Coach Sluder
Algebra II
Check Grades
Room. 280
Homeroom 9 -1
II. GRADING PROCEDURE
Grades will be determined on a “total points” basis. Opportunities for points will come only from quizzes, tests, randomly collected home work and / or class work assignments, and extra credit opportunities. (Please see the “Possible Extra Credit” sheet given to students on the first day of each nine weeks or on my web page ( http://colliervillehs.scs.k12.tn.us/~nsluder/Default.html ) for details about extra credit opportunities.) A “recommended homework assignment” will be given every day and reviewed the following day in class. (A list of the daily “recommended homework assignments” for my classes are also located on my web page). However, this homework will only be collected for a grade on a random basis at the discretion on the teacher. Therefore, it will be up to the student to stay current in their “recommended homework assignments” and up to the parent to check to make sure that their student is doing all of these home work assignments so that their student will be adequately prepared for quizzes and tests.
III. PARENTS ROLE
Parents should plan to take an active role in their students’ education. They may do this by checking:1. To make sure their student is present in class every day unless they are seriously ill. (Parents might also want to limit the number of days their student is allowed to miss even for school approved activities.) Statistics have shown over the past few years that students who miss more than 10 days of class (whatever the reasons) have great difficulty being successful in algebra II.
2. To make sure that their student is taking complete lecture and demonstration notes in class every day (This can be checked by making sure they have class notes concerning definitions and have recorded the various examples demonstrated each day.)
3. To make sure that their student is completing their “recommended homework assignment” every day and that their student is also checking their answers (for correctness) with the those provided in the back of the book.
4. To make sure that if their student is having any difficulty understanding the current material, they are asking questions in class and are asking the teacher to demonstrate more of those types of homework problems.
5. To make sure that their student is seeking tutoring help. (If after the additional demonstration in class the student still is not completely understanding the concept, or if the student has been absent and needs additional help in getting themselves caught up they should seek tutoring help.) I am available for tutoring every Monday through Friday before school beginning at 6:00 A.M. This tutoring is on a “first come first serve” basis so, students should plan to arrives early to insure themselves of actually receiving help. ( I award one tutoring point for each day a student receives my tutoring help. )
6. To make sure that their student is taking advantage of the online tutoring programs listed below:
http://www.glencoe.com/sec/math/algebra/algebra2/algebra2_05/http://www.webmath.com/index.html
IV. MATERIALS AND SUPPLIES
1. The Algebra II textbook.
2. A folder with pockets filled with notebook paper and a pencils.
3. A graphing calculator is required for all Algebra II students. (I recommend the students buy a “Texas Instruments TI-83 Graphing Calculator.” It is the only one that I will be demonstrating in class and if the student has any other brand or model they will be responsible for learning how to use it on their own.)
V. PREPAREDNESS
1. Student’s are to bring their supplies with them to class on a daily basis. Failure to do so may result in a discipline referral being written.
2. Each student is expected to to spend at least 30 minutes per night attempting to complete the “recommended homework assignment” and / or in quiz or test preparation.
3. It is expected that students take their textbook and their “recommended homework assignment” sheet home with them every day. This should be done in case the student is absent due to some unforeseen circumstance. The student will still be able to attempt any “recommended homework assignment” work before returning to school and/ or prepare for scheduled quizzes or tests.
4. Students are responsible for finding out about assignments missed during any absence from class and obtaining a copy of all class notes from a classmate. This should be done by acquiring an “assignment buddy” for the class and asking them for the current “recommended homework assignment.” Students may also discover the assignment missed during an absence by checking their syllabus or by checking my web page . Student's should then attempt the appropriate assignment before returning to school. If they are unsuccessful in understanding the material on their own, they should seek tutoring help from a classmate or from the teacher on the first day they return to school following any absence.
VI. HONESTY AND PERSONAL INTEGRITY
I place a great deal of trust and confidence in the students concerning being honest during all quizzes and tests. Cheating will result in a zero being recorded on that quiz or test, a discipline referral being written, parents being notified, a two day “In School Suspension” being assigned and an automatic “U” in conduct for that nine week grading period.
VII. CLASSROOM POLICIES
1. Be “in” your seat when the tardy bell rings. Student’s should also already have their pencils sharpened, the previous day's assignment out and on their desk, and begin reading the textbook concerning the current days assignment. Failure to do so may result in a tardy slip being written.
2. Always bring an “Admit Slip” from the Attendance Office with you to class on the first day you ` return from an absence. Failure to do so may result in a tardy slip being written.
3. Always be courteous and respectful to your teacher and to your classmates.
4. Raise your hand and wait to be recognized by the teacher before speaking out in class.
5. Use the restroom and water fountain between classes.
6. Always be awake and alert during class. Failure to do so may result in the student being required to stand for the remainder of class or a referral being written.
7. Tests and quizzes are listed on the class room white board at least a week in advance and are always announced in class several days in advance. These tests and quizzes will only cover material that has been discussed and demonstrated in class, followed by a “recommended homework assignment” and then reviewed the next day in class. It is therefore, the student’s responsibility to make up quizzes and tests missed during an excused absence. This can be accomplished by coming before school and taking a “make up” test or quiz. All “make up” work must be completed by 6:55 A.M. the second day after returning from an excused absence. (If the student is absent for an extended time, the student will be given an additional day for every day they missed. For example, if a student misses three days in a row. They will be given two days allowance for the first day they missed and an additional day allowance for both the second and third days they missed. This gives them a total of four days to make up their assignments and complete any and all of their “make up” quizzes or tests. (All “make up” quizzes and tests will cover the same material but will be a completely different version and/or type of the quiz or test.)
8. Students who are absent for any pre-planned school sponsored event (ie. Field trip, sports activity, band or chorus contest, etc.) are responsible for informing me several days in advance of the absence and for attempting any missed assignments before returning to school.
9. Remember that all rules set forth in the Shelby County and Collierville High School Student Handbooks are also applicable to this class.
10. In an effort to keep both you and your student aware of their current grade in this class at the end of both the 3RD, 6TH and 8TH weeks of each “nine week grading period” parents are expected to print their students grades off of the “Power Grade” web site. The student is then responsible for having that report signed by their parents and returned to me the following day for a grade.
11. Students who fail a chapter test may opt to take a “RETEST” over that material. In order to be illegible for the “RETEST” an student must: notify the teacher of their plans to take the “RETEST”, they must complete an additional assignment given by the teacher covering the material to be retested, and they must attend a morning tutoring session to answer any questions they have concerning the material. Both the original test score and the “RETEST” score will then be averaged into the students’ nine weeks grade.
FIRST
NINE WEEKS ALGEBRA II EXTRA CREDIT ASSIGNMENTS
YOU WILL HAVE THE OPPORTUNITY TO CHOOSE ONE OF THE FOLLOWING ASSIGNMENTS THIS NINE WEEKS AS AN EXTRA CREDIT POSSIBILITY. THE FOLLOWING GUIDELINES APPLY TO YOUR CHOICE:
1. POSSIBLE POINTS RANGE FROM 0-15
2. THE ASSIGNMENT IS DUE BY THE DATE LISTED ON THE RECOMMENDED ASSIGNMENT SHEET FOR THIS NINE WEEKS. NO CREDIT WILL BE GIVEN FOR LATE ASSIGNMENTS.
3. YOU ARE REQUIRED TO CHOOSE WHICH OF THE FOLLOWING ASSIGNMENTS YOU WANT TO
ATTEMPT ( INCLUDING THE PARTICULAR MATHEMATICIAN OR CONCEPT YOU WILL RESEARCH
) AND THEN GET YOUR TEACHER’S APPROVAL BEFORE YOU BEGIN THE ASSIGNMENT.
I. RESEARCH AND WRITE REPORT ON A FAMOUS MATHEMATICIAN OR MATH PRINCIPLE. YOU MUST THEN TURN IN A COPY OF THE PAPER AND A COPY OF THE RESEARCH MATERIAL YOU USED TO WRITE IT. IF YOU GET INFORMATION OFF OF THE INTERNET YOU MUST PRINT THE INFORMATION (NOT JUST THE URL NUMBER) AND INCLUDE THIS WITH THE OTHER RESEARCH MATERIAL. THE REPORT MUST BE AT LEAST TWO FULL PAGES HAVING ONE INCH MARGINS, BE DOUBLE SPACED, AND HAVE A FONT SIZE OF 12.
II. CREATE A COMPUTER SLIDE SHOW (OF AT LEAST 10 SLIDES) ILLUSTRATING A FAMOUS MATHEMATICIAN OR MATH PRINCIPLE. YOU MUST THEN TURN IN A PRINTOUT OF THE SLIDE SHOW, AND A COPY OF ALL THE RESEARCH MATERIAL YOU USED MUST ALSO BE ATTACHED TO THE BACK OF YOUR SLIDE SHOW PRINTOUT.
SECOND
NINE WEEKS ALGEBRA II EXTRA CREDIT ASSIGNMENTS
YOU WILL HAVE THE OPPORTUNITY TO CHOOSE THE FOLLOWING ASSIGNMENT THIS NINE WEEKS AS AN EXTRA CREDIT POSSIBILITY. THE FOLLOWING GUIDELINES APPLY TO YOUR CHOICE:
1. POSSIBLE POINTS RANGE FROM 0-15
2. THE ASSIGNMENT IS DUE BY THE DATE LISTED ON THE RECOMMENDED ASSIGNMENT SHEET FOR THIS NINE WEEKS. NO CREDIT WILL BE GIVEN FOR LATE ASSIGNMENTS.
I. ACCURATELY COMPLETE A PACKET OF REVIEW PROBLEMS FROM
CHAPTERS 1-6.
YOU WILL NEED TO ASK YOUR TEACHER FOR A COPY OF THE PACKET OF REVIEW PROBLEMS. PLEASE DO THIS WELL IN ADVANCE OF THE DECEMBER 12TH DUE DATE. YOU WILL THEN MAKE AN HONEST ATTEMPTED AT ACCURATELY COMPLETING ALL OF THE PROBLEMS. YOU WILL SHOW ALL OF YOUR WORK FOR THESE PROBLEMS EITHER ON THE REVIEW SHEET ITSELF OR ON SCRATCH PAPER. YOU WILL ATTACH ALL SCRATCH WORK TO THE BACK OF THE REVIEW PACKET WHEN YOU TURN IT IN.
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THIRD
NINE WEEKS ALGEBRA II EXTRA CREDIT ASSIGNMENTS
YOU WILL HAVE THE OPPORTUNITY TO CHOOSE ONE OF THE FOLLOWING ASSIGNMENTS THIS SIX WEEKS AS AN EXTRA CREDIT POSSIBILITY. HOWEVER, IF YOU CHOSE ONE OF THESE ASSIGNMENTS FOR FIRST WEEKS YOU MUST NOW CHOOSE THE OTHER ASSIGNMENT FOR THE THIRD NINE WEEKS. THE FOLLOWING GUIDELINES APPLY TO YOUR CHOICE:
1. POSSIBLE POINTS RANGE FROM 0-15
2. THE ASSIGNMENT IS DUE BY THE DATE LISTED ON THE RECOMMENDED ASSIGNMENT SHEET FOR THIS NINE WEEKS. NO CREDIT WILL BE GIVEN FOR LATE ASSIGNMENTS.
3. YOU ARE REQUIRED TO CHOOSE WHICH OF THE FOLLOWING ASSIGNMENTS YOU WANT TO
ATTEMPT ( INCLUDING THE PARTICULAR MATHEMATICIAN OR CONCEPT YOU WILL RESEARCH
) AND THEN GET YOUR TEACHER’S APPROVAL BEFORE YOU BEGIN THE ASSIGNMENT.
I. RESEARCH AND WRITE REPORT ON A FAMOUS MATHEMATICIAN OR MATH PRINCIPLE. YOU MUST THEN TURN IN A COPY OF THE PAPER AND A COPY OF THE RESEARCH MATERIAL YOU USED TO WRITE IT. IF YOU GET INFORMATION OFF OF THE INTERNET YOU MUST PRINT THE INFORMATION (NOT JUST THE URL NUMBER) AND INCLUDE THIS WITH THE OTHER RESEARCH MATERIAL. THE REPORT MUST BE AT LEAST TWO FULL PAGES HAVING ONE INCH MARGINS, BE DOUBLE SPACED, AND HAVE A FONT SIZE OF 12.
II. CREATE A COMPUTER SLIDE SHOW (OF AT LEAST 10 SLIDES) ILLUSTRATING A FAMOUS MATHEMATICIAN OR MATH PRINCIPLE. YOU MUST THEN TURN IN A PRINTOUT OF THE SLIDE SHOW, AND A COPY OF ALL THE RESEARCH MATERIAL YOU USED MUST ALSO BE ATTACHED TO THE BACK OF YOUR SLIDE SHOW PRINTOUT.
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FOURTH
NINE WEEKS ALGEBRA II EXTRA CREDIT ASSIGNMENTS
YOU WILL HAVE THE OPPORTUNITY TO CHOOSE THE FOLLOWING ASSIGNMENT THIS NINE WEEKS AS AN EXTRA CREDIT POSSIBILITY. THE FOLLOWING GUIDELINES APPLY TO YOUR CHOICE:
1. POSSIBLE POINTS RANGE FROM 0-15
2. THE ASSIGNMENT IS DUE BY THE DATE LISTED ON THE RECOMMENDED ASSIGNMENT SHEET FOR THIS NINE WEEKS. NO CREDIT WILL BE GIVEN FOR LATE ASSIGNMENTS.
I. ACCURATELY COMPLETE A PACKET OF REVIEW PROBLEMS FROM CHAPTERS
7-10 & 12.
YOU WILL NEED TO ASK YOUR TEACHER FOR A COPY OF THE PACKET OF REVIEW PROBLEMS. PLEASE DO THIS WELL IN ADVANCE OF THE MAY 17TH DUE DATE. YOU WILL THEN MAKE AN HONEST ATTEMPTED AT ACCURATELY COMPLETING ALL OF THE PROBLEMS. YOU WILL SHOW ALL OF YOUR WORK FOR THESE PROBLEMS EITHER ON THE REVIEW SHEET ITSELF OR ON SCRATCH PAPER. YOU WILL ATTACH ALL SCRATCH WORK TO THE BACK OF THE REVIEW PACKET WHEN YOU TURN IT IN.
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Algebra
II First Nine Weeks “Recommended
Homework Assignments” for 2007/2008
1ST NINE WEEKS
THE TEACHER RESERVES THE RIGHT TO MAKE ANY ADDITIONS (OR DELETIONS) TO THESE ASSIGNMENTS.
