Mr. Slater's Blog

Welcome to Mr. Slater's classes

Welcome to the wonderful world of math!

 

Be sure to bring your book and graphing calculator to class every day!

If you have any questions about your math class, you can email me at:  don.slater@cobbk12.org 

Or, since the school's voice mail system occasionally goes down, you can also call my cell number (770-658-8343) after school to reach me with questions.  If you need extra help, I'm generally available every morning before school from 7:45ish-8:15, or after school on Tuesdays through Fridays from 3:30-5:00.  (Monday afternoons is Math Team practice, open to anyone interested.)  I'm also available during 3rd and 4th period lunches to go over material with students (except for Mondays when I have lunch duty during 3rd period).

.

Antiderivatives over the break

As you head off for the Winter break, remember what we've done this last week before final exams.  We've started looking at finding antiderivatives in Section 4.9 -- the assignment was found on Pages 292-93: #13-41 odd, and #47-71 odd.  We also started finding the area within a bounded region by approximating it as the sum of a finite number of rectangles (since rectangles are the easiest geometric shape to find the area of).  The initial assignment was located on Pages 308-09: #3-25 odd.  Be sure that these assignments are all completed for the start of second semester -- if you've gotten behind with the end-of-semester rush and all the holiday hoopla, then make sure these are done over the break.  This will be your first homework check when you start back in January -- don't begin the semester at risk of losing retest opportunities!

Acc. Math 2 Exam Review

The best way to review for the Final Exam is to go back through and rework each of the six major tests that we've had this semester.  Each chapter test contained 12-18 multiple-choice questions, many of which will be very similar to those questions found on their Final Exam.  The Exam consists of 44 multiple-choice questions, and is worth a possible 110 points, counting bonus.  And students will have their graphing calculator available to use on this Exam.

The next best option to review would be to work through the four pages of review material students received last Monday (December 12th).  While these questions were not multiple-choice, they did contain a good assortment of the types of problems students should see on the Exam.  For those students who fully complete this review assignment and turn it in on the day of the exam (checked for completion, and spot-checked for accuracy), they can use this to replace their lowest test grade from throughout the semester (including the midterm).  For any students with a really low test grade (Statistics, perhaps?), this could add substantial points to their average.

Follow-up from exam day:  Surprisingly, there were half-a-dozen students who did not do this exam review at all and came into the exam unprepared -- I don't anticipate strong grades from them!  Unfortunatley, no only did this omission not prepare them for the Exam. but they don't get to  replace a lowest test grade with their Final Exam, either.  And a couple of ther students turned in their Exam Review with no names -- no way to identify their work and then replace their lowest test grade!   

Math 2 EOCT Review Answers

The Math 2 End of Course Test will be given during class on Wednesday, December 14th (Part 1) and Thursday, December 15th (Part 2).  This cumulative exam covers the entire Math 2 curriculum/book, and will count 15% of the Accelerated Math 2 total grade.  While individual questions on the EOCT are not particularly difficult, what makes this test hard is that it covers an entire book -- with topics that were started back in February in Accelerated Math 1 and not finished until December in Accelerated Math 2.

Just over a month ago students were given the Test Prep workbook which comes with their Math 2 textbook, which lists each of the 51 standards for the regular Math 2 course and gives five practice multiple-choice questions for each.  Directions were to select two problems minimally from each standard to work as a review, doing more of the problems if worked incorrectly or standards were difficult.  This workbook was to be finished by last Wednesday, December 7th.

In addition, students received practice chapter reviews each day last week, as we combined individual standards together to begin final preparations for the EOCT.  Answers to these chapter reviews are below:

 

Chapter 1 Answers:   1) B        2) C        3) B        4) C        5) B        6) D        7) D        8) A        9) C        10) D        11) A        12) A        13) D

 

Chapter 2 Answers:   1) C        2) D        3) A        4) B        5) B        6) C        7) B        8) D        9) A        10) C        11) D        12) A        13) B

 

Chapter 3 Answers:   1) D        2) A        3) A        4) C        5) C        6) B        7) C        8) C        9) C        10) D        11) B        12) B        13) A        14) C        15) B

 

Chapter 4 Answers:   1) C        2) C        3) D        4) A        5) B        6) B        7) D        8) B        9) C        10) D        11) B        12) C        13) C        14) B

 

Chapter 5 Answers:   1) A        2) B        3) C        4) B        5) A        6) C        7) A        8) D        9) B        10) C        11) A

 

Statistics Practice Test

The Statistics Test will be next Tuesday, December 13th.  I gave out this practice test to use for a review:  Download Stat Practice Test (pdf form)

I haven't had time to work all the problems, but these might be the answers to this practice test.

1)  It is a study because the cheating occured before the reporter asked questions.  Therefore he isn't dividing the responders into 2 groups to impose some sort of condition on one group - he's just observing what has already happened and gathering the data.

2)  Systematic

3)  Not every student had an equally likely chance to be questioned.  Only students who attended that football game and entered through that gate were chosen.  (Football players and band members, for example, were probably never considered.  Nor were any student who couldn't attend the game.)

4)  278/658 = .4225 

5)  This is a binomial because either they cheated or they didn't.  Therefore the answer is C(5, 2)(.4225)²(.5775)³ = .3438  (I stored the probabilities as I did the calculations on my calculator...)

