing Problems (1)-(6) below, as well as some of the textbook problems are eligible for presentation Thursday. Your explanation does not have to be perfect to receive full credit, but you should demonstrate significant thoughtfulness. Please stop by my office to pre-approve your presentation.
Everyone is required to present a homework problem to the class on or before Friday 6/6. You can choose which problem you would like to present, but you must come by my office and have the problem pre-approved and schedule the presentation. Problems are approved first-come, first served, and no more than 2 presentations will be done on any given day. Do not wait until the last minute! This presentation is worth half of your homework grade, or 5% of your final grade.
Solutions and Statistics for Exam 2 are posted below. (Correction to Solutions added 5/6)
Updated 5/6
There will be an "Exam 2 Redemption Quiz" sometime between 5/5 and 5/19 (inclusive). The exact date will not be announced in advance. The quiz will be given during the first 12-15 minutes of class (TBD). Late arrivals will not be given extra time, and no make-up quizzes will be given without a doctor's note or equivalent documentation of justified absence. The Quiz will consist of two problems selected (by me, verbatim) from Exam 2. There will be no partial credit - each problem will be awarded either 0 or 7 points, so the only possible scores on the quiz are 0, 7, or 14. In order to receive 7 points on a problem, you will need to use proper mathematical notation, show appropriate and sufficient algebraic work, and get the correct answer. These points will be added directly to the sum of your Exam scores after dropping your lowest Exam, so effectively they get added to your second lowest Exam score. Also, copies of the official "Solutions for Exam 2" are not permitted in the classroom until after 5/19. If I happen to see one in your possession on quiz day, you will not be allowed to take the quiz.
Exam 2 will be on be on Friday April 25, and will cover HW Poly.C - HW 5.Y. You will also be expected to be proficient in all the mathematics you have studied from first grade up through and including Exam 1.
In place of a Quiz Friday, I will be collecting HW Cubic.A as a Take-Home Quiz. In grading this Quiz, a heavy emphasis will be placed on neatness, presentation, and proper notation. If your work is sloppy or disorganized, expect a low Quiz grade (even if your work is mostly correct). Problem 2, Parts b) and c) will not be graded. Also, you are subject to BHSEC Queen's Academic Honesty Policy. This means that, while it's OK to seek help from a classmate to find an error or get "unstuck", your written work must be substantially your own. Simply copying a classmate's work (or allowing your work to be copied) is in violation of the Academic Honesty Policy and will be treated accordingly.
Solutions and Statistics for Exam 1 are posted below.
If your Exam 1 score is below 60, you are required to make an appointment with me to discuss it this week. Please sign up for appointments on the sheet outside of Room 719D.
Blank Copies of Old Tests are posted above under Resources. The Fall 2010 Tests are less relevant to this course, as the curriculum was different. Your Exam 1 will be a combination of the Spring 2013 Test 1 and Test 2 (Problems 1-5 & 8a only).
Exam 1 will be on be on Friday March 14, and will cover all the course material through Tuesday March 11 (HW Poly.B). Thursday March 13 will be a Review Day.
There will be a Quiz on Friday 2/14 (or if schools are closed that day, the first day that schools are open). The Quiz will cover HW 12.2 and HW 12.3A.
Welcome to Pre-Calculus
Homework (Updated 6/6)
(Note: You are responsible for all Homework posted and/or updated before 5:00 PM the school day before the due date. Due dates are subject to change, so please check them carefully.
HW 9.2
Page 642 Problems 15-29 (all)
Due Mon 6/9
HW 9.1
Page 634 Problems 7-39 odd
Notes:
1) (r, theta) and (r, theta + 2 k pi) (where k is any integer) represent the same point, since "theta" and "theta + 2 k pi" are co-terminal angles.
2) When a unique theta is requested, take -pi < theta <= pi, as in class rather than 0 <= theta < 2 pi, as in the book.
3) If r > 0, we interpret the point (-r, theta) to be identical to the point (r, theta + pi). That is, take the diametrically opposite point with r>0. You can further adjust the angle by adding (or subtracting) an integer multiple of "2 pi" so that your final angle is in the desired range.
Due Fri 6/6
HW 8.4B
The notations "arcsin(x)" and "arccos(x)" are sometimes used to denote the inverse sine and inverse cosine functions (respectively).
