PRE ALGEBRA MMS 8th Grade Math

Pre Algebra Mms 8th Grade Math-Free PDF

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Table of Contents,Unit 1 Exponents Unit 4 Linear Functions. CC STANDARDS COVERED 8 EE 1 8 EE 3 8 EE 4 CC STANDARDS COVERED 8 F 2 8 F 4 8 EE 5. 1 1 Operations with Exponents, 1 2 Negative Exponents 4 1 Equations of Linear Functions. 1 3 Negative Exponent Operations 4 2 Graphs of Linear Functions. 1 4 Scientific Notation and Appropriate Units 4 3 Tables of Linear Functions. 1 5 Scientific Notation Operations,Unit 5 Solving Equations. Unit 2 Similar and Congruent CC STANDARDS COVERED 8 NS 1 8 EE 2 8 EE 7. CC STANDARDS COVERED 8 G 1 8 G 2 8 G 3,8 G 4 8 G 5 5 1 Solving by Combining Like Terms. 5 2 Solving with the Distributive Property, 2 1 Constructing Dilations 5 3 Solving with Variables on Both Sides.
2 2 Constructing Reflections 5 4 Infinite No Solution and Creating Equations. 2 3 Constructing Rotations 5 5 Solving Exponent Equations. 2 4 Constructing Translations,2 5 Identifying Series and Determining. Congruence or Similarity Unit 6 Systems of Equations. 2 6 The Sum of Angles in a Triangle CC STANDARDS COVERED 8 EE 8. 2 7 Similar Triangles, 2 8 Parallel Lines Cut by a Transversal 6 1 Graphing with Slope Intercept Form. 6 2 Solving Systems via Graphing,6 3 Solving Systems via Substitution. Unit 3 Functions 6 4 Solving Systems via Elimination. CC STANDARDS COVERED 8 F 1 8 F 3 8 F 4 6 5 Solving Systems via Inspection. 8 F 5 8 EE 6,3 1 Intro to Functions,3 2 Graphing Functions. 3 3 Linear and Non Linear Functions,3 4 Exploring Linear Functions.
3 5 Increasing Decreasing Max and Min,3 6 Contextualizing Function Qualities. 3 7 Sketching a Piecewise Function,Unit 7 Irrational Numbers Unit 9 Bivariate Data. CC STANDARDS COVERED 8 NS 1 8 NS 2 8 EE 2 CC STANDARDS COVERED 8 SP 1 8 SP 2 8 SP 3. 7 1 Converting Fractions and Decimals, 7 2 Identifying Irrational Numbers 9 1 Constructing Scatter Plots. 7 3 Evaluation and Approximation of Roots 9 2 Analyzing Scatter Plots. 7 4 Comparing and Ordering Irrational Numbers 9 3 The Line of Best Fit. on a Number Line 9 4 Two Way Tables,7 5 Estimating Irrational Expressions. Unit 8 Geometry Applications,CC STANDARDS COVERED 8 G 6 8 G 7 8 G 8.
8 1 Pythagorean Theorem and Converse,8 2 2D Applications. 8 3 3D Applications,8 4 The Distance Between Points. 8 5 Volume of Rounded Objects,8 6 Solving for a Missing Dimension. 8 7 Volume of Composite Shapes,How to Use the Book. The two primary purposes for this book are to be a resource for understanding and a single place for. homework assignments As a resource you should read the sections in the book that you have a hard time. understanding in class This book won t replace the instruction that you receive from your teacher but it should. supplement that instruction That means it should help you understand better if you actually read through the. examples and think about what is being said, As a place for homework assignments this book puts all the homework directly after the explanation of.