8/13/07 H/W Sect. 1-1 PG. 9-10 #17-55 (O), 57-66 (A)
8/14/07 Turn in SIGNED "EXPECTATIONS FOR SUCCESS" SHEET
(10 pts.)
H/W Sect. 1-2 PG. 15-18 #19-69 (O), 72-86 (A) & Practice Quiz 1 (A)
H/W Sect. 1-3 PG. 24-27 #19-73 (O), 77-89 (A)
8/15/07 H/W Sect. 1-4 PG. 30-32 #17-51 (O), 53-79 (A)
8/16/07 TEST DIAGNOSTIC TEST OVER ALG. I MATERIAL (10 pts.)
H/W Review PG. 828-829 Sections 1-1, 1-2, 1-3, 1-4 (O)
8/17/07 H/W Sect. 1-5 PG. 37-39 #15-51 (O), 54-72
(A) & Practice Quiz 2 (A)
H/W Review TAKE GLENCOE QUIZZES 1-1/1-5
EXTRA CREDIT HAVE YOUR PARENT E-MAIL ME THIER CURRENT E-MAIL ADDRESS. (5 PTS.
POSSIBLE)
8/20/07 H/W Sect. 1-6 PG. 44-46 #15-51 (O), 55-75 (A)
8/21/07 QUIZ QUIZ SECTIONS 1-1/1-5 ( 56 pts.)
H/W Review TAKE GLENCOE CH. 1 TEST
H/W CH 1 Rev. PG. 47-50 # 1-51 (A)
8/22/07 Homework (Four AAA calculator batteries
and either a box of Kleenex,
a roll of paper towels
or a box of a dozen pencils)
H/W CH 1 Prac. Test PG. 51 # 1-33 (A)
8/23/07 TEST CHAPTER 1 TEST (100 PTS.)
Turn in PG. 51 # 1-33 (A) (5 PTS.)
8/24/07 H/W Sect. 2-1 PG. 60-62 #17-53 (O), 57-73 (A)
8/27/07 H/W Sect. 2-2 PG. 66-67 #15-59 (O), 62-78 (A)
8/28/07 H/W Sect. 2-3 PG. 72-74 #15-51 (O), 54-75 (A) & Practice Quiz 1 (A)
8/29/07 Turn in PG. 72-74
#15-51 (O), 54-75 (A) & Practice Quiz 1 (A) (5
PTS.)
H/W Sect. 2-4 PG. 78-80 #13-49 (O), 53-67(A)
8/30/07 H/W Sect. 2-6 PG. 93-95 #15-47 (O), 51-65 (A) & Practice Quiz 2 (A)
H/W Review TAKE GLENCOE QUIZZES 2-1/2-5
8/31/07 Turn in 3RD WEEK SIGNED PROGRESS REPORT RETURNED (10 pts.)
H/W Sect. 2-7 PG. 98-99 # 13-39 (O), 42-56 (A)
9/4/07 QUIZ QUIZ SECTIONS
2-1/ 2-4 & 2-6 ( 54 pts.)
H/W CH 2 REV. PG. 100-104 # 13-39 & 43-54 (A)
H/W Review TAKE GLENCOE CH. 2 TEST
9/5/07 H/W CH 2 Prac. Test PG. 105 # 1-29 & 33 (A)
H/W REVIEW GLENCOE CHAPTER 2 PRACTICE TEST
9/6/07 TEST CHAPTER 2 TEST (100 PTS.)
Turn in PG. 105 # 1-33 (A) (5 PTS.)
H/W REVIEW PG. 52-53 # 1-22 (A) & 106-107 # 1-23 (A)
H/W Review TAKE GLENCOE CH. 2 STANDARDIZED PRACTICE TEST
9/7/07 H/W Sect. 3-1 PG. 113-115 #13-47 (O), 50-79 (A)
9/10/07 TEST CHAPTERS 1 & 2
CUMULATIVE REVIEW TEST (100 PTS.)
H/W Sect. 3-1 PG. 113-115 #14-46 (E)
9/11/07 H/W Sect. 3-2 PG. 120-122 #13-49 (O), 52-70 (A) & Practice Quiz 1
(A) substitution method only
9/12/07 H/W Sect. 3-2 PG. 120-122 #13-49 (O) elimination method only
9/13/07 Turn in PG. 120-122 #13-49 (O) elimination method only (5 PTS.)
H/W Sect. 3-3 PG. 126-127 #13-33 (O), 40-54 (A)
9/14/07 H/W Sect. 3-4 PG. 132-135 #15-29 (O), 44-62 (A) & Practice Quiz 2
(A)
H/W Review TAKE GLENCOE QUIZZES 3-1/3-4
9/17/07 H/W Sect. 3-5 PG. 142-144 #13-25 (O), 33-44 (A)
9/18/07 QUIZ QUIZ SECTIONS 3-1/3-4 ( 49 pts.)
H/W CH 3 REV. PG. 145-148 # 1-28 (A)
H/W Review TAKE GLENCOE CH. 3 TEST
9/19/07 H/W CH 3 Prac. Test PG. 149 # 1-20 (A)
9/20/07 TEST CHAPTER 3 TEST (100 PTS.)
Turn in PG. 149 # 1-20 (A) (5 PTS.)
9/21/07 Turn in 6TH WEEK SIGNED PROGRESS REPORT RETURNED (10 pts.)
H/W Review ACT PRACTICE PROBLEMS WORKSHEET #1 PROBLEMS 1-30(A)
9/24/07 H/W Sect. 4-1 PG. 156-158 #11-31 (O), 35-57 (A)
9/25/07 H/W Sect. 4-2 PG. 164-166 #15-39 (O), 42-62 (A)
9/26/07 Turn in ACT PRACTICE PROBLEMS WORKSHEET #1 PROBLEMS 31-60 (A) (5 PTS.)
H/W Sect. 4-3 PG. 172-174 #13-33 (O), 45-60 (A) & Practice Quiz 1 (A)
9/27/07 H/W Sect. 4-4 PG. 179-181 #13-41 (A), 44-64 (A)
9/28/07 TEST ACT PRACTICE TEST #1 ( 50 PTS)
H/W REVIEW PG. 834-835 SECT. 4-1/4-4 (O)
10/1/07 Turn in PG. 834-835 SECT. 4-1/4-4 (O) (5 PTS.)
H/W Sect. 4-5 PG. 186-188 #15-43 (O), 48-75 (A)
10/2/07 H/W Sect. 4-6 PG. 192-194 #13-37 (O), 40-54 (A) & Practice Quiz 2
(A)
10/3/07 H/W Sect. 4-7 PG. 199-201 #11-41 (O), 45-77 (A)
H/W Review TAKE GLENCOE QUIZZES 4-1/4-7
10/4/07 H/W Sect. 4-8 PG. 206-208 #13-33 (O), 37-51 (A)
10/5/07 QUIZ QUIZ SECTIONS 4-1/4-7 ( 41 pts.)
EXTRA CREDIT EXTRA CREDIT DUE ( 15 POSSIBLE PTS.)
Turn in 8TH WEEK SIGNED PROGRESS REPORT RETURNED (10 pts.)
H/W CH 4 REV. PG. 208-214 # 1-48 (A)
H/W Review TAKE GLENCOE CH. 4 TEST
10/10/07 H/W CH 4 Prac. Test PG. 215 # 1-20 (A)
10/11/07 TEST CHAPTER 4 TEST (100 PTS.)
Turn in PG. 215 # 1-20 (A) (5 PTS.)
H/W Ch 1-3 Rev PG. 51 # 2-32 (E) & PG. 105 # 2-32 (E) & PG. 149 # 2-20
(E) & PG. 215 # 2-20 (E)
H/W Review TAKE GLENCOE CH. 4 STANDARDIZED PRACTICE TEST
10/12/07 H/W CUM. REVIEW Chapter 4 Cumulative Review Worksheet
Algebra
II Second Nine Weeks “Recommended
Homework Assignments” for 2007/2008
2ND NINE WEEKS
THE TEACHER RESERVES THE RIGHT TO MAKE ANY ADDITIONS (OR DELETIONS) TO THESE ASSIGNMENTS.
10/15/07 H/W Section 5-1 PG. 226-228 #19-59 (O), 64-84 (A)
10/16/07 TEST CHAPTERS 1-4 CUMULATIVE REVIEW TEST (100 PTS.)
H/W Review ACT PRACTICE PROBLEMS WORKSHEET #2 PROBLEMS 1-30 (A)
10/17/07 PSAT & PLAN TEST
ACT PRACTICE PROBLEMS WORKSHEET #2 PROBLEMS 31-60
(A)
10/18/07 Turn in ACT PRACTICE PROBLEMS WORKSHEET #2 PROBLEMS 31-60 (A) (5 PTS.)
H/W Section 5-2 PG. 231-232 #17-53 (O), 56-69 (A)
10/19/07 H/W Section 5-3 PG. 236-238 #15-57 (O), 60-74 (A) & Practice Quiz
1 (A)
10/22/07 TEST ACT PRACTICE TEST #2 ( 50 pts. )
H/W Section 5-3 PG. 236-238 #16-56 (E)
H/W Review TAKE GLENCOE QUIZZES 5-1/5-3
10/23/07 Turn in SIGNED REPORT CARD RETURNED ( 10 pts.)
H/W Section 5-4 PG. 242-244 #15-53 (O), 57-81 (A)
10/24/07 QUIZ QUIZ SECTIONS 5-1/5-3 ( 61 pts.)
H/W Section 5-4 PG. 242-244 #16-54 (E)
10/25/07 H/W Section 5-5 PG. 248-249 #17-61 (O), 65-82 (A)
10/26/07 ASVAB Test
H/W Section 5-5 PG. 248-249 #16-62 (E)
H/W Review TAKE GLENCOE QUIZZES 5-1/5-5
10/29/07 H/W REVIEW PG. 836-838 SECT. 5-1/5-5 (O)
10/30/07 QUIZ QUIZ SECTIONS
5-1/5-5 ( 69 pts.)
H/W REVIEW PG. 276-278 # 11-42 (A)
H/W Review TAKE GLENCOE QUIZZES 5-1/5-5
10/31/07 H/W REVIEW PG. 836-838 SECT. 5-1/5-5 (E)
11/1/07 TEST CHAPTER 5 SECTIONS 5-1/5-5 TEST (100 pts.)
Turn in PG. 836-838 SECT. 5-1/5-5 (E) (5 PTS.)
11/2/07 Turn in 3RD WEEK SIGNED PROGRESS REPORT RETURNED (10 pts.)
H/W Section 5-6 PG. 254-256 #15-53 (O), 57-82 (A) & Practice Quiz 2 (A)
11/5/07 H/W Section 5-6 PG. 254-256 #16-54 (E)
11/6/07 Turn in PG. 254-256 #16-54 (E) (5 PTS.)
H/W Section 5-7 PG. 261-262 #21-69 (O), 72-84 (A)
11/7/07 H/W Section 5-7 PG. 261-262 #22-68 (E)
H/W REVIEW TAKE GLENCOE QUIZZES 5-6/5-7
11/8/07 H/W Section 5-8 PG. 266-267 #13-41 (O), 45-59 (A)
11/9/07 QUIZ QUIZ SECTION
5-6/5-7 ( 58 pts.)
H/W Section 5-8 PG. 266-267 #14-42 (E)
11/13/07 H/W Section 5-9 PG. 274-275 #19-63 (O), 67-85 (A)
H/W REVIEW TAKE GLENCOE QUIZZES 5-6/5-9
11/14/07 H/W REVIEW PG. 838-839 Sections 5-6/5-8 (E)
11/15/07 QUIZ QUIZ SECTIONS
5-6/5-9 ( 47 pts.)
Turn in PG. 838-839 Sections 5-6/5-8 (E) (5 PTS.)
H/W REVIEW PG. 279-280 #43-75 (O)
H/W REVIEW TAKE GLENCOE QUIZZES 5-6/5-9
11/16/07 H/W REVIEW PG. 279-280 #44-74 (E)
11/19/07 H/W CUM. REVIEW Chapter 5 Cumulative Review Worksheet
11/20/07 TEST CHAPTER 5 SECTION 5-6/5-9 TEST (100 PTS. )
Turn in Chapter 5 Cumulative Review Worksheet (5 PTS.)
H/W Review TAKE GLENCOE CH. 5 STANDARDIZED PRACTICE TEST
11/26/07 H/W REVIEW PG. 51 (O), PG. 105 (O), PG. 149 (O), PG. 215 (O), PG. 281
(O)
11/27/07 TEST CHAPTERS 1-5 CUMULATIVE REVIEW TEST ( 100 PTS.)
11/28/07 H/W Section 6-1 PG. 291-293 #15-53 (O), 56-78 (A)
11/29/07 H/W Section 6-2 PG. 297-299 #15-45 (O), 49-72 (A)
11/30/07 Turn in 6TH WEEK SIGNED PROGRESS REPORT RETURNED (10 pts.)
H/W REVIEW PG. 839-840 Sections 6-1/6-2 (O)
12/3/07 H/W Section 6-3 PG. 304-305 #15-45 (O), 51-68 (A) & Practice Quiz
1 (A)
12/4/07 H/W Section 6-3 PG. 304-305 #14-40 (E)
\\\\\\\\\\\
12/5/07 Turn in PG. 304-305 #14-40 (E) (5 PTS.)
H/W Section 6-4 PG. 310-312 #15-51 (O),55-72 (A)
12/6/07 H/W Section 6-5 PG. 318-319 #15-43 (O), 47-66 (A)
H/W Review TAKE GLENCOE QUIZZES 6-1/6-4
12/7/07 Turn in PG. 318-319 #15-43 (O), 47-66 (A) (5 PTS.)
H/W Section 6-6 PG. 325-328 #15-51 (O), 55-71 (A) & Practice Quiz 2 (A)
12/10/07 QUIZ QUIZ SECTIONS
6-1/6-4 ( 42 pts.)
H/W Review PG. 839-841 Sections 6-1/6-6 (Every other Even Problem)
H/W Review TAKE GLENCOE QUIZZES 6-1/6-6
12/11/07 H/W Section 6-7 PG. 333-335 #15-47 (O), 51-71 (A)
12/12/07 QUIZ QUIZ SECTIONS
6-1/6-6 ( 55 pts.)
