Key to Unit 5 Review Assignment

page 282 Chapter Test (1-12 ALL)

page 306(20, 26, 40)

Unit 5 Quiz A Review Sheet

Unit 4 Practice Test #2 Answer Key - My apologies for the delay!

Unit 4 Practice Test Answer Key

Unit 3 Test Prep Problems - Answer Key

Here are the answers to Unit 3 review problems assigned in the previous post. Please check your answers and, if you have a question, send a comment to THIS post. Mrs. Skinner or Mr. Roeser will respond. This review session is open from now until 9:00 PM this evening. Please remember that you should also be consulting your study guide, as there are topics on the guide that are not covered by this problem set. Thanks for participating in this online review.

p. 148 Oral Exercises

#2 -st² and 3t²s; 2s²t and –s²t

Like terms are terms that have the same variable(s) and exponent(s).

#5 degree 8 (Add the exponents of all the variables.)

#7 degree 3

#9 degree 6

#12 -4x³ – 2x² + 6x – 5; cubic four-term polynomial

#14 p²q³ – 3pq⁴; degree 5 binomial

#16 -s²t² + 2s²t + 3st²; quartic trinomial

p. 149 Written Exercises

#43 2a³ + 2ab² + b³

pp. 153-154 Written Exercises

#20 -3r³s⁶

#34 0

To multiply monomials, multiply the coefficients, keep the same base, and add the exponents.

p. 157 Written Exercises

#16 16t¹⁶

#28 10x⁹y⁷

#48 8x⁸ⁿ

pp. 159-160 Written Exercises

#17 2x⁴ – 3x³y – x²y²

#40 Area = 2x² + 5x units²

pp. 162-163 Written Exercises

#16 10k² – 11k – 6

#34 -2a³ – 5a² + 11a - 4

p. 177 Self-Test 3

#3 The dimensions of the pond are 17 ft by 10 ft.

Unit 3 Test Prep Problems

Below are some problems from your textbook that you can work to prepare for the Unit 3 test. Answers will be posted on this blog at 7:00 PM on Thursday, October 27. Ms. Skinner and Mr. Roeser will be available from 7:00 to 9:00 PM to respond to questions that you may have. Send your questions as a comment to the post with the answer key, not as an e-mail. THIS PROBLEM SET IS NOT A SUBSTITUTE FOR THE STUDY GUIDE. THERE ARE ITEMS ON THE STUDY GUIDE THAT ARE NOT COVERED HERE.

p. 148 Oral Exercises

#2 – The textbook uses “similar monomials” to mean like terms.

In addition to naming the like terms, tell how you know which terms are like terms (go back to the definition of like terms).

#5, 7, 9 – Just state the degree of the entire monomial.

#12, 14, 16 – Rewrite in standard form, if necessary. Then classify each polynomial by degree and number of terms using vocabulary, not numbers.

p. 149 Written Exercises

#43 – Be sure your answer is in standard form.

pp. 153-154 Written Exercises

#20, 34

Also, state the rule for multiplying monomials.

p. 157 Written Exercises

#16, 28, 48

Yes, #48 is a little tougher, but just apply the same Multiplication Laws of Exponents that you used for the first two exercises in this set.

pp. 159-160 Written Exercises

#17, 40

pp. 162-163 Written Exercises

#16, 34 – Again, write answers in standard form

p. 177 Self-Test 3

#3 – Show all four steps as instructed.

Word Problem Practice

D=rt Problem:

Bill started biking from his home at 8:00AM at a rate of 16km/h.  His sister Julie started biking from the same house at 8:30AM at a rate of 20km/h.  If they are traveling along the same route, how long is it before Julie overtakes her brother?

HINT (They are heading in the same direction and will travel the same distance!)

CHART:

                  km/h              h                   km

   Bill           16              x + 0.5         16(x+0.5)

   Julie          20                 x                 20x

Equation:  16(x+0.5) = 20x

                   16x +8 = 20x

                           8 = 4x

                            2 = x   <--  Julie's time riding

                         2.5 = x + 0.5  <-- Bill's time riding

Check:

    2h(20km/h) = 40km

    2.5h(16km/h) = 40km

It will take Julie 2 hours to over take Bill on the bike ride.

Be sure to check back later as I will post more problems to help you study!

Review of Solving Equations

PRINT OUT THIS POST AND MAKE IT THE FIRST PAGE OF YOUR UNIT 2 NOTES!!!

UNIT 2: EQUATIONS

Unit 2 is all about solving linear equations. You've been solving equations for several years, and we expect Algebra students to enter the course with a high degree of proficiency in solving equations with integer coefficients. The first homework assignment in Unit 2 is a chance to knock the rust off your equation-solving skills and get ready for the new material that follows.

Here are our expectations for solving equations algebraically.