each section Since you can write in this book directly you are welcome to do your homework right in this book if. you have room to show your work You will probably end up using a separate sheet of paper to do homework on. concepts like solving equations but most units you ll have room to do the homework in this book. Included as a homework assignment are unit pre tests These pre tests should be completed at the start. of each unit so that your teacher can really zero in on what specific skills you still need help with and what skills. you already have mastered After that you should work on correcting the pre test which acts like a study guide. for the post test or end of the unit test Use the pre test to help you study. Please take care of this book as the construction is basic in nature in order to keep the costs down and. allow you to write in it This is your book and only yours It will not be passed on to students next year However. if you lose this book you may be asked to pay for a replacement Please treat this book gently and with respect. If along the way you notice any errors please let your teacher know so that the error can be corrected. for next year s students We need your help to make this book better and better Thank you in advance and. Unit 1 Exponents,1 1 Operations with Exponents,1 2 Negative Exponents. 1 3 Negative Exponent Operations,1 4 Scientific Notation and Appropriate Units. 1 5 Scientific Notation Operations,Pre Test Unit 1 Exponents. No calculator necessary Please do not use a calculator. Evaluate meaning multiply out the exponent giving your answer as a fraction when necessary. 5 pts 2 pts for only simplifying but not evaluating. 1 2 23 4 28 3 712 7 10,4 5 2 6 6 5 2, Determine if the following equations are true Justify your answer 5 pts 2 pts for answer 3 pts for justification. 7 2 7 2 3 8 83 2, Determine the appropriate exponent to make the equation true 5 pts no partial credit.
9 3 4 4 38 10, Write the following numbers in scientific notation 5 pts 2 pts for correct digits 3 pts for correct power of ten. 11 5 070 000 000 12 0 000 000 27, Write the following numbers in standard form 5 pts 2 pts for moving the decimal in the correct direction. 13 3 4 107 14 9 7 10 5, Choose the best unit of measurement for the following problems 5 pts no partial credit. 15 A plant grows approximately 3 10 4 meters per day Would this be best expressed using kilometers. meters or millimeters of growth per day, Estimate each of the following as a single digit times a power of ten Then compute each of the following giving. your answer in scientific notation 5 pts 2 pts for estimation 3 pts for scientific notation answer. 16 4 10 9 2 106 17 18 6 3 106 300 000, Answer the following questions giving both an estimated answer single digit times a power of ten and a.
precise answer scientific notation 5 pts 2 pts for estimation 3 pts for scientific notation answer. 19 A town has about 15 000 people living in it and the mayor wants to send each person 10 000 as a. celebration gift because the town won the Federal Lottery for Small Towns They d been buying tickets for years. and finally hit the jackpot How much money would the town need to give out this celebration gift. 20 A soccer ball has a volume of about 5 800 3 and a baseball 200 3 How many times bigger in volume is. a soccer ball than a baseball,1 1 Operations with Exponents. First let s start with a review of what exponents are Recall that 34 means taking four 3 s and multiplying. them together So we know that 34 3 3 3 3 81 You might also recall that in the number 34 three is. called the base and four is called the exponent Other reminds include that any number to the zero power is. equal to one so 50 1 and any number is equal to itself to the first power so 51 5. Sometimes it is easier to leave a number written as an exponent For example it is much easier to write. 5 instead of 95 367 431 640 625 Not only is sometimes simpler to write a number using exponents but many. operations are easier when the numbers are written as exponents. Multiplying Numbers with the Same Base, Let s examine the problem 34 34 and write the answer as an exponent Yes we could multiply it out as. a standard form number 81 81 6561 but let s keep it in exponential form to see if it is any easier. First let s expand the problem 34 34 3 3 3 3 3 3 3 3 Notice that the only. operation that is happening here is multiplication and that we are multiplying the same number That means we. can say the following 34 34 3 3 3 3 3 3 3 3 38 In short we see that 34 34 38 Do. you see a rule that we could generalize from this, Let s look at another example but this time with a variable. Can you find a rule that we can use when multiplying two exponent numbers with the same base Yes. we can add the exponents In other words 5 6 5 6 11 would be a quicker way to show work for this. problem Generalizing this we have the rule that, Will this work with numbers without the same base Let s find out by looking at 52 23 Many people. think that 52 23 105 but we know that 52 23 25 8 200 and that 105 100 000 So we see that. 52 23 105 is not true Therefore we know that we can only add the exponents when we have the same base. In fact if asked to simplify 42 72 we would either have to multiply it out as a regular number or else. leave it alone if we wanted it written using exponents. Dividing Numbers with the Same Base, If multiplying numbers with the same base meant that we could add the exponents what rule do you.
think we will discover when dividing numbers with the same exponent Let s find out by looking at an example. 47 4 4 4 4 4 4 4,45 4 4 4 4 4, Note that since only multiplication and division is happening five of fours in the denominator will cancel. they actually become one since four divided by four is one we just call it canceling with five of the fours in the. numerator That means we get the following,47 4 4 4 4 4 4 4 4 4. 45 4 4 4 4 4 1, Let s look at one more example using variables before generalizing a rule for dividing exponent numbers. with the same base, It looks like our rule is similar to the multiplication of exponent numbers with the same base but this time. we subtract the exponents This gives us the general rule of For now we will only deal with division. cases where the numerator exponent is larger than the denominator but think ahead to what would happen if. the denominator s exponent were larger What do you think would happen. A Power to a Power, We can also take exponents themselves to a power For example think of the problem 23 2 Following.