H/W CH 6 REV. PG. 336-340 # 1-59 (0)
H/W Review TAKE GLENCOE CH. 6 TEST
PASS OUT 1ST SEMESTER STUDY GUIDE
12/13/07 H/W CH 6 REV. PG. 336-340 # 2-58 (E)
12/14/07 TEST CHAPTER 6 TEST (100 PTS. )
Turn in PG. 336-340 # 2-58 (E) (5 PTS.)
Turn in 8TH WEEK SIGNED PROGRESS REPORT RETURNED (10 pts.)
EXTRA CREDIT EXTRA CREDIT DUE ( 15 POSSIBLE PTS.)
H/W REVIEW DO 1-100 OF SEMESTER EXAM STUDY GUIDE PROBLEMS
H/W Review TAKE GLENCOE CHAPTER 6 STANDARDIZED PRACTICE TEST
BEGIN MAKING REVIEW SHEET COVERING CH. 1-6 MATERIAL TO BE USED ON SEMESTER EXAM
12/17/07 Turn in STUDY GUIDE PROBLEMS 1-50 (5 PTS.)
REVIEW CH 6 TEST
H/W REVIEW DO 101-200 OF SEMESTER EXAM STUDY GUIDE PROBLEMS
H/W Review TAKE GLENCOE CHAPTER 6 STANDARDIZED PRACTICE TEST
CONTINUE MAKING REVIEW SHEET COVERING CH. 1-6 MATERIAL TO BE USED ON SEMESTER
EXAM
12/18/07 TEST EVERYONE TAKE FIRST HALF OF THE SEMESTER EXAM
H/W Review TAKE GLENCOE CHAPTER 6 STANDARDIZED PRACTICE TEST
CONTINUE MAKING REVIEW SHEET COVERING CH. 1-6 MATERIAL
TO BE USED ON SEMESTER EXAM
12/19/07 TEST 1ST SEMESTER EXAM OVER CHAPTERS 1-6 for Periods 4th, 5th, 6th
H/W Review TAKE GLENCOE CHAPTER 6 STANDARDIZED PRACTICE TEST
12/20/07 TEST 1ST SEMESTER EXAM OVER CHAPTERS 1-6 for Periods 1st, 2nd, 3rd
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Algebra
II Third Nine
Weeks “Recommended Homework Assignments” for 2007/2008
3RD NINE WEEKS
THE TEACHER RESERVES THE RIGHT TO MAKE ANY ADDITIONS (OR DELETIONS) TO THESE ASSIGNMENTS.
1/7/08 H/W Section 7-1 PG. 350-352 #17-47 (O), 57-70 (A)
1/8/08 Turn in PG. 350-352 #17-47 (O), 57-70 (A) (5 PTS.)
H/W Section 7-2 PG. 356-358 #13-35 (O), 41-66 (A)
H/W Review TAKE GLENCOE QUIZZES 7-1/7-2
1/9/08 H/W Section 7-3 PG. 363-364 #11-35 (O), 39-52 (A) & Practice Quiz
1 (A)
1/10/08 H/W Section 7-3 PG. 363-364 #12-38 (E)
1/11/08 QUIZ QUIZ SECTIONS 7-1/7-2 ( 36 PTS.)
H/W REVIEW PG. 842 SECTIONS 7-1/7-3 (O)
1/14/08 Turn in PG. 842 SECT. 7-1/7-3 (O) (5 PTS.)
H/W Section 7-4 PG. 368-370 #13-39 (O), 47-62 (A)
1/15/08 Turn in SIGNED REPORT CARD RETURNED ( 10 pts.)
H/W Section 7-4 PG. 368-370 #14-40 (E)
1/16/08 H/W Section 7-5 PG. 375-377 #13-39 (O), & 52-70 (A)
H/W Review TAKE GLENCOE QUIZZES 7-1/7-4
1/17/08 H/W REVIEW PG. 842-843 SECT. 7-1/7-5 (Every Other Even Problem)
1/18/08 QUIZ QUIZ SECTIONS 7-1/7-4 ( 62 PTS.)
H/W Section 7-5 PG. 375-377 #14-40 (E)
1/22/08 H/W Section 7-6 PG. 381-382 #13-41 (O), 44-61(A) & Practice Quiz
2 (A)
H/W Review TAKE GLENCOE QUIZZES 7-1/7-6
1/23/08 H/W Section 7-6 PG. 381-382 #12-32 (E)
1/24/08 QUIZ QUIZ SECTIONS 7-1/7-6 ( 69 PTS.)
H/W CH 7 REV. PG. 400-404 #1-53 (O)
H/W Review TAKE GLENCOE CH. 7 TEST
1/25/08 Turn in 3RD WEEK SIGNED PROGRESS REPORT RETURNED (10 pts.)
H/W CH 7 REV. PG. 400-404 #2-52 (E)
1/28/08 TEST CHAPTER 7 TEST ( 100 PTS.)
Turn in PG. 400-404 #2-52 (E) (5 PTS.)
H/W REVIEW ACT PRACTICE PROBLEMS WORKSHEET #3 PROBLEMS 1-30 (A)
1/29/08 H/W REVIEW ACT PRACTICE PROBLEMS WORKSHEET #3 PROBLEMS 31-60 (A)
1/30/08 Turn in ACT PRACTICE PROBLEMS WORKSHEET #3 (5 PTS.)
H/W Section 8-1 PG. 414-416 #11-39 (O), 43-59 (A)
1/31/08 H/W Section 8-2 PG. 424-425 #13-45 (O), 48-62 (A)
2/1/08 H/W Section 8-2 PG. 424-425 #12-44 (E)
2/4/08 H/W Section 8-3 PG. 429-431 #17-47 (O), 51-71 (A) & Practice Quiz
1 (A)
2/5/08 TCAP WRITNG TEST
H/W Section 8-4 PG. 438-440 #13-37 (O), 41-57 (A)
2/6/08 H/W Section 8-4 PG. 438-440 #14-36 (E)
H/W Review TAKE GLENCOE QUIZZES 8-1/8-3
2/7/08 TEST ACT PRACTICE TEST #3 ( 50 pts.)
H/W REVIEW PG. 845-846 Sections 8-1/8-4 (O)
2/8/08 QUIZ QUIZ SECTIONS 8-1/8-3 ( 58 PTS.)
Turn in PG. 845-846 Sections 8-1/8-4 (O) ( 5 PTS. )
H/W REVIEW PG. 845-846 Sections 8-1/8-4 (E)
2/11/08 H/W Section 8-5 PG. 445-448 #11-37 (O), 41-63 (A) & Practice Quiz
2 (A)
2/12/08 H/W Section 8-5 PG. 445-448 #12-36 (E)
H/W Review TAKE GLENCOE QUIZZES 8-1/8-5
2/13/08 H/W Section 8-6 PG. 451-452 #13-43 (O), 47-59 (A)
2/14/08 QUIZ QUIZ SECTIONS 8-1/8-5 ( 61 PTS.)
H/W Section 8-6 PG. 451-452 #12-42 (E)
2/15/08 Turn in 6TH WEEK SIGNED PROGRESS REPORT RETURNED (10 pts.)
H/W Section 8-7 PG. 458-460 #11-37 (O), 44-72 (A)
H/W Review TAKE GLENCOE QUIZZES 8-1/8-7
2/19/08 H/W Section 8-7 PG. 458-460 #12-36 (E)
2/20/08 QUIZ QUIZ SECTIONS 8-1/8-7 ( 63 PTS.)
H/W CH 8 REV. PG. 461-466 # 1-49 (O)
H/W Review TAKE GLENCOE CH. 8 TEST
EXTRA CREDIT Extra Credit Due (Math-a-thon Problems ) (20pts.)
2/21/08 H/W CH 8 REV. PG. 461-466 # 2-50 (E)
2/22/08 TEST CHAPTER 8 TEST ( 100 PTS.)
Turn in PG. 461-466 # 2-50 (E) (5 PTS.)
2/25/08 H/W Section 9-1 PG. 476-478 #15-47(O), 50-70 (A)
2/26/08 H/W Section 9-1 PG. 476-478 #14-46 (E)
2/27/08 Turn in PG. 476-478 #14-46 (E) (5 PTS.)
H/W Section 9-2 PG. 482-484 #15-49 (O), 52-61 (A) & Practice Quiz 1 (A)
H/W REVIEW TAKE GLENCOE CH. 7 & 8 TESTS
2/28/08 H/W Section 9-3 PG. 489-490 #17-45 (O), 52-66 (E)
2/29/08 TEST CHAPTERS 7 & 8
CUMULATIVE REVIEW TEST (100 PTS.)
H/W REVIEW PG. 847-848 SECT. 9-1/9-3 (O)
3/3/08 H/W REVIEW PG. 847-848 SECT. 9-1/9-3 (E)
H/W Review TAKE GLENCOE QUIZZES 9-1/9-3
3/4/08 H/W Section 9-4 PG. 496-498 #15-53 (O), 46-73 (A) & Practice Quiz
2 (A)
3/5/08 QUIZ QUIZ SECTIONS 9-1/9-3 ( 39 PTS.)
H/W Section 9-4 PG. 496-498 #14-52 (E)
3/6/08 H/W Section 9-5 PG. 502-504 #13-35 (O), 39-61 (A)
H/W Review TAKE GLENCOE QUIZZES 9-1/9-5
3/7/08 Turn in 8TH WEEK SIGNED PROGRESS REPORT RETURNED (10 pts.)
EXTRA CREDIT EXTRA CREDIT DUE ( 15 POSSIBLE PTS.)
H/W Section 9-6 PG. 510-511 #11-39 (O), 42-54 (E)
3/10/08 QUIZ QUIZ SECTIONS 9-1/9-5 ( 64 PTS.)
H/W CH 9 REV. PG. 513-516 # 1-37 (O)
H/W Review TAKE GLENCOE CH. 9 TEST
3/11/08 H/W CH 9 REV. PG. 513-516 # 2-38 (E)
3/12/08 TEST CHAPTER 9 TEST ( 100 PTS.)
Turn in PG. 513-516 # 2-38 (E) (5 PTS.)
H/W Review TAKE GLENCOE CH. 7 & 8 & 9 TESTS
3/13/08 H/W CH 7 - 9 REV. PG. 405 # 1-25 (O) & PG. 467 # 1-25 (O) & PG.
517 # 1-25 (O)
3/14/08 TEST CHAPTER 7-9 REVIEW TEST ( 100 PTS.)
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Algebra II Fourth Nine
Weeks “Recommended Homework Assignments” for 2007/2008
4TH NINE WEEKS
THE TEACHER RESERVES THE RIGHT TO MAKE ANY ADDITIONS (OR DELETIONS) TO THESE ASSIGNMENTS.
3/24/08 H/W Section 7-7 PG. 387-389 #17-55 (O), 58-81 (A)
3/25/08 H/W Section 7-8 PG. 393-394 #15-43 (O), 46-61 (A)
3/26/08 H/W Section 7-9 PG. 398-399 #15-31 (O), 39-49 (A)
H/W Review TAKE GLENCOE QUIZZES 7-1/7-9
3/27/08 H/W Review PG. 844 SECTIONS 7-7 THRU 7-9 (A)
3/28/08 QUIZ QUIZ SECTIONS 7-7/7-9 ( PTS.)
Turn in PG. 844 SECTIONS 7-7 THRU 7-9 (A) (5 PTS.)
H/W Section 10-1 PG. 528-530 #21-65 (O), 69-89 (A)
3/31/08 H/W Section 10-1 PG. 528-530 #22-64 (E)
4/1/08 Turn in SIGNED REPORT CARD RETURNED ( 10 pts.)
H/W Section 10-2 PG. 536-538 #21-69 (O), 74-90 (A) & Practice Quiz 1 (A)
4/2/08 H/W Section 10-2 PG. 536-538 #22-68 (E)
4/3/08 H/W REVIEW PG. 849 SECT. 10-1/10-2 (O)
H/W Review TAKE GLENCOE QUIZZES 10-1/10-2
4/4/08 Turn in PG. 849 SECT. 10-1/10-2 (O) (5 PTS.)
H/W Section 10-3 PG. 544-546 #13-33 (O), 49-66 (A)
4/7/08 QUIZ QUIZ SECTIONS 10-1/10-2 ( 35 PTS. )
H/W Section 10-3 PG. 544-546 #14-34 (E)
4/8/08 H/W Section 10-4 PG. 549-551 #17-55 (O), 60-77 (A)
4/9/08 H/W Section 10 -5 PG. 557-558 # 21-53 (O), 64-80 (E) & Practice Quiz
2 (A)
H/W Review TAKE GLENCOE QUIZZES 10-1/10-5
4/10/08 H/W CH 10 REV. PG. 849-850 SECTIONS 10-1 THRU 10-5 (E)
4/11/08 QUIZ QUIZ SECTIONS 10-1/10-5 ( 71 PTS.)
Turn in 3RD WEEK SIGNED PROGRESS REPORT RETURNED (10 pts.)
H/W CH 10 REV. PG. 566-570 # 1-61 (O)
H/W Review TAKE GLENCOE CH. 10 TEST
4/14/08 H/W CH 10 REV. PG. 566-570 # 2-60 (E)
4/15/08 TEST CHAPTER 10 TEST ( 100 PTS.)
Turn in PG. 566-570 # 2--60 (E) (5 PTS.)
H/W REVIEW ACT PRACTICE PROBLEMS WORKSHEET #4
4/16/08 Turn in ACT PRACTICE PROBLEMS WORKSHEET #4 PROBLEMS 1-30 (5 PTS.)
CH 7-10 REV. PG. 405 # 2-24 (E) & PG. 467 # 2-24 (E) & PG. 517 # 2-24
(E) & PG. 571 # 2-30 (E)
4/17/08 H/W Section 12-1 PG. 635-637 #10-23 (A), 26-63 (A)
4/18/08 H/W Section 12-2 PG. 641-643 # 13-35 (A), 39-72 (A)
4/21/08 TEST ACT PRACTIC TEST #4 ( 50 PTS. )
H/W REVIEW PG. 854 Section 12-1/12/2 (A)
4/22/08 H/W CUM. REVIEW Chapter 10 Cumulative Review Worksheet
H/W Review TAKE GLENCOE CH. 7 & 8 & 9 7 10 TESTS
4/23/08 Turn in Chapter 10 Cumulative Review Worksheet (5 PTS.)
H/W Section 12-3 PG. 648-650 # 19-59 (O), 64-82 (A) & Practice Quiz 1 (A)
H/W Homework GLENCOE CHAPTER 10 STANDARDIZED PRACTICE TEST
4/24/08 TEST CHAPTERS 7-10 CUMULATIVE REVIEW TEST (100 PTS.)
