Resources (Updated 1/28)
Syllabus
Announcements (Updated 6/17)
Solutions for the Final Exam are posted here.
The Final Exam will be held Monday 6/10 during Periods 2 & 3 (9:55 AM -11:40 PM) in Room 640.
Solutions for Test 5 are posted below.
Please bring all your old Tests with you to class on Mon 6/3, as well as any other questions or problems you may have.
Appointment sign-up sheets for the remainder of the semester are posted outside room 719D. Please use them!
Test 5 will be on Friday May 31.
Solutions and Statistics for Test 4 are posted below.
Test 4 will be Monday 5/13.
Solutions and Statistics for Test 3 are posted below.
Test 3 will be Tuesday 4/23. It will cover Rational Functions (Sec 4.5 + material not in book), Partial Fractions (Sec 10.8), Exponential & Logarithmic Functions (Sec 5.1-5.4, Practice Test), Composing Logarithms with simple Algebraic Functions (material not in book), and Even/Odd Functions (material not in book).
Solutions and Statistics for Test 2 are posted below.
There will be a "Test 2 Redemption Quiz" sometime between 4/8 and 4/12 (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 Test 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 your Test 2 score.
Test 2 will be Friday 3/15 and cover Permutations & Combinations, the Binomial Theorem, and Polynomials. The relevant textbook sections in the order we discussed them are 13.1, 13.2, 12.6, 4.2, 4.4, & 4.1. You are not responsible for any material and/or problem types that we did not cover in those sections, but you are responsible for the material that we covered in class which is not in the book (e.g. Binomial Theorem in Sigma Notation, Cardano's Method, Polynomial Factoids, etc.)
Solutions and Statistics for Test 1 are posted below.
Test 1 will be Friday 2/15 and cover textbook sections 12.1, 12.2, 12.3, & 12.5.
Welcome to Pre-Calculus.
Homework (Updated 5/28 - All Remaining Assignments Are Posted)
HW 9.3C
Page 652 Problems 81-91 odd
Due Mon 6/3
HW 9.3 B
Page 652 Problems 57, 59 (calculate the quotient only - you should have already converted to polar coordinates in the HW 9.3A)
Page 652 Problems 65-79 odd
Due Thu 5/30
HW 9.3A
In all the below problems, express theta = arg(z) as an angle satisfying -pi < theta <= pi, as in class rather than 0 <= theta < 2 pi, as in the book.
Page 652 Problems 27, 31, 35, 39, 43, 47
Page 652 Problems 49, 51 (product only - polar form means you do NOT evaluate the cosine and sine - just multiply magnitudes and add the angles, then adjust the resulting angle to a co-terminal angle satisfying -pi < theta <= pi)
Page 652 57-63 odd (product only)
Due Tue 5/28
HW 9.1B/9.2
Page 634 Problems 41-59 odd
Page 643 Problems 15, 16, 18, 19, 21
Due Fri 5/24
HW 9.1
Page 634 Problems 7-39 odd (Take -pi < theta <= pi, as in class rather than 0 <= theta < 2 pi, as in the book.)
Due Thu 5/23 (page number corrected and due date changed)
HW 8.5
Page 616 Problems 7-67 (every other odd) (7, 11, 15, ..., 63, 67)
Due Mon 5/20
HW 8.2A
1) Page 587 Problems 7, 9, 11, 15
2) Page 606 Problems 37-40, 45-48 (use the double-angle and/or the addition/subtraction formulas)
3) Derive Addition Formulas for cos(x + y + z) and sin (x + y + z) NOT by starting with the formulas for cos(x+y) and sin(x+y) , but instead by using Euler's Identity, as we did in class.
4) Do these calculations using Euler's Identity.
Due Thu 5/16
HW 8.4C - Revised
Using the definition arcsec(x) = arccos(1/x) :
1) Sketch the graph of y = arcsec(x).
2) Sketch the graph of y = cos(arcsec(x)). (Hint: write in "algebraic form", find the domain and the range, even or odd?)
3) Sketch the graph of y = sin(arcsec(x)). (Hint: write in "algebraic form", find the domain and the range, even or odd?)
4) Sketch the graph of y = arctan(tan(x)). (Hint: similar to y = arcsin(sinx) that we did in class - but fundamentally different)
5) Study the super-cool proof of the formulas for cos(u+v) and sin(u+v) that we did in class, then try to reproduce it without looking. (This will not be on Test 4)
Due Fri 5/10
HW 8.4B
The notations "arcsin(x)" and "arccos(x)" are sometimes used to denote the inverse sine and inverse cosine functions (respectively).
Consider:
1) tan(arcsin(x))
2) csc(arccos(x))
For each function, write in "algebraic form", find the domain and the range, and find the even and odd component functions.
