Resources (Updated 9/25)
Office Hours
Tuesday Period 3, Period 4, & Period 7, Room 719D
You may also drop by Room 719D whenever I am free (see Dr. Freeman's Daily Schedule posted above), and I will be happy to help you, if I am available. If you would like to guarantee my availability, or require more than 10 minutes, I would invite you to schedule an appointment, either by email or in person.
Blank Copies of Old Exams (solutions can be found on the corresponding pages of this website)
Announcements (Updated 1/12)
Exam 3 (and possibly the Problem Set as well ) will be graded and available for pickup on Tuesday 1/16 at 9:00 AM.
Blank copies of Exams from this semester have been added to the folder.
The Final Exam will be on Wednesday 1/17 from 1:35 PM to 3:20 PM (Periods 6 & 7) in Room 722.
Exam 3 Solutions are posted below.
Happy Snow Day! The Exam will be the next day we have class (probably tomorrow Fri 1/5).
The Problem Set is now due at 2:30 PM on Wed 1/3. No late work will be accepted.
Quiz 9 will be Friday 12/15, Quiz 10 will be Friday 12/22, and Exam 3 will be Thursday 1/4. There will be no Quizzes in January.
Exam 2 Solutions are posted below.
Please note the updated Problem Set 1 below!
Exam 2 will be on Fri 12/1 and will cover all material discussed in class through Wed 11/29.
Quiz 8 will be on Mon 11/20 and will cover HW 11.7.
Quiz 6 on Friday 11/3 will cover HW Poly.A, Poly.B, and Poly.C. The Rational Roots Theorem may also be useful.
Exam 1 Solutions are posted below.
Exam 1 will be on Friday 10/27 and will cover through HW Poly.B.
Quiz 4 on Friday 10/13 will cover HW 13.5.
The first Quiz will be on Wednesday 9/20 (there is no school on 9/21 & 9/22).
Welcome to Pre-Calculus.
Problem Sets (Updated 12/8)
Problem Set 1 (Problems 3 and 4 added on 12/8)
Homework (Updated 1/10)
(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.)
Note: You can check your answers to the even numbered problems using Wolfram Alpha.
HW 7.5 (Inverse Trig Functions)
Page 509 Problems 1, 2, 3-9 odd, 23-43 odd
Also, sketch the graph of y = arctan(tan(x)). (Hint: similar to y = arcsin(sinx) that we did in class - but fundamentally different)
Due Thu 1/11
HW Trig Graphing
Page 522 Problems 29-47 odd. Also graph:
(1) y = sin(1/x) (by plotting points and using your knowledge of the sine function) - optional Alg 2 PS Problem
(2) y = (sin x) / x (by plotting points and using your knowledge of the sine function) - optional Alg 2 PS Problem
(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 1/11
HW UC-Practice
Page 433 Problems 11-34 and/or Page 482 Problems 3-24. 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 or using Wolfram Alpha.
Due Wed 1/3
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 Wed 1/3
HW EO2 (Even/Odd Part 2)
Do these problems.
Due Wed 12/20
HW EO1 (Even/Odd Part 1)
Do these problems.
Problem 2 Answers: f odd, g neither, h even, q, even, z both
Due Mon 12/18
HW GLC (Graphing Log Compositions)
Make sure that you can do these problems. (Several of them we did in class).
Due Before Exam 3 Review
HW 5.R (Exponential & Logarithmic Function Chapter Review)
Page 391-2, Problems 5-67 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 Fri 12/15
HW 5.3 (Logarithmic Functions)
Page 360-1 Problems Any/All. You are responsible for being able to do these problems. Do as many as you need to do for practice.
Also, these log problems distributed in class. If no base is specified on the logarithm, use any base - it will not affect the answer.
Due Mon 12/11
HW 5.1 (Exponential Functions)
Page 345-6 Problems Any/All. You are responsible for being able to do these problems. Do as many as you need to do for practice.
Due Fri 12/8
HW 3.7 (Inverse Functions)
Page 247 Problems Any/All. You are responsible for being able to do these problems. Do as many as you need to do for practice.
Also for the quadratic function f(x) = x^2 + 3x - 2, find the restricted domains for which the function will be invertible, and the inverse fucntion will be a half-parabola, and formulas for the corresponding inverse fucntions (like the example we did at the end of class).
Due Thu 12/7
HW RF w/ Abs Val Part 2
These problems distributed in class.
Due Before Exam 3 Review
HW RF w/ Abs Val Part 1
For Problem 63 in HW RF.3 below, try inserting some absolute values signs here and there (using both the factored and non-factored forms of the function). Graph the modified function, and check your graph using Desmos. Do this for at least 3 modified versions of the function.
Due Mon 12/4
HW RF.2
Find the vertices of the hyperbolas for the other three problems in HW RF.1 (We did one in class.) Estimate the decimal values of the coordinates and makes sure they are consistent with your graphs.