H/W Section 12-3 PG. 648-650 # 20-60 (E)
H/W Review TAKE GLENCOE QUIZZES 12-1/12-3
4/25/08 H/W Section 12-6 PG. 667-670 # 9-35 (O), 40-64 (A) & Practice Quiz
2 (A)
4/28/08 QUIZ QUIZ SECTIONS 12-1/12-3 ( 44 PTS.)
H/W Section 12-6 PG. 667-670 # 10-36 (E)
4/29/08 H/W Section 12-7 PG. 674-675 # 12-26 (A), 29-44 (A)
4/30/08 H/W Section 2-5 PG. 84-86 # 6-18 (A), & 22-42 (A)
H/W Review TAKE GLENCOE QUIZZES 12-1/12-3 & 12-6/12-7 & 2-5
5/1/08 H/W Review PG. 854-856 Sections 12-1, 12-2, 12-3, 12-6, 12-7 (O) & PG.
831 Section 2-5 (O)
5/2/08 QUIZ QUIZ SECTIONS
12-1, 12-2, 12-3 & 12-6 and Section 2-5 ( 56 PTS.)
Turn in 6TH WEEK SIGNED PROGRESS REPORT RETURNED (10 pts.)
H/W Review PG. 687-691 # 8-18 & 26-32 (A) & Worksheets over Permutation,
Combinations and Probability
H/W Review TAKE GLENCOE QUIZZES 12-1/12-3 & 12-6/12-7 & 2-5
5/5/08 H/W CH 12 REV. PG. 854-856 Sections 12-1, 12-2, 12-3, 12-6, 12-7 (E) & PG.
831 Section 2-5 (E)
5/6/08 TEST CHAPTER 12 TEST
SECTIONS 12-1, 12-2, 12-3, 12-6, 12-7 & SECTION
2-5 ( 100 PTS.)
Turn in PG. 854-856 Sections 12-1, 12-2, 12-3, 12-6, 12-7
(E) & PG. 831 Section
2-5 (E) (5 PTS.)
H/W CH 5 REV. PG. 276-280 (O)
H/W Review TAKE GLENCOE CH. 5 & 6 TESTS
5/7/08 H/W CH 6 REV. PG. 336-340 (O)
BEGIN MAKING REVIEW SHEET COVERING MATERIAL FROM CH. 1-12
TO BE USED ON "REVIEW
TEST" AND SEMESTER EXAM
5/8/08 TEST CHAPTER 5-6 REVIEW TEST ( 100 PTS.)
H/W CH 7 REV. PG. 400-404 (O)
H/W Review TAKE GLENCOE CH. 7 & 8 TESTS
CONTINUE MAKING REVIEW SHEET COVERING MATERIAL FROM CH.
1-12 TO BE USED ON "REVIEW
TEST" AND SEMESTER EXAM
5/9/08 H/W CH 8 REV. PG. 461-466 (O)
CONTINUE MAKING REVIEW SHEET COVERING MATERIAL FROM CH.
1-12 TO BE USED ON "REVIEW
TEST" AND SEMESTER EXAM
5/12/08 TEST CHAPTER 7-8 REVIEW TEST ( 100 PTS.)
H/W CH 9 REV. PG. 513-516 (E)
H/W Review TAKE GLENCOE CH. 9 & 10 TESTS
CONTINUE MAKING REVIEW SHEET COVERING MATERIAL FROM CH.
1-12 TO BE USED ON "REVIEW
TEST" AND SEMESTER EXAM
5/13/08 H/W CH 10 REV. PG. 566-570 (O)
CONTINUE MAKING REVIEW SHEET COVERING MATERIAL FROM CH.
1-12 TO BE USED ON "REVIEW
TEST" AND SEMESTER EXAM
5/14/08 TEST CHAPTER 9-10 REVIEW TEST ( 100 PTS.)
H/W CH 12 REV. PG. 687-691 # 8-18 & 26-32 (A) & Worksheets over Permutation,
Combinations and Probability
CONTINUE MAKING REVIEW SHEET COVERING MATERIAL FROM
CH.
1-12 TO BE USED ON "REVIEW
TEST" AND SEMESTER EXAM
5/15/08 H/W REVIEW STUDY GUIDE PROBLEMS #'S 1-50
CONTINUE MAKING REVIEW SHEET COVERING MATERIAL FROM CH.
1-12 TO BE USED ON "REVIEW
TEST" AND SEMESTER EXAM
5/16/08 TEST CH 12 REVIEW TEST ( 100 PTS.)
Turn in 8TH WEEK SIGNED PROGRESS REPORT RETURNED (10 pts.)
EXTRA CREDIT EXTRA CREDIT DUE ( 15 POSSIBLE PTS.)
H/W REVIEW STUDY GUIDE PROBLEMS #'S 51-100
H/W Review TAKE GLENCOE CH. 7 & 8 & 9 & 10 & 12 TESTS
CONTINUE MAKING REVIEW SHEET COVERING MATERIAL FROM CH.
1-12 TO BE USED ON "REVIEW
TEST" AND SEMESTER EXAM
5/19/08 TEST EVERYONE TAKES THE FIRST HALF OF THE SEMESTER EXAM
H/W REVIEW UNDERCLASSMEN DO STUDY GUIDE PROBLEMS #'S 101-150
CONTINUE MAKING REVIEW SHEET COVERING MATERIAL FROM CH.
1-12 TO BE USED ON "REVIEW
TEST" AND SEMESTER EXAM
5/20/08 TEST SENIORS (Take second half of exam periods 4, 5, 6)
H/W REVIEW UNDERCLASSMEN FINISH STUDY GUIDE PROBLEMS #'S 151-200
CONTINUE MAKING REVIEW SHEET COVERING MATERIAL FROM CH.
1-12 TO BE USED ON "REVIEW
TEST" AND SEMESTER EXAM
5/21/08 TEST SENIORS (Take second half of exam periods 1, 2, 3)
H/W REVIEW UNDERCLASSMEN FINISH STUDY GUIDE PROBLEMS #'S 201-250
5/22/08 TEST UNDERCLASSMEN (Take second half of exam periods 4, 5, 6, )
5/23/08 TEST UNDERCLASSMEN (Take second half of exam periods 1, 2, 3)
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Web
Addresses of tutoring programs and practice tests for Algebra
II
http://www.glencoe.com/sec/math/algebra/algebra2/algebra2_05/
http://www.Glencoe.com/sec/math/
http://www.hotmath.org/home2/hotmath_home.jsp
http://www.yahoo.com/science/mathematics
http://forum.swarthmore.edu/dr.math/
http://mathforum.com/mathmagic
http://64.78.42.182/free-ed/Math/Algebra/Algebra01_VidLect.asp
List of possible parent actions which might help your student become more successful academically
Encourage them to spend “whatever time it takes” for
them to complete all of their home work. Different students have more
difficulty in different subjects or with different assignments in the same
subject.
So, help them to understand that they may have to spend extra time in these
areas
or subjects to be successful.
Encourage them to ask questions in class and to take complete notes of class lecture and demonstrations.
Require them to bring all of their books home every night. The Shelby County
Policy recommends that the average high school student should have between
1.5 and 2.5 hours of home work five nights a week (Monday through Thursday
and at sometime during the weekend.) Require your student to have a minimum
of 1.5 to 2.5 hours of “set“ study time in a supervised area (like the dining room or kitchen table) where you can make sure they are actually spending their study time wisely. Parents should check to make sure that all assignments for all classes are completed each night before the “set“ study
time is over. If these assignments are not completed the study time should
be extended until all work is completed. If your student completes all
of their home work quickly, the remaining time should be spent in reviewing
previous
work which was difficult for them. Students could also preview their
future
assignments.
If the teacher has not already given out a syllabus for their class require your student to have an assignment notebook. The student should then write the daily assignment down in this notebook and have the teacher sign beside the assignment each day. If there is no new assignment in the class for the day, still have the student write out the words “ no new assignment” and have the teacher sign beside this notation.
Encourage your student to take advantage of study groups or tutoring opportunities.
They could work with one or more friends on a daily basis who are doing
well in the class in which your student is not being successful. You could
also,
check on the Collierville High School web page or call your students’ guidance
counselor to find out the time when teachers offer tutoring help You
might contact your students guidance counselor to obtain a list of Beta
club members
who may serve as student tutors. Private tutors may also be helpful if
these suggestions are not convenient for you or your student.
Encourage your student to take advantage of some or all of a teacher’s
extra credit opportunities. However, be aware that not all teachers offer
extra credit opportunities.
Encourage your student to organize their work and social schedules in such a manner as to ensure time for them to obtain an appropriate amount of sleep. Students who suffer from sleep deprivation do not pay attention in class.
Steps
for helping your student to be “ Successful”
1) Encourage them to “Spend what ever time it takes” for
them to be successful.
2) Encourage them to ask question in class and take complete notes of class lecture and demonstrations.
3) Require them to bring their books home every night , because I assign approximately
30 minutes of homework every night. ( One good tool to help a student if they
get stuck on a home work problem is the (
http://www.glencoe.com/sec/math/algebra/algebra2/algebra2_05/ ) web
site.
4) Require them to have a minimum “set” study time at the dining
room or kitchen table where you can make sure that they are actually
spending their study time wisely. (MONDAY THRU THURSDAY AND AT SOME TIME DURING
THE WEEKEND.
5) Encourage them to spend extra time (above the 30 minutes of home work each night) in preparation for quizzes and tests. One good way to help them prepare for a quiz or test is to go to the web site created by the publishers of our book and take practice quizzes or tests online.
(
http://www.glencoe.com/sec/math/algebra/algebra2/algebra2_05/ )
6) Encourage your student to take advantage of tutoring opportunities.
1) I tutor each Monday and Friday morning from 6:15 - 6:55 A. M.
2) Private tutors may also be helpful if these times are not convenient for your or your student.
7) Encourage your student to take advantage of
some or all of my extra credit
opportunities.
1) Extra credit assignments (these are listed on their assignment sheets meets given to each student at the beginning of each grading period).
2) Attendance and participation at the before school tutoring sessions.
“ALGEBRA II - FORMULA AND ALGORITHM” PACKET "
CHAPTER 1
SECTION 1-1
ORDER OF OPERATIONS (PEMDAS)
1. PLEASE - (PARENTHESIS, BRACKETS, BRACES, DIVISION LINE, ABSOLUTE VALUE SYMBOLS, RADICALS, GREATEST INTEGER SYMBOLS)
2. EXCUSE- (EXPONENTS)
3. MY DEAR - (MULTIPLICATION AND DIVISION ARE DONE AT THE SAME TIME FROM LEFT TO RIGHT)
4. AUNT SALLY (ADDITION AND SUBTRACTION AT THE SAME TIME FROM LEFT TO RIGHT)
SECTION 1-2/3
NATURAL NUMBERS = N = {1,2,3,4,....}
WHOLE NUMBERS = W = {0,1,2,3,4,....}
INTEGERS = Z = {...., - 4, - 3, - 2, - 1,0,1,2,3,4,....}
RATIONAL NUMBERS = Q = {NUMBERS THAT IN DECIMAL FORM EITHER REPEAT OR TERMINATE}
IRRATIONAL NUMBERS = I = { NUMBERS THAT IN DECIMAL FORM DO NOT REPEAT OR TERMINATE}
REAL
NUMBERS
= R = ANY NUMBER THAT IS RATIONAL OR IRRATIONAL
PROPERTIES OF REAL NUMBERS
1) COMMUTATIVE PROPERTY OF ADDITION a + b = b + a
2) COMMUTATIVE PROPERTY OF MULTIPLICATION a * b = b * a
3) ASSOCIATIVE PROPERTY OF ADDITION ( a + b ) + c = a + ( b + c )
4) ASSOCIATIVE PROPERTY OF MULTIPLICATION ( a * b ) * c = a * ( b * c )
5) ADDITIVE IDENTITY a + 0 = a
6) MULTIPLICATIVE IDENTITY a * 1 = a
7) ADDITIVE INVERSE a + ( - a ) = 0
8) MULTIPLICATIVE INVERSE a * ( - 1 / a ) = 1
9) DISTRIBUTIVE PROPERTY a ( b + c ) = a * b + a * c and ( b + c ) a = b * a + c * a
10) REFLEXIVE PROPERTY OF EQUALITY a = a
11) SYMMETRIC PROPERTY OF EQUALITY if a = b then b = a
12) TRANSITIVE PROPERTY OF EQUALITY if a = b and b = c then a = c
13) MULTIPLICATIVE PROPERTY OF ZERO a * 0 = 0
14) ADDITION OR SUBTRACTION PROPERTY OF EQUALITY - YOU CAN ADD OR SUBTRACT THE SAME NUMBER TO BOTH SIDES OF AN EQUATION AND NOT CHANGE ITS’ EQUALITY
15) MULTIPLICATION OR DIVISION PROPERTY OF EQUALITY - YOU CAN MULTIPLY OR DIVIDE THE SAME NUMBER ON BOTH SIDES OF AN EQUATION AND NOT CHANGE ITS’ EQUALITY
16) SUBSTITUTION PROPERTY OF EQUALITY - WHEN YOU REPLACE A VALUE (OR AN EXPRESSION) IN AN EQUATION WITH A VALUE FOR WHICH IT IS EQUAL. (i. e. - for any numbers a and b, if a = b then a may be replaced by b any where in that equation.)