Due Tue 5/7
HW 8.4A - Due Date Revised
Page 605 Problems 1-35 odd
Due Mon 5/6 (all problems that do not involve the inverse tangent function)
Due Thu 5/9 (remaining problems, involving the inverse tangent function)
HW Trig Graphing
Page 564 Problems 29-47 odd. Also try to graph (1) y = sin(1/x) and (2) y = (sin x) / x by plotting points and using your knowledge of the sine function.
Due Thu 5/2
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 Mon 4/29
HW Test.3
Make sure you can do all the Test 3 problems neatly, comfortably, and efficiently. (Solutions are posted below.) Take particular note of any mistakes that you made and come up with your own strategy for making sure you do not make the same mistakes in the future. If there is anything on Test 3 that you do not understand, make an appointment with me or attend the Learning Commons this week to get it resolved.
Due Fri 4/26
HW Trig.0
We will do a concise review (and some extensions) of Trigonometry next. To assess your current understanding, complete the Test that I just gave on this topic in Trigonometry. Hopefully, you will find this Test to be fairly easy. A blank copy can be found here.
Due Thu 4/25
HW EO2 - MODIFIED
Do Even/Odd Homework Problems 1 & 2. Problem 2b) is optional, as it is more difficult and requires careful use of piecewise-defined functions, but you should be able to do the other parts of problem 2). Skip Problems 3 & 4 for now, and instead do these problems. This material will be on Test 3.
Due Mon 4/22 - No Class Friday
HW EO1/Review
Do Even/Odd Homework Problem 1 & Start Reviewing for Test 3!
Due Thu 4/18
HW 5.ZZ
Do these problems.
Due Tue 4/16
HW 5.Z
Do these problems.
Due Mon 4/15
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 when possible.
Due Fri 4/12
HW 5.1A
Page 385 Problems 29, 31, 35, 37
Due Tue 4/9
HW 5.0
We will do a concise review (and some extensions) of exponential and logarithmic functions next. To assess your current understanding, complete the Test that I just gave on this topic in Trigonometry. A blank copy can be found here.
Due Mon 4/8
HW 10.8B
Page 768 Problems 29, 33, 35, 41
Due Fri 4/5
HW 10.8A
Page 768 Problems 15-23 odd
Due Thu 4/4
HW RF.2
Page 361 Problems 53, 55, 61, 63
"Use a graphing device to confirm you answer" is optional
Due Fri 3/22
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 x-coordinates 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 Thu 3/21
Bring in any questions, problems, or issues you would like to discuss relevant to Test 2 (or Test 1) on Thu 3/14HW P.E
Page 316 Problems 19-31 odd, 35
Due Tue 3/12
HW Cubic.B
More fun with Cubic Equations
Due Mon 3/11
HW Cubic.A
Perform the substitution trick described in class and outlined here. This is called "depressing the cubic equation".
Due Mon 3/11 - Try It Again!
HW P.D
Page 346 Problems 38, 39, 40, 58, 68
Due Thu 3/7
HW P.C
Page 324 Problems 31-39 odd, Problems 46 & 58. Hint: If all the coefficients of a polynomial are integers and the leading coefficient (a_n) equals one, then any rational zeroes must be integers and must be (positive or negative) factors of the constant term (a_0).
Due Tue 3/5
HW P.B
Page 324 Problems 11, 12, 55; Page 346 Problem 44 (hint: you'll need to find an integer root by guess and check first)
Due Mon 3/4
HW P.A
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.
Due Fri 3/1
HW 12.Z
Page 917 Problem 51 & Page 943 Problem 57 (just two problems!)
Due Thu 2/28
HW 12.Y
Make sure you can do all the Test 1 problems neatly, comfortably, and efficiently. (Solutions are posted below.) Take particular note of any mistakes that you made and come up with your own strategy for making sure you do not make the same mistakes in the future. If there is anything on Test 1 that you do not understand, make an appointment with me or attend the Learning Commons this week to get it resolved.
Due Tue 2/26
HW 12.6
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)]
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
Due Mon 2/24
HW 13.2
Page 943 Problems 29, 31, 47, 51, 52, 53, 56, 61
Due Fri 2/22
HW 12.X
Make sure you can neatly, comfortably, and efficiently do all the induction problems that we have gone over in class.
Due Thu 2/14
HW 12.5B
Page 907 Problems 9, 10, 11, 20, 23
Due Tue 2/12
HW 12.5A
Page 907 Problems 3, 4, 5, 15, 17, 19
Due Mon 2/11
HW 12.3
Page 892 Problems 5-59 odd
Due Thu 2/7
HW 12.2B
Page 885 Problems 39-55 odd
Due Tue 2/5
HW 12.2A
Page 885 Problems 1-37 odd
Due Mon 2/4
HW 12.1B
Page 878 Problems 31-45 odd, 53-67 odd
Due Fri 2/1
HW 12.1A
Page 878 Problems 1-15 odd, 23-29 odd.
Due Thu 1/31
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 1/31
Test Results (Updated 6/4)
Note: All Test Statistics are before adding make-up points (if applicable).
Test 1
Test 2
Test 3
Test 4
Test 5
Statistics