6)  C(5, 2)(.4225)²(.5775)³ + C(5, 3)(.4225)³(.5775)² + C(5, 4)(.4225)⁴(.5775) + (.4225)⁵ = .7008

7)  1/sqrt(658) = .038984 = 3.9%

8)  A

9)  C

10)  D

11)  C

12)  E

13)  This is binomial because you have 2 options.  I should have included the word "inclusively" here to get the answer 0.8906 or "exclusively to get .6563

14)  I'm using a normal curve on this one since the n value is 1000 and I'm given the standard deviation.  I typed in normalcdf((480-500)/15.8, (520-500)/15.8)) and pressed enter to get .7944.  However, just out of curiosity, I also typed this information in a list and got an overflow.:-(

Introduction to Statistics

As we begin our final unit of this semester (and the last chapter to be covered on the Math 2 EOCT next month), we reviewed measures of central tendency (mean, median, and mode) and measures of dispersion (range, inner-quartile range, mean absolute deviation) that were covered in middle school math and Accelerated Math 1.  New concepts covered included standard deviation, normal curve, and z-scores.  All of this is contained in the accompanying power point presentation.  To see it, download Statistics Introduction here.  Homework for next week are the odd problems on Page 262 and page 266.

Math 2 EOCT

Accelerated Math 2 students will be taking the Math 2 End of Course Test during class on Wednesday, December 14th (Part 1) and Thursday, December 15th (Part 2).  This cumulative exam covers the entire Math 2 curriculum/book, and counts for 15% of the Accelerated Math 2 total grade.  While individual questions on the EOCT are not particularly difficult, what makes this test hard is that it covers an entire book -- with topics that were started back in February in Accelerated Math 1 and will not be finished until December in Accelerated Math 2.

Today, students received the Test Prep workbook which comes with their Math 2 textbook, which lists each of the 51 standards for the regular Math 2 course and gives five practice multiple-choice questions for each.  Each day over the next three weeks or so, students should take about 15-20 minutes and review three of these standards.  Students should select two problems minimally from each standard to work as a review, check answers in the back of the workbook, and then do more of these problems if the first two were worked incorrectly or standards were difficult.  This workbook should be finished by the first week in December in order for students to be on track for their Math 2 EOCT.

lim (sin x)/x or lim x/(sin x), as x approaches 0

Using the concept of the Squeeze Theorem we developed yesterday, we looked at the unit circle and found a triangle with sides of cos x and sin x, a sector of the circle that larger, and a larger still triangle that's tangent to the circle.  (See student's class notes for drawings and more detailed explanation!)  This allowed us to set up a three-part inequality based on area relationships, which could then be algebraically maneuvered into the functions in question.  The big question remaining:  how do we come up with those boundary functions? -- think about restrictions on sine and cosine ranges, the definition of absolute value inequalities, or maybe it's hust luck! (NAAAAH!)  This weekend finish up Page 103: $9-39 odd, and then 6-8. 

Enjoy your Labor Day break!

Chapter 1 ReTest Opportunity

     As announced last week, remember the ReTest opportunity for Chapter 1 that will take place after school on Tuesday (September 6th).  This is available for anyone, regardless of their grade on the original test.  It will be a brand new test, covering the material in Chapter 1 - not just the original test with simply numbers changed.  It will have the same format - 16 questions worth 112 possible points, with approximately two-thirds multiple choice and the remainder free response.  If you choose to take the ReTest, it will become your new test grade and your original grade will be rescaled to become a 10 point quiz grade.  The ReTest does not allow the use of graphing calculators - so problems are designed to all be worked algebraically.  We will start right after school (come whenever you're ready), and you can stay and work on this ReTest as long as you want, within reason (I'd like to go eat by 8:00, at least).  Hopefully, after looking back over your original test and reviewing Chapter 1 thoroughly, you know if you've mastered this material and it will be worthwhile to take the ReTest.  Good luck!

Squeeze Theorem

After answering questions from last night's homework for about half the period, we started looking at a new algebraic technique to possibly evaluate limits of indeterminant form -- the Squeeze Theorem, or sometimes called the Sandwich Theorem.  Basically, we are looking at evaluating a limit for a function that we cannot seem to do.  Instead, we'll find a "back door" way to find its value, by coming up with two boundary functions (one larger than f(x), one smaller), whose limits do exist as x approaches a and are the same value, and we'll force the function in question betweenL and L.  We then used this squeeze theorem technique to look at the lim (sin x)/x as x approaches 0, but ran out of time about halfway through.  We'll pick up class tomorrow at this point. 

Evaluating Limits Algebraically

Since the AP Calculus Exam is 65% non-calculator, and my retests are all done without a graphing calculator, there is a real need to be able to evaluate limits algebraically in this course.  Although we've looked at limits graphically (and had to deal with issues of zooming, resizing the window, pixel resolution, etc.) and numericqally (where we had to zoom, or look for a pattern with messy decimal results), algebraically evaluating a limit may be the surest way to know the result.  Unfortunately, when substituting in the value of x, it isnot uncommon to end up with an indeterminant form -- zero/zero, infinity/infinity, infinity - infinity, zero^zero, etc.  In that case, the function expression will need to be manipulated, and you know a lot of possibilities:  factoring and cancelling out common factors, rationalizing a denominator or numerator, getting a common denominator for fractions, using a trig identity, contemplating properties of exponents or logarithms, etc.  If your chosen technique does not seen to work, then try another option.  Tonight's assignment gives you a lot of chances to manipulate indeterminant form limits -- Page 98: #7-51 odd.  (I especially liked problems # 29, 35, and 47.)