STEPS TO SOLVE AN EQUATION
1) SIMPLIFY BOTH SIDES OF THE EQUAL SIGN ( USING THE ORDER OF OPERATIONS )
2) ISOLATE THE CHOSEN VARIABLE ON ONE SIDE OF THE EQUAL SIGN ( USING ADDITION OR SUBTRACTION. )
3) GET THE CHOSEN VARIABLE BY ITSELF. (WITH NOTHING ADDED TO OR SUBTRACTED FROM IT)
4) AND GET THE COEFFICIENT OF THE CHOSEN VARIABLE TO EQUAL POSITIVE ONE. ( BY USING MULTIPLICATION OR DIVISION)
5) CHECK YOUR ANSWER BACK INTO THE ORIGINAL EQUATION TO MAKE SURE THAT IT IS A TRUE STATEMENT
SECTION 1-4
ABSOLUTE VALUE | a | = a and | - a | = a (THE DEFINITION OF ABSOLUTE VALUE
IS THE DISTANCE SOME NUMBER IS FROM ZERO) (THAT IS WHY THE ABSOLUTE VALUE
OF A NUMBER
CAN NEVER BE A NEGATIVE NUMBER BECAUSE IT REPRESENTS A DISTANCE AND DISTANCES
ARE ALWAYS POSITIVE)
STEPS FOR SOLVING ABSOLUTE VALUE EQUATIONS
1) ISOLATE THE ABSOLUTE VALUE TERM
2) TAKE WHATEVER IS INSIDE THE ABSOLUTE VALUE SYMBOLS AND SET IT EQUAL TO WHATEVER IS ON THE OTHER SIDE OF THE EQUAL SIGN AND SOLVE FOR THE VARIABLE
3) THEN TAKE WHATEVER IS INSIDE THE ABSOLUTE VALUE SYMBOLS AND SET IT EQUAL TO THE OPPOSITE OF WHATEVER IS ON THE OTHER SIDE OF THE EQUAL SIGN AND SOLVE FOR THE VARIABLE
4) CHECK THESE TWO ANSWERS BACK INTO THE ORIGINAL ABSOLUTE VALUE EQUATION TO SEE WHICH ONE OR ONES WORK (IF NEITHER VALUE WORKS BACK IN THE ORIGINAL EQUATION THEN THERE IS “NO SOLUTION” TO THE PROBLEM)
SECTION 1-5
IMPORTANT FACTS ABOUT INEQUALITIES - IF YOU MULTIPLY OR DIVIDE “BOTH SIDES” OF
AN INEQUALITY BY A NEGATIVE NUMBER YOU HAVE TO REVERSE THE INEQUALITY SYMBOL
STEPS FOR SOLVING AN INEQUALITY
1) SIMPLIFY BOTH SIDES OF THE INEQUALITY SIGN ( USING THE ORDER OF OPERATIONS )
2) ISOLATE THE CHOSEN VARIABLE ON ONE SIDE OF THE INEQUALITY SIGN ( USING ADDITION OR SUBTRACTION. )
3) GET THE CHOSEN VARIABLE BY ITSELF. (WITH NOTHING ADDED TO OR SUBTRACTED FROM IT)
4) AND GET THE CHOSEN VARIABLES’ COEFFICIENT EQUAL TO POSITIVE ONE. ( BY USING MULTIPLICATION OR DIVISION) (REMEMBER THAT IF YOU MULTIPLY OR DIVIDE BOTH SIDES OF A INEQUALITY BY A NEGATIVE NUMBER YOU MUST FLIP THE INEQUALITY SYMBOL)
5) CHECK YOUR ANSWER BACK INTO THE ORIGINAL INEQUALITY TO MAKE SURE THAT IT IS A TRUE STATEMENT
STEPS FOR GRAPHING INEQUALITIES ON A NUMBER LINE
1) AFTER YOU HAVE COMPLETELY SOLVED THE INEQUALITY.
2) DRAW A NUMBER LINE AND LABEL IT WITH APPROPRIATE NUMBERS (MAKING SURE TO INCLUDE THE NUMBER YOU SOLVED FOR IN STEP 1)
3) IF THE INEQUALITY SYMBOL IN YOUR ANSWER IS A “GREATER THAN OR EQUAL” OR A “LESS THAN OR EQUAL TO” SYMBOL DRAW A “CLOSED IN” CIRCLE ABOVE THE NUMBER SOLVED FOR IN STEP 1 AND SKIP TO STEP 5. (IF NOT GO TO STEP 4.)
4) IF THE INEQUALITY SYMBOL IN YOUR ANSWER IS A “STRICTLY GREATER THAN” OR A “STRICTLY LESS THAN” SYMBOL DRAW AN “OPEN” CIRCLE ABOVE THE NUMBER SOLVED FOR IN STEP 1
5) IF THE INEQUALITY SYMBOL IN YOUR ANSWER IS A “GREATER THAN OR EQUAL” OR A “STRICTLY GREATER THAN” SYMBOL DRAW A RAY WITH A STARTING POINT AT YOUR CIRCLE POINTING TO THE RIGHT. IF NOT SKIP TO STEP 6.
6) IF THE INEQUALITY SYMBOL IN YOUR ANSWER IS A “LESS THAN OR EQUAL” OR A “STRICTLY LESS THAN” SYMBOL DRAW A RAY WITH A STARTING POINT AT YOUR CIRCLE POINTING TO THE LEFT.
SECTION 1-6
STEPS FOR SOLVING ABSOLUTE VALUE INEQUALITIES ON A NUMBER LINE
1) ISOLATE THE ABSOLUTE VALUE TERM (MEANING TO GET THIS TERM ON ONE SIDE OF THE INEQUALITY SYMBOL BY ITSELF WITH ITS’ COEFFICIENT EQUAL TO ONE)
2) NOW WE MUST LOOK AT THE POSITIVE POSSIBILITY 1. WRITE WHATEVER IS INSIDE THE ABSOLUTE VALUE SYMBOLS USING THE SAME INEQUALITY SYMBOL AND WHATEVER IS ON THE OTHER SIDE OF THE INEQUALITY SYMBOL 2. SOLVE FOR THE VARIABLE
3) NOW WE MUST LOOK AT THE NEGATIVE POSSIBILITY 1. WRITE WHATEVER IS INSIDE THE ABSOLUTE VALUE SYMBOLS USING THE OPPOSITE INEQUALITY SYMBOL AND THE OPPOSITE OF WHATEVER IS ON THE OTHER SIDE OF THE INEQUALITY SYMBOL 2. SOLVE FOR THE VARIABLE
4) TO SEE THE SOLUTION IN GRAPH FORM GRAPH BOTH OF YOUR SOLUTIONS ON THE NUMBER LINE
CHAPTER 2
SECTION 2-1
QUADRANT SIGNS OF COORDINATES
I ( + , + )
II ( - , + )
III ( - , - )
IV ( + , - )
THE “DOMAIN” OF A RELATION IS THE SET OF ALL “X” VALUES
THAT SATISFY THAT RELATION
THE “RANGE” OF A RELATION IS THE SET OF ALL “Y” VALUES
THAT SATISFY THAT RELATION
A RELATION IS A FUNCTION IF AND ONLY IF EACH ELEMENT OF THE DOMAIN OF THAT
RELATION GOES TO ONE AND ONLY ONE ELEMENT OF THE RANGE OF THAT RELATION
FUNCTIONAL NOTATION -THE EQUATION y = 3x + 2 CAN BE WRITTEN I N FUNCTIONAL
NOTATION AS f (x) = 3x + 2
TO FINDING THE SOLUTION FOR A FUNCTION AT A GIVEN DOMAIN VALUE SUBSTITUTE
THAT VALUE INTO THE FUNCTION WHERE EVER THERE IN AN “ x ” EXAMPLE
IF f (x) = 4 x + 5 THEN f (6) = 4 (6) + 5 OR f (6) = 24 + 5 f (6) = 29
SECTION 2-2
LINEAR EQUATIONS IN STANDARD FORM ARE ALWAYS IN THE FORM OF A x + B y = C
1. WHERE
1. “A” ,”B”, AND “C” ARE INTEGERS AND
2. “A” IS POSITIVE
3. THE GREATEST COMMON FACTOR OF “A” ,”B”, AND “C” IS 1
4. “x” AND “y” ARE BOTH RAISED TO THE POSITIVE ONE POWER).
2. THE ONLY EXCEPTIONS TO THIS ARE OUR TWO TYPES OF SPECIAL LINES:
1. VERTICAL LINES ARE ALWAYS IN THE FORM OF x = SOME NUMBER ( EXAMPLE; x = -2 )
2. HORIZONTAL LINES ARE ALWAYS IN THE FORM OF y = SOME NUMBER ( EXAMPLE; y = 4 )
TO FIND THE SLOPE OF A LINE IF GIVEN THE LINE IN STANDARD LINEAR FORM
USE THE FORMULA SLOPE = m = ( - A )
/ B
THE “ x “ - INTERCEPT IS THE POINT AT WHICH THE LINE INTERSECTS THE “ X ” AXIS
AND IF THE EQUATIONS IS IN STANDARD FORM THE “ X ” INTERCEPT
IS EQUAL TO C / A
THE “ y “ - INTERCEPT IS THE POINT AT WHICH THE LINE INTERSECTS THE “Y” AXIS
AND IF THE EQUATIONS IS IN STANDARD LINEAR FORM THE “Y” INTERCEPT
IS EQUAL TO C / B
SECTION 2-3
THE SLOPE OF A LINE IF GIVEN TWO POINTS ON THE LINE IS THE RELATION
OF THE LINES’ RISE
OVER ITS’ RUN AND CAN BE FOUND GIVEN TWO POINTS USING THE FORMULA SLOPE
= m = ( y2 - y1 ) / ( x2 - x1 )
PERPENDICULAR LINES ARE LINES WHOSE SLOPES ARE NEGATIVE RECIPROCALS OF ONE
ANOTHER
PARALLEL LINES ARE LINES WHOSE SLOPES ARE THE EQUAL TO ONE ANOTHER.
SECTION 2-4
LINEAR EQUATIONS IN SLOPE-INTERCEPT FORM ARE ALWAYS IN THE FORM OF
y = m x + b WHERE “ m ” IS THE SLOPE AND “ b ” IS THE “ y “ -
INTERCEPT
LINEAR EQUATIONS IN “POINT-SLOPE” FORM ARE ALWAYS IN THE FORM OF
( y - y1 ) = m ( x - x1 ) WHERE “ m ” IS THE SLOPE AND “ x1 ” IS
THE “ X “ VALUE IN THE GIVEN ORDERED PAIR AND “ y1” IS
THE “ Y “ VALUE IN THE GIVEN ORDERED
LINEAR EQUATIONS IN FUNCTIONAL NOTATION FORM ARE ALWAYS IN THE FORM
OF f ( x ) = m x + b WHERE “ m ” IS THE SLOPE AND “ b ” IS THE “ y “ -
INTERCEPT
SECTION 2-6
CONSTANT FUNCTION - A LINEAR EQUATION OF THE FORM f ( x )
= some # FOR WHICH THE SLOPE IS ZERO. ALL CONSTANT FUNCTIONS FORM HORIZONTAL
LINES. THEY ARE ALWAYS
IN THE
FORM OF f ( x ) =SOME NUMBER( EXAMPLE; f ( x ) = 4 )
DIRECT VARIATION FUNCTION - A LINEAR EQUATION OF THE FORM
f ( x ) = m x + b
IDENTITY FUNCTION - A LINEAR EQUATION OF THE FORM f ( x )