For each function, write in "algebraic form", find the domain and the range, and find the even and odd component functions.
1) tan(arcsin(x))
2) csc(arccos(x))
Using the definition arcsec(x) = arccos(1/x) :
3) Sketch the graph of y = arcsec(x).
4) Sketch the graph of y = cos(arcsec(x)). (Hint: write in "algebraic form", find the domain and the range, even or odd?)
5) Sketch the graph of y = sin(arcsec(x)). (Hint: write in "algebraic form", find the domain and the range, even or odd?)
6) Sketch the graph of y = arctan(tan(x)). (Hint: similar to y = arcsin(sinx) that we did in class - but fundamentally different)
Due Mon 6/2 (Extended)
HW 8.4A
Page 605 Problems 1-39 odd
Due Thu 5/22 (all problems that do not involve the inverse tangent function)
Due Fri 5/23 (remaining problems, involving the inverse tangent function)
HW Double-Angle Identities, etc.
Read Section 8.3 in the textbook (not covered in class, but should be review from Trig)
You do not need to memorize the identities used to do these problems, but should know that they exist and how to use them if needed.
Page 596 1-7 odd, 22, 41, 47
Due Tue 5/20
HW Sum, Diff, & Euler ID's
1) Page 587 Problems 7, 11, 15, 28, 29, 46 (first simplify using sum/diff ID's)
2) Do these calculations using Euler's Identity.
Due Mon 5/19
HW Trig Graphing
Page 564 Problems 29-47 odd. Also graph:
(1) y = sin(1/x) (by plotting points and using your knowledge of the sine function)
(2) y = (sin x) / x (by plotting points and using your knowledge of the sine function)
(3) y = sin|x| and y = |sinx| (by using your knowledge of the absolute value and sine functions)
(4) y = | |sin x| - 1 | (by using your knowledge of transformations, and the absolute value and sine functions)
(5) y = sin|x - pi/4| and y = cos|x - pi/4| (by using your knowledge of transformations, and the absolute value and sine functions)
(6) y = ln(sin x) and y = ln|sin x| (by using your knowledge of the logarithmic, absolute value, and sine functions)
Due Thu 5/15 (Enhanced & Extended)
HW UC-Practice
Page 476 Problems 9-31 odd and/or Page 524 Problems 3-21 odd. Do as many or as few of these as you need. Your objective should be to be able to answer any of these types of questions in around 10 seconds (starting from scratch, without a UC in front of you) with 100% accuracy. Check your answers in the back of the book.
Due - No Specific Due Date
HW Trig.0
We will do a concise review (and some extensions) of Trigonometry next. To assess your current understanding, complete the exam that can be found here.
Due Fri 5/9
HW EO4
Do Even/Odd HW3.
Due Thu 5/8
HW EO3
Do Problem 3-4 on Even/Odd HW1.
Due Thu 5/8 (Extended)
HW EO2
Do Problem 2 only on Even/Odd HW1.
Also, consider the proposition: "If f(x) is neither even nor odd and g(x) is neither even nor odd then f(x)g(x) is neither even nor odd."
Prove or provide a counterexample.
Due Mon 5/5
HW EO1
Do Problem 1 only on Even/Odd HW1 and then do all of the Problems on Even/Odd HW2.
Due Thu 5/1
HW 5.Z
Due Tue 4/29
HW 5.Y
Revist these problems
Due Thu 4/10
HW 5.X
Page 431, Problems 1-65 odd. You are not required to do them all, but do any that that look difficult or interesting to you, and check your answers in the back of the book.
Find explicit "calculator ready", rather than decimal solutions. Interpret "log x" to mean base 10 logarithm, but do not use this notation in your written work.
Due Thu 4/10 (Extended)
HW RF.1
Page 361 Problems 33-36
In addition, put each rational function into the form r(x) = A + B / (x - C)
In addition, find the coordinates (x,y) of the two "vertices" of each hyperbola y = r(x), as done in class
"Use a graphing device to confirm you answer" is optional
Due Fri 4/4
HW 10.8B
Page 768 Problems 31-41 odd, 42
Due Thu 4/3
HW 10.8A
Page 768 Problems 15-29 odd
Due Tue 4/1
HW Cubic.B
Do the 2 Problems I assigned during class.