Due Mon 11/27
HW RF.1
Page 326 Problems 41, 42, 43, 44
In addition, put each rational function into the form r(x) = A + B / (x - C)
In addition, describe the behavior near the asymptotes using the notation demonstrated in class.
"Use a graphing device to confirm you answer" is optional
Due Wed 11/22
HW 11.7 (Partial Fractions)
Page 735 Problems 3-43 odd
You should complete as much as you can for Wed 11/15. If you come across a problem where the denominator has a quadratic factor with no real zeroes (e.g. Problems 7, 9, & 11), you should defer that problem until after we discuss Case 3 and Case 4 on Wednesday.
Due Thu 11/16
HW Cubic.C
Do these problems.
Due Mon 11/13 (Note: One or both of these problems may be collected and count as a Quiz!)
HW Cubic.B
Do these problems.
Due Fri 11/10 (but do at least one for Thu 11/9 !)
HW Cubic.A
Do this problem.
Due Wed 11/8 . (if you have not yet done this problem, do HW Cubic.B first)
HW Poly.D (Updated 11/3)
Page 303 Problems 41, 47, 49, 51
Page 313 Problems 45, 49, 53, 57, 61, 65, 67, 70, 72
Page 286 Problems 27-39 odd (graphs). You should have already factored Problems 27-39 odd in HW Poly.C.
Also make sure you can graph quadratic functions such as Page 272 Problems 23-32 as discussed in class Friday 11/3. "Standard Form" in the textbook means what I usually call "Vertex Form".
Due Mon 11/6
HW Poly.C
Page 286 Problems 27-39 odd, 30, 36. 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 294 Problems 57, 58, 62-68 (all).
Due Wed 11/1
HW Poly.B
Page 294 Problems 53-56 (all), 69
Due Thu 10/26
HW Poly.A
Page 293 Problems 13, 14, 19, 21, 23
Due Wed 10/25
HW 14.6C
(1) Page 869 Problem 82. Is there a term that does not depend on b? If so, find it. Spring 2013 Test 2 Problems 4 and 5, and this problem.
Due Mon 10/23
HW 14.6B
Page 866 Problems 29-45 odd
Due Fri 10/20
HW 14.6A
Page 866 Problems 5-15 odd, 23, 24 [Note that, in the book, "Find the 24th term" means the term with k = 23 (since k starts at zero)]
Due Thu 10/19
HW Pascal's Triangle
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 Wed 10/18
HW 14.2
Page 888-9 Problems 23, 27, 31, 45, 49, 55, 56, 63, 71, 77
Due Mon 10/16
HW 13.5B (Mathematical Induction)
Stewart Page 857 Problems 3-25 odd (you should also be able to write Problems 3-13 odd in sigma notation).
Due Thu 10/12
HW 13.5A (Mathematical Induction Test Drive)
Stewart Page 857 Problems 1, 2, 20
Due Fri 10/6
HW 13.3D
1) Calculate the area of the Koch Snowflake, using the table from class.
2) Do the Geometric Series Problem distributed in class.
Due Thu 10/5
HW 13.3C (Fun with Series)
Complete the Series Problems on the handout distributed in class and check your answers (Problem 7 corrected 10/4). Also try checking a couple of the answers
using Wolfram Alpha. For example, cut and paste: "sum 3^(1-2k) / 2^(1-3k) from k = 0 to infinity"
Due Wed 10/4
HW 13.3B (Geometric Sequences Part B)
Stewart Page 844 Problems 49-61 odd, 66, 70
Due Wed 10/4
HW 13.3A (Geometric Sequences Part A)
Stewart Page 844 Problems 9-47 odd
Due Mon 10/2
HW 13.2B (Arithmetic Sequences Part B)
Stewart Page 836-7 Problems 43-53 odd, 59
Due Thu 9/28
HW 13.2A (Arithmetic Sequences Part A)
Stewart Page 836-7 Problems 5-41 odd
Due Wed 9/27
HW 13.1B (Summation Notation)
Stewart Page 830-1 Problems 33-47 odd, 49-53 odd (use Wolfram Alpha), 55-69 odd
Due Mon 9/25
HW 13.1A (Sequences)
Stewart Page 830-1 Problems 3-17 odd, 25-31 odd
Due Mon 9/18
HW 0.2 (Find the Next Term)
Complete the Find the Next Term worksheet distributed in class.
Due Fri 9/15
HW 0.1 (Inputs & Outputs)
Complete the Functions on Sets worksheet distributed in class. For each problem, consider whether it make sense (or changes the answer!) if the inputs and outputs are regarded as sequences rather than sets. Rock Star Bonus: For Problem 10, find a function as described that is "one-to-one".
Due Thu 9/14
HW 0.0 (Email)
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 Mon 9/18
Exam Results (Updated 1/8)
Note: All Exam Statistics are before adding make-up points (if applicable).
Exam 1
Statistics
Student Work
Exam 2
Statistics
Student Work
Exam 3
Statistics
Solutions (Correction: In problem 3, the even part of g(x) evaluated at +1 and -1 should be 5/4)
Student Work