= m x + b WHERE b = 0 THE GRAPH OF AN IDENTITY FUNCTION WILL ALWAYS PASS THROUGH
THE ORIGIN
ABSOLUTE VALUE FUNCTION - AN EQUATION OF THE
FORM f ( x ) = a | m x + b | (+/-) c WHERE ” a “ , “ b “AND “ c “ EQUAL
ZERO. ABSOLUTE VALUE FUNCTIONS WILL ALWAYS GRAPH AS A “VEE” SHAPE
STEPS GRAPHING ABSOLUTE VALUE FUNCTIONS
1. MAKE A TABLE USING AT LEAST THE FOLLOWING DOMAIN { -2, -1, 0, 1, 2 } VALUES
2. SOLVE FOR EACH OF THE CORRESPONDING RANGE VALUES FOR THESE DOMAIN VALUES
3. PLOT THESE POINTS ON THE COORDINATE PLANE
4. IF THE GRAPH DOES NOT FORM A “VEE” SHAPE CHOOSE ADDITIONAL DOMAIN VALUES BOTH LESS
5. THAN -2 AND GREATER THAN 2 UNTIL THE POINTS BEGIN TO FORM THE “VEE” SHAPE
GREATEST INTEGER FUNCTION - A
TYPE OF STEP FUNCTION DESCRIBED BY f ( x ) = [ x ] WHERE THE VALUE OF f (
x ) IS EQUAL
TO THE GREATEST INTEGER
THAT
IS LESS
THAN OR EQUAL TO “ x ” FOR EXAMPLE IF f ( x ) = [ 6.2 ] THEN
f ( x ) = 6
STEPS FOR GRAPHING GREATEST INTEGER FUNCTIONS
1. MAKE A TABLE USING AT LEAST THE FOLLOWING DOMAIN { 0, .1, .2, .3, .4, .5, .6, .7, .8, .9, 1 } VALUES
2. SOLVE FOR EACH OF THE CORRESPONDING RANGE VALUES FOR THESE DOMAIN VALUES
3. PLOT THESE POINTS ON THE COORDINATE PLANE.
4. USE THE PATTERN FORMED TO GENERALIZE THE STEP GRAPH FOR ALL OTHER NUMBERS.
SECTION 2-7
STEPS FOR GRAPHING LINEAR INEQUALITIES
1) CHECK TO SEE IF THE INEQUALITY IS WRITTEN IN SLOPE INTERCEPT FORM. ( IF NOT REWRITE THE INEQUALITY INTO THIS FORM. )
2) PLOT THE “ Y “ INTERCEPT ON YOUR COORDINATE PLANE
3) USE THE SLOPE TO LOCATE AND PLOT ANOTHER POINT ON THE LINE
4) IF THE INEQUALITY SYMBOL IS STRICTLY LESS THAN “ < “ OR STRICTLY GREATER THAN “ > ” THEN CONNECT THESE TWO PLOTTED POINTS WITH A DOTTED LINE. IF THE INEQUALITY SYMBOL IS LESS THAN OR EQUAL TO “ ≤ “ OR GREATER THAN OR EQUAL TO “ ≥ ” THEN CONNECT THESE TWO PLOTTED POINTS WITH A SOLID LINE
5) IF THE INEQUALITY SYMBOL IS STRICTLY LESS THAN “ < “ OR IS LESS THAN OR EQUAL TO
“ ≤ “ SHADE THE AREA UNDER THE LINE. IF THE INEQUALITY IS STRICTLY GREATER THAN “ > ” OR GREATER THAN OR EQUAL TO “ ≥ ” SHADE THE AREA ABOVE THE LINE
CHAPTER 3
SECTION 3-1
PARALLEL LINES - IF THE SLOPES OF TWO LINES ARE EQUAL BUT THE “ y “ -
INTERCEPTS OF THE TWO LINES ARE DIFFERENT THEN THE LINES ARE PARALLEL. THE LINES
THEN HAVE “NO SOLUTIONS” AND THE LINES ARE SAID TO BE “ INCONSISTENT”
COLLINEAR LINES - IF THE SLOPES OF TWO LINES ARE EQUAL AND THE “ y “ -
INTERCEPTS OF THE TWO LINES ARE THE SAME THEN THE LINES ARE COLLINEAR (THEY ARE
SAME LINE). THESE LINES HAVE “INFINITELY MANY SOLUTIONS” AND ARE
SAID TO BE “CONSISTENT AND DEPENDENT”
LINES THAT INTERSECT AT ONE POINT - IF THE SLOPES OF TWO LINES ARE DIFFERENT
THEN THE LINES INTERSECT AT EXACTLY ONE POINT AND THE LINES ARE SAID TO BE “CONSISTENT
AND INDEPENDENT”
STEPS FOR GRAPHING A SYSTEM OF LINEAR EQUATIONS
1) CHECK TO SEE IF BOTH OF THE EQUATIONS ARE WRITTEN IN GOOD SLOPE INTERCEPT FORM. (IF NOT REWRITE THE EQUATIONS INTO THIS FORM )
2) PLOT THE “Y” - INTERCEPT OF THE FIRST EQUATION ON YOUR COORDINATE PLANE AND USE THE SLOPE TO LOCATE AND PLOT ANOTHER POINT ON THE LINE OF THE FIRST EQUATION
3) CONNECT THESE POINTS WITH A SOLID LINE
4) PLOT THE “Y” - INTERCEPT OF THE SECOND EQUATION ON YOUR THE SAME COORDINATE PLANE AND USE THE SLOPE TO LOCATE AND PLOT ANOTHER POINT ON THE LINE OF THE SECOND EQUATION
5) CONNECT THESE POINTS WITH A SOLID LINE
6) FIND THE COORDINATES FOR THE POINT OF INTERSECTION OF THESE TWO LINES. WRITE YOUR ANSWER AS AN ORDERED PAIR AND CHECK YOUR ANSWERS BACK INTO BOTH OF THE ORIGINAL EQUATIONS TO MAKE SURE THEY MAKE BOTH STATEMENTS TRUE AT THE SAME TIME
SECTION 3-2
STEPS FOR SOLVING A SYSTEM OF EQUATIONS USING THE “SUBSTITUTION METHOD” -
1) CHOOSE ONE OF THE EQUATIONS. THEN CHOOSE ONE OF THE VARIABLES IN THAT EQUATION AND SOLVE FOR IT. (HINT: IF POSSIBLE, CHOOSE THE EQUATION THAT HAS A VARIABLE WITH A COEFFICIENT OF “ONE”)
2) SUBSTITUTE THE VALUE FOUND IN STEP 1 INTO THE OTHER EQUATION AND SOLVE FOR THE STILL UNKNOWN VARIABLE.
3) SUBSTITUTE THE VALUE FOUND IN STEP 2 BACK INTO THE ORIGINAL EQUATION AND SOLVE FOR THE STILL UNKNOWN VARIABLE
4) CHECK YOUR ANSWERS BACK INTO BOTH OF THE ORIGINAL EQUATIONS TO MAKE SURE THEY MAKE BOTH STATEMENTS TRUE AT THE SAME TIME.
STEPS FOR SOLVING A SYSTEM OF EQUATIONS USING THE “ELIMINATION METHOD”
1) MAKE SURE ALL EQUATIONS ARE WRITTEN IN GOOD STANDARD LINEAR EQUATION FORM THEN LINE THE EQUATIONS UP DIRECTLY UNDER ONE ANOTHER SO THAT TERMS WITH THE SAME VARIABLES ARE DIRECTLY UNDER EACH OTHER.
2) CHECK TO SEE IF YOU CAN SIMPLY ADD THE TWO EQUATIONS AND HAVE ONE OF THE VARIABLES ELIMINATE. (IF NOT, YOU WILL HAVE TO CHOOSE WHICH VARIABLE YOU WISH TO ELIMINATE AND THEN DECIDE WHAT NUMBER OR NUMBERS TO MULTIPLY ONE OR BOTH OF THE EQUATIONS BY IN ORDER TO COMPLETE STEP 2.
3) ONCE ONE OF THE VARIABLES HAS BEEN ELIMINATED SOLVE FOR THE OTHER VARIABLE.
4) THEN SUBSTITUTE THE VALUE SOLVED FOUND IN STEP 3 BACK INTO ONE OF THE ORIGINAL EQUATIONS AND SOLVE FOR THE OTHER VARIABLE.
5) CHECK YOUR ANSWERS BACK INTO BOTH OF THE ORIGINAL EQUATIONS TO MAKE SURE THEY MAKE BOTH STATEMENTS TRUE AT THE SAME TIME.
SECTION 3-3
STEPS FOR GRAPHING SYSTEMS OF LINEAR INEQUALITIES
1) CHECK TO SEE IF ALL OF THE INEQUALITY ARE WRITTEN IN GOOD SLOPE INTERCEPT FORM. (IF NOT REWRITE INTO THIS FORM.)
2) PLOT THE Y INTERCEPT OF THE FIRST INEQUALITY ON YOUR COORDINATE PLANE
3) USE THE SLOPE OF THE FIRST INEQUALITY TO LOCATE AND PLOT ANOTHER POINT ON THE LINE
4) IF THE INEQUALITY SYMBOL IS STRICTLY LESS THAN “ < “ OR STRICTLY GREATER THAN “ > ” THEN CONNECT THE TWO PLOTTED POINTS WITH A DOTTED LINE
5) IF THE INEQUALITY SYMBOL IS LESS THAN OR EQUAL TO “ ≤ “ OR GREATER THAN OR EQUAL TO “ ≥ ” THEN CONNECT THE TWO PLOTTED POINTS WITH A SOLID LINE
6) IF THE INEQUALITY SYMBOL IS STRICTLY LESS THAN “ < “ OR IS LESS THAN OR EQUAL TO
“ ≤ “ SHADE THE AREA UNDER THE LINE7) IF THE INEQUALITY IS STRICTLY GREATER THAN “ > ” OR GREATER THAN OR EQUAL TO “ ≥ ” SHADE THE AREA ABOVE THE LINE
8) REPEAT STEPS 2 THROUGH 7 FOR ALL OTHER INEQUALITIES IN THE SYSTEM
9) THE AREA WHICH IS SHADED IN THE GRAPH OF ALL INEQUALITIES OF THE SYSTEM AT THE SAME TIME IS YOUR ANSWER
SECTION 3-4
STEPS FOR FINDING THE MAXIMUM AND MINIMUM OF A SYSTEMS OF LINEAR INEQUALITIES
1) CHECK TO SEE IF ALL OF THE INEQUALITY ARE WRITTEN IN GOOD SLOPE INTERCEPT FORM. (IF NOT REWRITE INTO THIS FORM.)
2) PLOT THE Y INTERCEPT OF THE FIRST INEQUALITY ON YOUR COORDINATE PLANE
3) USE THE SLOPE OF THE FIRST INEQUALITY TO LOCATE AND PLOT ANOTHER POINT ON THE LINE
4) IF THE INEQUALITY SYMBOL IS STRICTLY LESS THAN “ < “ OR STRICTLY GREATER THAN “ > ” THEN CONNECT THE TWO PLOTTED POINTS WITH A DOTTED LINE
5) IF THE INEQUALITY SYMBOL IS LESS THAN OR EQUAL TO “ ≤ “ OR GREATER THAN OR EQUAL TO “ ≥ ” THEN CONNECT THE TWO PLOTTED POINTS WITH A SOLID LINE
6) IF THE INEQUALITY SYMBOL IS STRICTLY LESS THAN “ < “ OR IS LESS THAN OR EQUAL TO
“ ≤ “ SHADE THE AREA UNDER THE LINE7) IF THE INEQUALITY IS STRICTLY GREATER THAN “ > ” OR GREATER THAN OR EQUAL TO “ ≥ ” SHADE THE AREA ABOVE THE LINE
8) REPEAT STEPS 2 THROUGH 7 FOR ALL OTHER INEQUALITIES IN THE SYSTEM
9) THE AREA WHICH IS SHADED IN THE GRAPH OF ALL INEQUALITIES OF THE SYSTEM AT THE SAME TIME IS YOUR ANSWER
10) FIND THE VERTICES OF THE FEASIBLE REGION.
11) SUBSTITUTE THE “X” AND “Y” VALUES FOR EACH ORDERED PAIR OF THE VERTICES INTO THE FUNCTION TO FIND BOTH THE MAXIMUM AND MINIMUM VALUES.
SECTION 3-5
THE STANDARD FORM OF AN EQUATION IN A PLANE IS A x + B y + C z = D WHERE “A”, “B”, “C”,
AND “D” ARE ALL REAL NUMBERS AND “A”, “B”,
AND “C” DO NOT EQUAL ZERO
STEPS FOR SOLVING A SYSTEM OF THREE EQUATIONS AND THREE VARIABLES USING THE “ELIMINATION METHOD”
1) LINE THE EQUATIONS UP DIRECTLY UNDER ONE ANOTHER IN GOOD STANDARD FORM FOR EQUATION OF A PLANE SO THAT TERMS WITH THE SAME VARIABLES ARE DIRECTLY UNDER EACH OTHER.
2) CHOOSE THE FIRST TWO EQUATIONS AND THEN CHOOSE THE VARIABLE YOU WISH TO ELIMINATE.
3) CHECK TO SEE IF YOU CAN SIMPLY ADD THE TWO EQUATIONS AND HAVE THE CHOSEN VARIABLE ELIMINATE. (IF NOT, YOU WILL HAVE TO DECIDE WHAT NUMBER OR NUMBERS TO MULTIPLY ONE OR BOTH OF THE EQUATIONS BY IN ORDER TO COMPLETE STEP 2.)
4) USE THE SECOND PAIR OF TWO EQUATIONS AND ELIMINATE THE SAME VARIABLE FROM THESE TWO EQUATIONS AS YOU DID IN STEP 2.
5) CHECK TO SEE IF YOU CAN SIMPLY ADD THE TWO EQUATIONS AND HAVE THE CHOSEN VARIABLE ELIMINATE. (IF NOT, YOU WILL HAVE TO DECIDE WHAT NUMBER OR NUMBERS TO MULTIPLY ONE OR BOTH OF THE EQUATIONS BY IN ORDER TO COMPLETE STEP 2.)
6) ONCE ONE VARIABLE HAS BEEN ELIMINATED FROM BOTH OF THE FIRST AND SECOND SETS OF EQUATIONS, TAKE THE TWO EQUATIONS WITH THE TWO VARIABLES THAT YOU SOLVED FOR IN STEPS 3 AND 5 AND USE ELIMINATION A THIRD TIME ON THEM .
7) THEN SUBSTITUTE THE VALUE SOLVED FOUND IN STEP 6 BACK INTO ONE OF THE EQUATIONS USE IN STEP 6 AND SOLVE FOR THE OTHER VARIABLE.
8) ONCE YOU HAVE TWO OF THE VARIABLES SOLVED FOR, SUBSTITUTE THESE TWO BACK INTO ONE OF THE ORIGINAL EQUATIONS TO FIND THE STILL UNKNOWN VARIABLE.
9) WRITE YOUR ANSWER AS AN ORDERED TRIPLE AND CHECK YOUR ANSWERS BACK INTO ALL THREE OF THE ORIGINAL EQUATIONS TO MAKE SURE THEY MAKE ALL THREE STATEMENTS TRUE AT THE SAME TIME.
CHAPTER 4
SECTION 4-1
A “ MATRIX” IS A SYSTEM OF ROWS AND COLUMNS AND IS USUALLY NAMED
USING AN UPPERCASE LETTER FOLLOWED BY A SUBSCRIPTED DESCRIPTION OF THE NUMBER
OF ROWS AND THE NUMBER OF COLUMNS IN THE MATRIX. (FOR EXAMPLE A 2
x 3 MEANS MATRIX “ A “ HAS
TWO ROWS AND THREE COLUMNS)
MATRICES ARE EQUAL IF AND ONLY IF
1) THEY BOTH HAVE THE SAME DIMENSIONS
2) AND CORRESPONDING ELEMENTS ARE EQUAL
SECTION 4-2
TO ADD OR SUBTRACT MATRICES
1) IN ORDER FOR THEM TO BE ABLE TO BE ADDED OR SUBTRACTED THEY MUST BOTH HAVE THE SAME DIMENSIONS
2) THEN ADD OR SUBTRACT THE CORRESPONDING ELEMENTS
3) THE ANSWER WILL BE A MATRIX WITH THE SAME DIMENSIONS AS THE ORIGINAL MATRICES THAT WERE ADDED OR SUBTRACTED BUT THE NEW ELEMENTS WILL BE THE SUMS OR DIFFERENCES OF THE CORRESPONDING ELEMENTS
SCALAR MULTIPLICATION OF A MATRIX (A NUMBER) - JUST MULTIPLY EVERY
ELEMENT IN THE MATRIX BY THAT SCALAR. SCALAR MULTIPLICATION IS USED
IN THE DILATION
( THE
REDUCTION OR ENLARGEMENT) OF A GEOMETRIC FIGURE
SECTION 4-3
MATRIX MULTIPLICATION IS “ NOT “ COMMUTATIVE
MATRIX MULTIPLICATION (MULTIPLYING A MATRIX BY A MATRIX)
1) TO BE ABLE TO MULTIPLY TWO MATRICES YOU MUST HAVE THE SAME NUMBER OF COLUMNS IN THE “LEFT HAND” MATRIX AS YOU HAVE ROWS IN THE “RIGHT HAND” MATRIX ( IF NOT THE MULTIPLICATION CANNOT BE PERFORMED AND IT IS SAID TO BE “UNDEFINED” FOR THE TWO MATRICES
2) IF THE MULTIPLICATION CAN BE DONE IT IS A “ROW BY COLUMN” MULTIPLICATION
SECTION 4-4
STEPS TO TRANSLATE A GEOMETRIC FIGURE ABOUT THE COORDINATE PLANE USING MATRICES
1) MAKE A “COORDINATE MATRIX” USING THE VERTICES OF THE GEOMETRIC FIGURE. (WHERE THE FIRST ROW OF THE MATRIX CONTAINS ALL OF THE “ X “ COORDINATES AND THE SECOND ROW CONTAINS ALL OF THE CORRESPONDING “ Y “ COORDINATES)
2) ADD TO THIS “COORDINATE MATRIX” A MATRIX OF THE SAME DIMENSIONS. ( WHERE THE FIRST ROW IS DETERMINED BY THE NUMBER OF UNIT TO THE RIGHT OR LEFT THAT YOU WISH TO TRANSLATE THE GEOMETRIC FIGURE AND THE SECOND ROW IS DETERMINED BY THE NUMBER OF UNITS UP OR DOWN THAT YOU WISH TO TRANSLATE THE GEOMETRIC FIGURE)
3) THE RESULTING MATRIX WILL BE THE COORDINATES FOR THE NEW TRANSLATED GEOMETRIC FIGURE.