Due Mon 3/31
HW Cubic.A
Problem 1: Prove Cardano's Method Step 1, using the handout from class.
Problem 2: Give Cardano's Method a try on this cubic equation.
Due Thu 3/27
HW Poly.E
Page 316 Problems 1, 3, 23-35 odd. You should have already factored Problems 23-35 odd in HW Poly.B.
Due Mon 3/24
HW Poly.D
Page 334 Problems 41, 43, 45
Page 346 Problems 41, 45, 49, 53, 57, 61, 63, 66, 68
Due Fri 3/21
HW Poly.C
Page 324 Problems 61, 62, 63, 65, 66
Page 346 Problems 31-39 odd
Due Thu 3/20
HW Poly.B
Page 316 Problems 23-35 odd, 26, 32. Just factor each polynomial into the form P(x) = a(x - c1)(x - c2)...(x - cn), where {c1, c2, ... cn} are the zeroes and 'a' is a real constant. DO NOT GRAPH.
Page 324 Problems 54, 55, 56, 67. For problems 55 & 56 you will need to use long division to find the other zeroes.
Due Thu 3/13
HW Poly.A
Page 324 Problems 11, 12, 17, 19, 21
Due Tue 3/11
HW 12.6B
Page 917 Problem 51, 52, 53; Page 920 Problem 79
Due Mon 3/10
HW 12.6A
Page 917 Problems 21-37 odd [Note that, in the book, "Find the 24th term" means the term with k = 23 (since k starts at zero)]
Due Mon 3/10 (Extended)
HW 13.2
Page 943 Problems 29, 31, 47, 51, 52, 53, 56, 61
Also, redo the proof of the identity C(n,k-1) + C(n,k) = C(n+1,k), referring to your class notes only as necessary. Repeat until you can do it without referring to your class notes.
Due Tue 3/4
HW 12.5B
Page 907 Problems 10, 11, 15, 19, 20, 23
For Problems 10 & 11, make sure you can write the proposition using sigma notation.
Due Fri 2/28 (but complete as much as possible for Thu 2/27)
HW 12.5A
Page 907 Problems 3, 4, 17
For Problems 3 & 4, make sure you can write the proposition using sigma notation. For Problem 3, verify the proposition using the arithmetic series sum formula, but also prove independently using mathematical induction.
Due Thu 2/27
Check out WolframAlpha at http://www.wolframalpha.com/ and type in (or cut and paste): sum from n = 2 to infinity of (1-5^n)/(-7)^n
Is that cool or what? WolframAlpha may become your best friend when you take Calculus. Try verifying a couple of the other FWS problems by editing the input formula. Be careful with parentheses and order of operations. Note WolframAlpha echos back what you are asking in standard mathematical notation, so you can check that you typed it correctly. Of course, you won't have access to Wolfram Alpha on exams.
HW FWS (Fun with Series)
Due Thu 2/27 (Revised)
HW 12.3B
Page 892 Problems 47-59 odd, 62
Due Mon 2/24
HW 12.3A
Page 892 Problems 5-45 odd
Due Fri 2/14
HW 12.2
Page 885 Problems 1-49 odd, 55
Due Thu 2/13 (but complete as much as possible for Tue 2/11)
HW 12.1B
Page 878 Problems 31-45 odd, 53-67 odd
Due Mon 2/10
HW 12.1A
Page 878 Problems 1-15 odd, 23-29 odd.
Due Fri 2/7
HW 0.0
Please send me a short introductory email describing yourself, your interests, your career aspirations, your feelings toward mathematics, and your mathematical experience here at BHSEC. Also, please include the phone number and the email address of your parent/guardian. (This is required, even if you have done it for a previous course.)
Due by 9AM Thu 2/6
Note: All Test Statistics are before adding make-up points (if applicable).
Exam 1
Solutions (There is an error in the final step of Problem 10. The denominator should be -1 so the answer becomes sqrt(2) -1.)
Exam 2
Solutions (The last line in the solution to Problem 8 should read "-1 = -A". Most people dealt with the minus sign in the denominator differently - by using "-x" as a factor in the expansion - which is also valid and yields different equations but the same final expansion. You should convince yourself of this!)
Student Work
Exam 3
Statistics
Solutions (While the general shape of the graph in Problem 5B is correct, the "slope" of the graph near the endpoints +/- 2 should be vertical)
Student Work