our order of operations we know that we have to do the parentheses first which means we get 23 2 82 64. However what if we wanted to leave our answer as a number to a power Note the following. 23 2 23 23 2 2 2 2 2 2 26, Again can you see a rule here Let s look at an example with a variable to help again. 4 3 4 4 4 12, For a power to a power when using the same base we get the rule that you can multiply the exponents. This generalizes to,Lesson 1 1, Perform the following operations leaving your answer as a number to a power Remember that the parentheses. can mean multiply as well,1 53 57 2 129 120 3 4 410 5. 6 7 54 5 8 3 6 2 9 9 11 5,Evaluate meaning multiply out the exponents.
10 32 32 11 12,13 14 53 1 50 15 14 2, Determine if the following equations are true Justify your answer. 16 122 127 126 123 17 18 5 2 2 5,19 510 2 55 5 20 21 5 5 10 0. 22 2 6 23 73 72 24 35 1, Determine the appropriate exponent to make the equation true. 25 25 2 23 23 26 27 34 3 36,28 510 2 5 5 29 30 9 98 93 5. 31 3 5 32 68 68 33 37 1,1 2 Negative Exponents, Last time we learned that when we divide exponent numbers with the same base we can subtract the.
exponents We only examined problems where the numerator had a higher exponent than the denominator but. what would happen if the denominator had the higher exponent Let s look. 55 5 5 5 5 5, Notice that three of the fives will cancel remember that they really become one because five divided. by five is one That means we are left with the following. 53 5 5 5 1 1,5 5 5 5 5 5 5 5 5, However by following our rule from last time we know that we can also subtract the exponents which. Since 5 2 and also by the transitive property we know that 5 2 We can now. 55 55 52 52, generalize this rule to say the following for any positive integer. Negative Exponent as the Reciprocal, Another helpful way to think about negative exponents is as the reciprocal Remember that the. reciprocal of an integer is one over that integer because a number times its reciprocal must equal one So 4 2. means the reciprocal of 42 which is or Notice that 42 1 proving that we have the reciprocal. One last note is that except for scientific notation we never leave negative exponents in a solution We. also take the reciprocal so that our exponent is positive Let s look at a few more examples Notice that we can. evaluate the integer powers but the variables to a power we have to leave the exponent. 1 1 1 1 1 1 1 1,3 3 2 4 10 5 13 1,33 27 24 16 105 100 000 131 13.
Lesson 1 2, Evaluate the following negative exponents giving your answer as a fraction. 1 5 3 2 2 2 3 3 2 4 7 2 5 4 3 6 10 3,7 10 2 8 1 14 9 6 2 10 2 4 11 9 1 12 5 2. 13 10 4 14 8 1 15 3 4 16 6 1 17 4 2 18 11 1, Simplify the negative exponents giving your answer as a fraction. 19 3 20 2 21 5 22 6 23 11 24 13,25 1 26 4 27 20 28 9 29 7 30 10. 1 3 Negative Exponents Operations, Now that we know negative exponents mean reciprocal we can perform operations with negative.
exponents just like we did with positive exponents Consider the following example of the multiplication rule. Notice that we still added the exponents but just need to write our answer as a fraction if we have a negative. exponent left after multiplication,53 5 5 53 5 5 2 2. 47 4 5 47 5 42 16, Now let s look at a division example Remember that we found we can subtract the exponents as long as. we have the same base,52 2 54 625,4 1 3 4 4 4, Finally we can see that the power to a power rule still works with negative exponents We simply multiply. the exponents,3 2 2 34 81,Lesson 1 3, Evaluate the following exponents operations giving your answer as a fraction where necessary. 1 53 5 4 2 129 12 7 3 4 4 10,5 6 4 5 7 23 6 22 7 8 122 12 4.
9 10 11 5 3 2 59 12 0 4 10, Determine if the following equations are true Justify your answer. 1 PRE ALGEBRA 8th Grade A Common Core State Standards Textbook By Mr Bright and Ms Hecht 2014 Any part of this document may be freely modified copied or distributed in any way as long as you claim ownership of your modifications

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