STEPS TO DILATE THE PERIMETER OF A GEOMETRIC FIGURE USING MATRICES
1) MAKE A “COORDINATE MATRIX” USING THE VERTICES OF THE GEOMETRIC FIGURE. (WHERE THE FIRST ROW OF THE MATRIX CONTAINS ALL OF THE “ X “ COORDINATES AND THE SECOND ROW CONTAINS ALL OF THE CORRESPONDING “ Y “ COORDINATES)
2) PERFORM SCALAR MULTIPLICATION USING THE SCALE FACTOR.
STEPS TO REFLECT A GEOMETRIC FIGURE USING MATRICES
1) MAKE A “COORDINATE MATRIX” USING THE VERTICES OF THE GEOMETRIC FIGURE. (WHERE THE FIRST ROW OF THE MATRIX CONTAINS ALL OF THE “ X “ COORDINATES AND THE SECOND ROW CONTAINS ALL OF THE CORRESPONDING “ Y “ COORDINATES)
2) MULTIPLY USING THE APPROPRIATE “REFLECTION MATRIX” ON THE LEFT HAND SIDE OF THE “COORDINATE MATRIX”.
STEPS TO ROTATE A GEOMETRIC FIGURE USING MATRICES
1) MAKE A “COORDINATE MATRIX” USING THE VERTICES OF THE GEOMETRIC FIGURE. (WHERE THE FIRST ROW OF THE MATRIX CONTAINS ALL OF THE “ X “ COORDINATES AND THE SECOND ROW CONTAINS ALL OF THE CORRESPONDING “ Y “ COORDINATES)
2) MULTIPLY USING THE APPROPRIATE “ROTATION MATRIX” ON THE LEFT HAND SIDE OF THE “COORDINATE MATRIX”.
SECTION 4-5
STEPS TO FIND THE VALUE OF SECOND ORDER DETERMINANTS
1) THE MATRIX MUST BE A SQUARE 2 x 2 MATRIX IN THE FORM THE MATRIX LISTED AS A "KEY CONCEPT" ON PAGE 182 IN YOUR TEXTBOOK.
2) THEN THE VALUE OF THE DETERMINANT IS FOUND BY THE FORMULA (a d ) - ( b c )
FINDING THE VALUE OF A THIRD ORDER DETERMINANT USING THE EXPANSION
OF MINORS METHOD SEE THE "KEY CONCEPT" LISTED ON PAGE 183 OF THE
TEXTBOOK
FINDING THE VALUE OF A THIRD ORDER DETERMINANT USING THE DIAGONAL
METHOD SEE
THE FORMULA LISTED ON THE BOTTOM OF PAGE 183 OF THE TEXTBOOK
THE FORMULA FOR FINDING THE AREA OF A TRIANGLE USING DETERMINANTS AND THE COORDINATES FOR THE VERTICES OF THE TRIANGLE SEE THE "KEY CONCEPT" LISTED ON PAGE 184 OF THE TEXTBOOK
SECTION 4-6
STEPS FOR SOLVING A SYSTEM OF TWO EQUATIONS AND TWO VARIABLES USING
CRAMER’S
RULE SEE THE "KEY CONCEPT" LISTED ON PAGE 189 OF THE TEXTBOOK
STEPS FOR SOLVING A SYSTEM OF THREE EQUATIONS AND THREE VARIABLES USING CRAMER’S RULE SEE THE "KEY CONCEPT" LISTED ON PAGE 191 OF THE TEXTBOOK
SECTION 4-7
THE INVERSE OF A 2 x 2 MATRIX SEE THE "KEY CONCEPT" LISTED ON PAGE
196 OF THE TEXTBOOK
AN IDENTITY MATRIX IS A SQUARE MATRIX WITH “1’S” FOR
EVERY ELEMENT ON THE PRINCIPAL DIAGONAL AND ZEROS FOR ALL OTHER ELEMENTS
ANY MATRIX MULTIPLIED BY THE APPROPRIATE IDENTITY MATRIX IS THE MATRIX THAT
YOU STARTED WITH
SECTION 4-8
STEPS FOR SOLVING A SYSTEM OF TWO EQUATIONS AND TWO VARIABLES USING
INVERSE MATRICES SEE EXAMPLES 3 AND 4 LISTED ON PAGE 204
OF THE TEXTBOOK
CHAPTER 5
SECTION 5-1
MONOMIAL - A NUMBER, A VARIABLE, OR A PRODUCT OF NUMBERS AND VARIABLES
THE DEGREE OF A MONOMIAL IS THE SUM OF THE EXPONENTS THE VARIABLES IN THAT
MONOMIAL. FOR EXAMPLE THE DEGREE OF THE MONOMIAL 6x2y3z4 IS 2 + 3 + 4 OR
DEGREE 9
NEGATIVE EXPONENTS a - n = 1 / a n
PRODUCT OF POWERS a m * a n = a m + n
POWER OF POWERS ( a m ) n = a m n
POWER OF PRODUCT ( a b ) m = a m * b m
POWER OF A MONOMIAL ( a m b n ) p = a m p * b n p
QUOTIENT OF POWERS a m / a n = a m - n
ZERO EXPONENTS - ANY NUMBER OR VARIABLE
( EXCEPT THE NUMBER ZERO) RAISED TO THE ZERO POWER EQUALS ONE
SCIENTIFIC NOTATION - A NUMBER WRITTEN IN THE FORM OF a *
10^ n WHERE 1 ≤ a < 10
AND “ n “ IS AN INTEGER
SECTION 5-2
THE DEGREE OF A POLYNOMIAL IS THE HIGHEST OF THE DEGREES OF ITS MONOMIAL
TERMS. FOR EXAMPLE THE DEGREE OF THE POLYNOMIAL 6x2y3 + 2xy2 - 7xy IS DEGREE
5 BECAUSE
THE HIGHEST DEGREE OF ITS MONOMIAL TERMS IS FROM THE TERM 6x2y3 WHICH IS
5
BINOMIAL - TWO MONOMIALS COMBINED BY ADDITION OR SUBTRACTION
TRINOMIAL - THREE MONOMIALS COMBINED BY ADDITION OR SUBTRACTION
POLYNOMIAL - ONE OR MORE MONOMIALS COMBINED BY ADDITION OR SUBTRACTION
LIKE TERMS- YOU CAN ONLY COMBINE ( ADD OR SUBTRACT) LIKE TERMS (EXAMPLES;
TERMS WITH THE SAME VARIABLES RAISED TO THE SAME POWER OR RADICALS WITH THE
SAME
ROOTS AND THE SAME RADICANDS)
USE THE DISTRIBUTIVE PROPERTY TO MULTIPLY A MONOMIAL TIMES A POLYNOMIAL
USE THE FOIL METHOD TO MULTIPLY TWO BINOMIALS TOGETHER F the first terms, O
the outer terms, I the inner terms, and L the last terms.
SECTION 5-3
TO DIVIDE A POLYNOMIAL BY A MONOMIAL
1) SIMPLIFY THE POLYNOMIAL IN THE NUMERATOR (IF POSSIBLE)
2) DIVIDE EACH “MONOMIAL TERM” OF THE “ NUMERATOR POLYNOMIAL” BY THE “ MONOMIAL TERM “ OF THE DENOMINATOR
STEPS TO DIVIDE POLYNOMIALS BY POLYNOMIALS USING LONG DIVISION:
1) MAKE SURE THAT THE DIVIDEND AND THE DIVISOR ARE BOTH POLYNOMIALS IN DESCENDING ORDER WITH SPACE HOLDERS FOR EACH DEGREE
2) FIND THE MONOMIAL BY WHICH YOU WILL HAVE TO MULTIPLY THE “ LEADING MONOMIAL OF THE DIVISOR” BY TO GET THE “ LEADING MONOMIAL OF THE DIVIDEND “
3) MULTIPLY THE ENTIRE POLYNOMIAL OF THE DIVISOR BY THE MONOMIAL FOUND IN STEP 2 AND SUBTRACT THE RESULTING POLYNOMIAL FROM THE DIVIDEND
4) BRING DOWN THE NEXT MONOMIAL TERM FROM YOUR ORIGINAL DIVIDEND AND REPEAT STEPS 2 AND 3 UNTIL THE DIVISOR WILL NO LONGER DIVIDE INTO THE REMAINDER
5) WRITE THE REMAINDER DIVIDED BY THE DIVISOR AND ADD THIS TERM TO THE POLYNOMIAL QUOTIENT
6) IF THE REMAINDER IS ZERO THEN THE QUOTIENT AND THE DIVISOR ARE BOTH FACTORS OF THE ORIGINAL DIVIDEND) IF THE REMAINDER IS ZERO THEN THE QUOTIENT IS A FACTOR OF THE ORIGINAL DIVIDEND
STEPS TO DIVIDE POLYNOMIALS BY POLYNOMIALS USING SYNTHETIC DIVISION:
1) MAKE SURE THAT THE DIVIDEND AND THE DIVISOR ARE BOTH POLYNOMIALS IN DESCENDING ORDER WITH SPACE HOLDERS FOR EACH DEGREE
2) MAKE SURE THAT THE DIVISOR IS IN THE FORM OF (OR CAN BE PUT IN THE FORM OF) x - a WHERE “ x “ IS A VARIABLE WHOSE COEFFICIENT AND EXPONENT ARE BOTH ONE AND “ a “ IS A REAL NUMBER. ( IF THIS CANNOT BE DONE THEN IT IS IMPOSSIBLE TO USE THIS METHOD AND YOU WILL HAVE TO USE LONG DIVISION TO DIVIDE THE POLYNOMIALS.)
3) WRITE “ a “ IN A BRACKET TO SET IT A PART
4) ON THE SAME LINE WRITE THE COEFFICIENTS OF THE DIVIDEND
5) LEAVE A ONE LINE SPACE IMMEDIATELY UNDER THESE COEFFICIENTS AND DRAW A N ADDITION LINE
6) CARRY THE FIRST COEFFICIENT DOWN IMMEDIATELY UNDER THE ADDITION
7) MULTIPLY THE NUMBER “ a “ BY THIS COEFFICIENT AND WRITE THE PRODUCT IMMEDIATELY UNDER THE SECOND COEFFICIENT
8) ADD THE SECOND COEFFICIENT AND THE PRODUCT RESULTING FROM STEP 7. WRITE YOUR SUM UNDER THE ADDITION LINE
9) REPEAT STEPS 7 AND 8 FOR ALL OF THE REMAINING COEFFICIENTS
10) THE LAST SUM TO BE BROUGHT DOWN UNDER THE ADDITION LINE IS ALWAYS YOUR REMAINDER AND SHOULD BE WRITTEN OVER THE DIVISOR
11) THE NEXT SUM IMMEDIATELY TO THE LEFT OF THE REMAINDER IS ALWAYS THE CONSTANT OF THE POLYNOMIAL QUOTIENT
12) THE NEXT SUM IMMEDIATELY TO THE LEFT OF THE CONSTANT IS ALWAYS THE COEFFICIENT OF THE FIRST DEGREE TERM OF THE POLYNOMIAL QUOTIENT
13) KEEP REPEATING THE PATTERN IN STEP 12 UNTIL ALL OF THE SUMS ARE COEFFICIENTS OF ONE DEGREE HIGHER TERMS OF THE POLYNOMIAL QUOTIENT
14) THE DEGREE OF THE POLYNOMIAL QUOTIENT SHOULD ALWAYS BE ONE LESS THAN N THAT OF THE ORIGINAL DIVIDEND
15) IF THE REMAINDER IS ZERO THEN THE QUOTIENT AND THE DIVISOR ARE BOTH FACTORS OF THE ORIGINAL DIVIDEND
SECTION 5-4
GREATEST COMMON FACTOR - THE LARGEST NUMBER THAT WILL EVENLY DIVIDE INTO TWO
OR MORE NUMBERS
STEPS IN FACTORING BINOMIALS:
I) TRY TO FACTOR OUT THE GREATEST COMMON FACTOR.
2) CHECK TO SEE IF THE BINOMIAL IS A “DIFFERENCE OF PERFECT SQUARES”`
1. IS THE FIRST TERM A PERFECT SQUARE?
2. IS THE ABSOLUTE VALUE OF THE SECOND TERM A PERFECT SQUARE?
3. IS IT A DIFFERENCE ? (IS IT A SUBTRACTION EXPRESSION ?)
4. THEN THE FACTORIZATION IS IN THE FORM OF ( “the square root of the first term” + “the square root of the second term” ) times ( “the square root of the first term” - “the square root of the second term” )
3) CHECK TO SEE IF THE BINOMIAL IS A “SUM OF PERFECT CUBES”
1. IS THE FIRST TERM A PERFECT CUBE?
2. IS THE SECOND TERM A PERFECT CUBE?
3. IS IT A SUM ? (IS IT A N ADDITION EXPRESSION ?)
4. THEN THE FACTORIZATION IS IN THE FORM OF ( a +b ) ( a 2 - ab + b 2 ) WHERE
“ a ” REPRESENTS THE CUBE ROOT OF THE FIRST TERMS OF THE ORIGINAL BINOMIAL AND “ b ” REPRESENTS THE CUBE ROOT OF THE SECOND TERM OF THE ORIGINAL BINOMIAL4) CHECK TO SEE IF THE BINOMIAL IS A “DIFFERENCE OF PERFECT CUBES”
1. IS THE FIRST TERM A PERFECT CUBE?
2. IS THE SECOND TERM A PERFECT CUBE?
3. IS IT A DIFFERENCE ? ( IS IT A SUBTRACTION EXPRESSION ? )
4. THEN THE FACTORIZATION IS IN THE FORM OF ( a - b ) ( a 2 +ab + b 2 ) WHERE “ a ”REPRESENTS THE CUBE ROOT OF THE FIRST TERMS OF THE ORIGINAL BINOMIAL AND “ b ” REPRESENTS THE CUBE ROOT OF THE SECOND TERM OF THE ORIGINAL BINOMIAL
5) IF THE BINOMIAL IS NOT FACTORABLE USING ANY OF THESE METHODS THEN IT IS “ PRIME ”.
STEPS IN FACTORING TRINOMIALS:
1) TRY TO FACTOR OUT THE GREATEST COMMON FACTOR.
2) CHECK TO SEE IF THE TRINOMIAL IS A “PERFECT SQUARE TRINOMIAL”
1. IS THE FIRST TERM A PERFECT SQUARE?
2. IS THE THIRD TERM A PERFECT SQUARE?
3. IS THE ABSOLUTE VALUE OF THE SECOND TERM EQUAL TO TWICE THE SQUARE ROOT OF THE FIRST TERM TIMES THE SQUARE ROOT OF THE THIRD TERM?