Solving

a. Always begin by simplifying the expressions on both sides of the equation completely. Simplifying typically involves getting rid of parentheses by distributing, then adding like terms. After you simplify both sides, you obtain what is called the "simplified equation". This is an important checkpoint. WE MUST SEE THE SIMPLIFIED EQUATION IN YOUR WORK. Some students may be able to get to the simplified equation in one step, others may need more than one step. That doesn't matter. What does matter is that you show the simplified equation. FOR THE TIME BEING STARTING WITH TODAY'S HOMEWORK ASSIGNMENT, YOU MUST DRAW A BOX AROUND THE SIMPLIFIED EQUATION. [See example below.]

b. Once you get to the simplified equation, you begin doing the algebraic inverses to isolate the variable. (By algebraic inverses, we mean adding the same quantity to both sides or multiplying or dividing both sides by the same quantity.) The expectation is that Algebra students do the inverses mentally and do NOT write the inverses on paper.

Checking

a. Do checks in the ORIGINAL equation. You do not need to re-copy the equation, but you must show a straight substitution step where you just replace the variables in the original equation with the solution. In other words, when the reader looks at the first, substitution step of your check, the reader should be able to "see" the original equation.

b. After substituting, you simplify the numerical expressions on both sides of the equation. If there are grouping symbols, you must show the simplified value of the expression inside the grouping symbols. [See example below.]

c. We do not require a check on every equation. We will tell you when to check.

Solution Set

a. Whether or not you are required to do a check, always finish your work with a "therefore" statement (3-dot triangle), followed by the solution in braces.

b. If your solution did not check and you could not find your error, write "Does not check" in place of the solution set. Never write a solution set if you can't get your solution to check!

Study the examples below carefully and follow them when doing assignment 2A.

Mrs. Skinner's Algebra Students

Be sure  to have your Unit 1 Quiz A in class tomorrow in your Test/Quiz section of your binder.

Algebra Adage - Hints!

A few hints for the Algebra Adage Homework!!
    Remember if its a fraction it should stay in fraction from until you have simplified the numerator and denominator to single values that can then be divide.

F:   1 - (-2) +3|4 - (5+6) +7|  --> Treat absolute value signs as parentheses -- complete operations inside the inner most parentheses first!!  
    1 - (-2) + 3|4 - 11 +7|
    1 - (-2) + 3|-7+7|
    1 - (-2) + 3|0|
     1 + 2 + 0
        3 + 0
           0

M: |-1| - (-2)-3(-4)-(-5)(-6)-(-7)  --> Identify what has to be multiplied and what is being added
    |-1| - (-2)-3(-4)-(-5)(-6)-(-7)  --> The blue values are being multiplied!!  You can also think of what is green as -1 times the number.
     1+2 +12 - 30 +7  --> Be sure to add from left to right start with the first two terms and them go from there.  Don't combine terms in the middle.

Hope these hints help!!  Enjoy your weekend!
     

Practice: Set Notation and Set Operations Answer Key (Classwork)

1a. Rule: {all real numbers between -1 and 3 inclusively}
     Set-Builder: {x: -1 < x < 3}
     Interval: [-1, 3]

1b. Rule: { all real numbers greater than 2}
      Set-Builder: { x: x > 2}
      Interval: (2, infinity)

1c. Rule {all real numbers between -2 and 0 exclusively}
     Set-Builder: {x : -2 < x < 0}
     Interval: (-2, 0)

1d.  Rule {all real numbers less than or equal to 1}
       Set-Builder: {x : x < 1}
       Interval: ( negative infinity, 1]

3b.  A' = {-1, 1, 3, 5}
       B' = {-1, 0, 1, 3, 4, 5}
    A U B = {-2, 0, 2, 4}
    A n B = {-2, 2}

3c.  B is a sub set of A since all the elements in set B are in set A.

4b. S' is all Iroquois Middle School Students who are not in Student Council
      S n E is all of the 8th graders that are in Student Council

5a. A'             5b.  (A U B)'             5c. (A n B)'           5d.   A n B n C        
5e. A n B      5f.  (A n C) U (B n C)

6a. R          6b.   { } --> null set or empty set        6c. I      6d.  N

Hope this helps!!

Set Operations

In class on Monday, you will receive a packet entitled "Set Notation and Set Operations". Here is a site with a video and notes that review the operation of complementation (finding the complement of a set):

http://www.crctlessons.com/complement-of-a-set.html

Note that this site uses the "prime" (apostrophe) notation to indicate the complement of a set, e.g., A' means "the complement of set A". There are other notations for the complement of a set, as shown in the packet. You should be familiar with all of these notations. Also, note the definition and notation for null set and empty set, which are synonyms referring to the set that contains no elements.

This video reviews the set operations of intersection and union:

http://www.youtube.com/watch?v=Hek8Y3FlAm0

Note the use of interval notation. :-)

After you've completed the practice exercises in the packet, check your answers below (sorry for the small print).

Please bring your questions to class tomorrow and be ready to practice set operations.

Mr. R

Welcome to the Iroquois Middle School Accelerated Algebra Blog

Welcome!!

Mr. Roeser and Mrs. Skinner are excited to host this blog during the 2011 - 2012 school year!  We will be posting info about the material covered in class, tips on homework assignments, and study guides for tests/quizzes.  Become a follower of the blog so that you don't miss out on any posts!