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-8:20, 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 lunch periods to go over material with students (except for Mondays when I have lunch duty during 3rd period).

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Arcs and Central Angles

     What is the relationship between the measure of an arc and the central angle of the circle?  New terminology includes arc notation, minor arcs, major arcs, semicircles, and central angles.  The assignment is found on Pages 195-196: #1-37 odd.

Benchmark Testing

     Students in Accelerated Math I took their last benchmark test today - another practice test leading up to next month's EOCT.  Results should help provide feedback on student strengths and weaknesses, and assist students as they prepare for the actual EOCT on May 13-14.

Series Test Tomorrow!

     At long last, tomorrow is our final contest test for AP Calculus topics, as we test over Chapter 10.  Students should know how to test for convergence (partial sums, comparison test, limit comparison test, alternating series test, ratio test, root test, etc.), as well as how to create power series, Taylor Series (centered at x=c), or Maclauren Series (centered at x=0).  Classtime was spent allowing students to present problems at the board, ask questions, or puruse the solution book to their testbook, searching out last minute questions and fine-tuning their understanding of series.  Since so much of being proficient at series is based on experiences learned through the struglling with problems, I'm concerned for a number of students on tomorrow's test becauase they have done so few homework practice problems over the past month - it may be a very long night for them to fully master the material!

Using Properties of Tangents

      Students worked in small groups to understand and present the examples and guided practice problems found in Section 6.1 (reinforcing the terminology explored in yesterdays's learning task).  The assignment, due on Friday because of Thursday's benchmark testing), is found on Pages 186-187: #1-25, and Page 188: #1-8.

Multiple-choice Series Practice

     Students were given 46 sample multiple-choice questions on Series, in prepartion of Thursday's test over Chapter 10 (which is all multiple-choice!).  Students should know how to test for convergence (partial sums, comparison test, limit comparison test, alternating series test, ratio test, root test, etc.), as well as how to create power series, Taylor Series (centered at x=c), or Maclauren Series (centered at x=0).  Problems #9 and 25 are particularly "AP worthy", although all of these questions are good.

Sunrise on the First Day of a New Year Learning Task

     Students worked in small groups through today's Learning Task, which introduced and explored a number of terms associated with circles - chord, secant, tangent, diameter, radius, etc.  In particular, how are they related, and what properties do they exhibit?  Download Sunrise on the First Day Learning Task if you need another copy of the task.

Test Tomorrow!

     Our Test over Quadratic Equations is tomorrow, April 2nd.  In your Math 2 book the test covers Sections 1.1-1.3, 3.1, 3.2, and 3.4-3.8.  Students got a review worksheet covering solving quadratic equations by factoring, graphing, completing the square, and the quadratic formula, which they worked on in class - answers were posted in the room and are also posted in the hall outside my room for anyone who wants to check tomorrow morning.  Furthermore, working through the Unit 1 anf Unit 3 Tests in your Math 2 book would provide additional practice.  Then at the end of class I gave students a practice test review worksheet - 45 problems virtually identical to questions on tomorrow's test.  Download Quadratic Equations & Complex Numbers Test Review here, if you've misplaced your copy.  I am not providing answers to this review - you need to call your "study buddies" from class tonight to compare answers and work out issues.  I will be available tomorrow morning if you still have unanswered problems...

Improper Integrals

     What happens when we want to find the area contained by an unbounded region, say under the curve y=1/x^2, above the x-axis, from x=1 to infinity?  This produces an improper integral, which does not fit our definition of a definite integral to evaluate.  Fortunately, we can use the limiting process (the basis of Calculus) to handle this situation in many cases.  Unfortunately, not all improper integrals converge (like not all infinte series you studied in Algebra II or Analysis converged), so part of the trick is to identify when it converges and when it diverges.  Practice with these sorts of problems can be found on Page 474: #5-35 odd.  Countdown to your next test is now under 48 hours - have you mastered Sections 8.1, 11.2, 11.4, 6.2, 6.5, and 7.7 in preparation?

Working on Work

     Continuing our discussion of Work (defined as Force * Distance), students finished up Section 6.5 in their book.  Today's assignment is found on Pages 412-413: #16-21 all, and 26-31 all.  Their next Test will be this Thursday (March 26th) over Other Applications of the Integral (Sections 8.1, 11.2, 11.4, 6.5, and 7.7)

Review for Tomorrow's Quiz

     Students worked on a Review Worksheet in preparation for tomorrow's Quiz over Complex Numbers.   They had about 35 minutes of class time to work together on this, and answers were posted in the room for students to check as questions arose.  (Answers are also posted outside my room for anyone who wants to stop by tomorrow morning and check additional problems.)  If students did ok on this review, and successfully worked through the Practice Quiz posted on my blog last Friday, they should be ready to ace tomorrow's Quiz.  The Quiz covers simplifying square roots of negative numbers to get complex numbers; simplifying i raised to a power;  adding, subtracting, multiplying, and dividing complex numbers (including rationalizing denominators by multiplying by the conjugate); and solving quadratic equations to get complex answers.  In the Math 2 book, tomorrow's Quiz covers sections 1.1-1.3.