4. THEN THE FACTORIZATION IS IN THE FORM OF (a + b)2 OR (a - b)2. WHERE “a” REPRESENTS THE SQUARE ROOT OF THE FIRST TERM OF THE ORIGINAL TRINOMIAL AND “b” REPRESENTS THE SQUARE ROOT OF THE THIRD TERM OF THE ORIGINAL TRINOMIAL. (THE SIGN OF THE FACTORIZATION IS DETERMINED BY THE SIGN OF THE SECOND TERM OF THE ORIGINAL TRINOMIAL)
3) THE SEVEN-STEP METHOD.
1. PUT THE TRINOMIAL IN DESCENDING ORDER.
2. FIND THE PRODUCT OF THE COEFFICIENT OF THE FIRST TERM AND THE COEFFICIENT OF THE THIRD TERM.
3. LIST ALL THE PAIRS OF INTEGERS THAT ARE FACTORS OF THE PRODUCT FOUND IN STEP 2.
4. FIND THE SUM OF EACH PAIR OF INTEGER FACTORS FOUND IN STEP 3 (UNTIL YOU FIND THE PAIR OF FACTORS WHOSE SUM IS EQUAL TO THE MIDDLE TERM OF THE ORIGINAL TRINOMIAL.)
5. USE THIS PAIR OF FACTORS TO SUBSTITUTE INTO THE ORIGINAL TRINOMIAL USING THE FORM
a x2 + ( ? + ? ) x + c
6. DISTRIBUTE THE VARIABLE THROUGH THE PARENTHESIS. YOU WILL THEN HAVE A FOUR-NOMIAL.
7. THE FOLLOW THE STEPS FOR FACTORING A FOUR-NOMIAL
4) IF THE TRINOMIAL IS NOT FACTORABLE USING ANY OF THESE METHODS THEN IT IS “ PRIME ”.
STEPS FOR FACTORING A FOUR-NOMIAL:
1. TRY TO FACTOR OUT THE GREATEST COMMON FACTOR.
2. TRY TO FACTOR THE FOUR NOMIAL BY GROUPING.
1. GROUP THE FOUR-NOMIAL INTO PAIRS
2. FACTOR OUT THE GREATEST COMMON FACTOR OF EACH PAIR, TO FORM TWO BINOMIALS.
3. TRY TO FACTOR THE FOUR NOMIAL BY GROUPING THE FOUR - NOMIAL INTO BINOMIAL AND MONOMIAL PAIRS .
1. GROUP THE FOUR-NOMIAL INTO THE FORM ( x + a ) 2 - b 2 SO THAT THE FINAL
2. FACTORIZATION IS IN THE FORM OF
[ ( x + a ) + b2 ] * [ ( x + a ) - b 2 ]
4. IF THE FOUR-NOMIAL IS NOT FACTORABLE USING ANY OF THESE METHODS IT IS “ PRIME ”.
5. TRY TO FACTOR OUT THE GREATEST COMMON FACTOR.
6. TRY TO FACTOR THE FOUR NOMIAL BY GROUPING.
1. GROUP THE FOUR-NOMIAL INTO PAIRS
2. FACTOR OUT THE GREATEST COMMON FACTOR OF EACH PAIR, TO FORM TWO BINOMIALS.
7. TRY TO FACTOR THE FOUR NOMIAL BY GROUPING THE FOUR - NOMIAL INTO BINOMIAL AND 8. MONOMIAL PAIRS .
1. GROUP THE FOUR-NOMIAL INTO THE FORM ( x + a ) 2 - b 2 SO THAT THE FINAL
2. FACTORIZATION IS IN THE FORM OF
[ ( x + a ) + b2 ] * [ ( x + a ) - b 2 ]
9. IF THE FOUR-NOMIAL IS NOT FACTORABLE USING ANY OF THESE METHODS IT IS “ PRIME ”.
SECTION 5-5
PRIME NUMBERS ARE NUMBERS WHOSE ONLY FACTORS ARE ONE AND THEMSELVES. EXAMPLES
: { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 43, . . . }
SECTION 5-6
PRODUCT PROPERTY OF SQUARE ROOTS √ab = √a * √b
QUOTIENT PROPERTY OF SQUARE ROOTS √ a / b = √a / √b
FOUR THINGS THAT MUST BE TRUE FOR A RADICAL TO BE IN SIMPLEST RADICAL FORM
1) THE INDEX (OR ROOT) IS AS SMALL AS POSSIBLE
2) THE RADICAND HAS NO FACTORS RAISED TO A POWER GREATER THAN OR EQUAL TO INDEX.
3) THE RADICAND IS NOT A FRACTION.
4) NO RADICAL APPEARS IN THE DENOMINATOR.
TO ADD OR SUBTRACT RADICALS EXPRESSIONS
1) SIMPLIFY EACH RADICAL TERM FIRST
2) THEN COMBINE (ADD OR SUBTRACT) TERMS WITH THE SAME ROOTS (INDEXES) AND THE SAME RADICANDS.
TO MULTIPLY A MONOMIAL AND A POLYNOMIAL WHICH CONTAIN RADICAL TERMS
1) MULTIPLY EACH TERM IN THE RADICAL EXPRESSION BY THE MONOMIAL
2) THEN SIMPLIFY EACH PRODUCT
3) THE COMBINE LIKE TERMS TO MULTIPLY TWO BINOMIALS WHICH CONTAIN RADICAL TERMS
1) USE THE “ FOIL “ METHOD
2) THEN COMBINE LIKE TERMS
SECTION 5-7
DEFINITION OF RATIONAL EXPONENTS - FOR ANY NON ZERO REAL
NUMBER “ b “ AND
ANY INTEGERS “ m “ AND “ n “, WITH n > 1, b m /
n = n b m EXCEPT WHEN b < 0 AND n IS EVEN
SECTION 5-8
THE VALUES THAT SATISFY AN EQUATION ARE CALLED THE “ ROOTS “, THE “ SOLUTIONS “ OR
THE “ ZEROS “ OF THE EQUATIONS
STEPS FOR SOLVING A RADICAL EQUATION WHERE THE VARIABLE IS IN THE RADICAND
1. ISOLATE THE RADICAL THAT CONTAINS THE VARIABLE ( IF THERE ARE MORE THAN ONE RADICALS THAT CONTAIN VARIABLES ISOLATE ONE OF THEM)
2. GET RID OF THE RADICAL BY RAISING BOTH SIDES OF THE EQUATION TO THE APPROPRIATE POWER (REMEMBER TO INCLUDE ABSOLUTE VALUES WHERE NECESSARY )
3. IF THERE IS STILL A RADICAL THAT CONTAINS A VARIABLE REPEAT STEPS ONE AND TWO
4. SOLVE THE REMAINING EQUATIONS
5. CHECK YOUR ANSWERS BACK INTO THE ORIGINAL EQUATION TO SEE IF THEY MAKE THE EQUATION TRUE (ONLY INCLUDE IN YOUR FINAL ANSWER, SOLUTIONS THAT MAKE THE ORIGINAL EQUATION TRUE. ALL OTHER ANSWERS ARE “EXTRANEOUS SOLUTIONS” AND SHOULD NOT BE INCLUDED IN THE FINAL ANSWER.)
STEPS FOR SOLVING A RADICAL INEQUALITIES WHERE THE VARIABLE IS IN THE RADICAND
1. ISOLATE THE RADICAL THAT CONTAINS THE VARIABLE ( IF THERE ARE MORE THAN ONE RADICALS THAT CONTAIN VARIABLES ISOLATE ONE OF THEM)
2. GET RID OF THE RADICAL BY RAISING BOTH SIDES OF THE EQUATION TO THE APPROPRIATE POWER (REMEMBER TO INCLUDE ABSOLUTE VALUES WHERE NECESSARY. ALSO REMEMBER THAT IF YOU MULTIPLY OR DIVIDE BOTH SIDES OF AN INEQUALITY BY A NEGATIVE NUMBER YOU MUST REVERSE THE INEQUALITY SYMBOL. )
3. IF THERE IS STILL A RADICAL THAT CONTAINS A VARIABLE REPEAT STEPS ONE AND TWO
4. SOLVE THE REMAINING INEQUALITY (USE THIS ANSWER AS ONE OF THE CRITICAL VALUES IN STEP SIX.)
5. YOU MUST ALSO FIND ANY EXCLUDED VALUES. TO DO THIS SET EACH RADICAND THAT CONTAINS A VARIABLE “GREATER THAT OR EQUAL” TO ZERO. (USE ALL OF THESE ANSWERS AS CRITICAL VALUES IN STEP SIX.)
6. TRY A NUMBER LOWER THAN YOUR LOWEST CRITICAL VALUE FOUND IN STEPS 4 AND 5 TO SEE IF IT MAKE THE ORIGINAL INEQUALITY A TRUE STATEMENT. REPEAT THIS PROCESS WITH EACH SUCCESSIVE CRITICAL VALUE FROM STEPS 4 AND 5 UNTIL YOU ARE YOU OF THE CORRECT INTERVAL OF YOU ANSWER.
7. CHECK YOUR ANSWER BACK INTO THE ORIGINAL EQUATION TO SEE IF THEY MAKE THE EQUATION TRUE (ONLY INCLUDE IN YOUR FINAL ANSWER, SOLUTIONS THAT MAKE THE ORIGINAL EQUATION T RUE. ALL OTHER ANSWERS ARE “EXTRANEOUS SOLUTIONS” AND SHOULD NOT BE INCLUDED IN THE FINAL ANSWER.)
STEPS FOR SOLVING A RADICAL EQUATION WHERE THE VARIABLE IS NOT IN THE RADICAND
1. SIMPLIFY BOTH SIDE OF THE EQUATION
2. GET ALL OF THE TERMS THAT CONTAIN THE VARIABLE ON THE SAME SIDE OF THE EQUATION
3. GET THE TERM THAT CONTAINS THE VARIABLE ON THAT SIDE OF THE EQUAL SIGN BY ITSELF (THAT MEANS WITH NOTHING ADDED TO IT OR SUBTRACTED FROM IT)
4. GET THE COEFFICIENT OF THE CHOSEN VARIABLE EQUAL TO ONE (BY MULTIPLYING OR DIVIDING BY THE APPROPRIATE NUMBER)
5. SIMPLIFY YOUR ANSWER
6. CHECK YOUR ANSWERS BACK INTO THE ORIGINAL EQUATION TO SEE IF THEY MAKE THE ORIGINAL EQUATION TRUE (ONLY INCLUDE IN YOUR FINAL ANSWER, SOLUTIONS THAT MAKE THE ORIGINAL EQUATION TRUE. ALL OTHER ANSWERS ARE “EXTRANEOUS SOLUTIONS” AND SHOULD NOT BE INCLUDED IN THE FINAL ANSWER.)
SECTION 5-9
IMAGINARY NUMBERS
BY DEFINITION √ -1 = i then
i2 = -1
i3 = - i
i4 = 1also remember that i0 = 1
COMPLEX NUMBERS ARE ALWAYS WRITTEN IN THE a + bi FORM WHERE “ a “ IS
THE REAL NUMBER PART AND “ bi “ IS THE IMAGINARY PART
TWO COMPLEX NUMBERS ARE EQUAL IF AND ONLY IF THE REAL NUMBER PARTS ARE EQUAL
AND THE IMAGINARY NUMBER PARTS ARE EQUAL
THE CONJUGATE OF “ a + bi “ IS “ a - bi “
CHAPTER 6
SECTION 6-1/6-2
GOOD STANDARD QUADRATIC EQUATION FORM IS y = a x 2 + b x + c
STEPS FOR SOLVING QUADRATIC EQUATIONS BY GRAPHING
1) CHECK TO MAKE SURE THAT THE EQUATION IS WRITTEN IN GOOD STANDARD FORM y = a x 2 + b x + c
2) FIND THE AXIS OF SYMMETRY BY USING THE EQUATION x = ( - b /2 a )
3) SET UP A CHART AND CHOOSE AT LEAST 5 VALUES FOR “ X” AND SOLVE FOR THE CORRESPONDING VALUES FOR “ y .“ ( use the value for “ X” at the axis of symmetry and also choose at least two values for “ X” on either side of the axis of symmetry. )
4) PLOT THE ORDERED PAIRS FOUND IN STEP 2 AND GRAPH IN THE PARABOLA
5) THE “ X ” - INTERCEPTS ARE THE SOLUTIONS (also called the “roots” or “zeros”) TO THE EQUATION
6) CHECK EACH OF THE POSSIBLE SOLUTIONS FOUND IN STEP 5 BACK INTO THE ORIGINAL EQUATION TO MAKE SURE THAT IT IS AN ACTUAL SOLUTION. ( IF THERE ARE NO “ X ” - INTERCEPTS OR IF NONE OF THE POSSIBLE ANSWERS WORK WHEN CHECKED BACK INTO THE ORIGINAL EQUATION THEN THERE ARE “NO REAL ROOTS” OR THERE IS “ NO SOLUTION “ TO THE EQUATION. )
SECTION 6-3
STEPS FOR SOLVING QUADRATIC EQUATIONS USING FACTORING
1) MAKE SURE THAT THE EQUATION IS IN “ GOOD STANDARD QUADRATIC EQUATION FORM “ ( THAT IS ax2 + bx + c = 0 FORM )
2) FACTOR THE POLYNOMIAL COMPLETELY
3) SET EACH FACTOR THAT CONTAINS A VARIABLE EQUAL TO ZERO AND SOLVE FOR THE VARIABLE
4) CHECK EACH OF THE POSSIBLE ANSWERS BACK INTO THE ORIGINAL EQUATION TO MAKE SURE THAT IT IS A SOLUTION. ( IF NONE OF THE POSSIBLE ANSWERS WORK WHEN CHECKED BACK INTO THE ORIGINAL EQUATION THEN THERE IS “ NO SOLUTION “ TO THE EQUATION. )
SECTION 6-4
STEPS FOR SOLVING QUADRATIC EQUATIONS USING THE “ COMPLETING THE SQUARE “ METHOD
1) MAKE SURE THAT THE EQUATION IS IN “ GOOD STANDARD QUADRATIC EQUATION FORM “ ( THAT IS ax2 + bx + c = 0 FORM )
2) CHECK TO MAKE SURE THAT THE COEFFICIENT OF THE QUADRATIC TERM (OF THE