PREPARED BY: J. LLOYD HARRIS 07/17

Transcription

1 PREPARED BY: J. LLOYD HARRIS 07/17

2 Table of Contents Introduction Page 1 Section 1.2 Pages 2-11 Section 1.3 Pages Section 1.4 Pages Section 1.5 Pages Section 1.6 Pages Section 1.7 Pages Section 1.8 Pages Section 2.1 Pages Section 2.2 Pages Section 2.3 Pages Section 2.4 Pages Section 2.5 Pages Section 2.6 Pages Section 2.8 Pages Section 9.1 Pages Section 3.1 Pages Section 3.2 Pages Section 3.3 Pages Section 3.4 Pages Section 5.1 Pages Section 5.2 Pages Section 5.3 Pages Section 5.4 Pages Section 5.5 Pages Section 5.6 Pages Section 10.1 Pages

3 INTRODUCTION The videos that go along with this study guide were recorded in an actual MAT 0012, Developmental Arithmetic with Algebra class during the summer of If you have any questions or comments about the videos or this study guide, please contact Mr. Lloyd Harris at (850) ext or by at ROAD TO SUCCESS Since this course is an E-Learning course, the method of instruction is primarily a selfstudy one. You are expected to demonstrate sufficient self-discipline and self-motivation to complete all unit tests and the final exam within the designated time. To be successful, you should follow these steps: 1. Begin the lesson by looking at the objectives listed here in the study guide. The study guide follows the section numbers of the textbook. 2. Watch the video for the section you are studying. While watching the video, follow the study guide, answer the questions in the study guide, work the problems provided in the study guide, and take notes as if you were sitting in a classroom. Stop or pause the video as needed to catch up or copy something down. 3. Once you have viewed the video, look at the study guide and the textbook for further examples, steps or procedures, etc. 4. Try the homework. The answers to the odd numbered problems are in the back of the textbook. Some homework problems are explained on the videos for each section. The number of homework problems explained varies for each section. Homework is abbreviated H.W. on the videos. 5. Complete the homework, quizzes and reviews in MyMathLab for each test. 6. HOW TO STUDY FOR TESTS!!! The best way to study for a test is to take your objectives for each section and find corresponding problems from the homework. Take these problems and make yourself a practice test. Without looking at your notes, take the practice test. This will tell you where you are weak and need to study further. Do the review for the test in MyMathLab. 7. The Math Lab on campus provides free tutoring. 1

4 SECTION 1.2 Symbols and Sets of Numbers I. OBJECTIVES At the conclusion of this lesson you should be able to: 1. Translate sentences into mathematical statements. 2. Identify integers, rational numbers, irrational numbers, and real numbers. 3. Find the absolute value of a real number. II. PROCEDURE While watching the video, follow this study guide and take notes in the study guide as if you were sitting in a classroom. Stop or pause the video as needed to catch up or copy something down. Natural Numbers Whole Numbers Integers {..., 3, 2, 1,0,1,2,3,...} Rational Numbers 2

5 Irrational Numbers Real Numbers

6 RATIONAL NUMBERS IRRATIONAL NUMBERS REAL NUMBERS 4

7 1 2 8, 5, 2,, 0, 3, 4.3, a. Natural Numbers b. Whole Numbers c. Integers d. Rational Numbers e. Irrational Numbers f. Real Numbers 5

8 1 5.3, 5, 3, 1,, 0, 1.2, 4, 12 9 a. Natural Numbers b. Whole Numbers c. Integers d. Rational Numbers e. Irrational Numbers f. Real Numbers 6

9 True or False Every rational number is an integer. Every natural number is positive. Every rational number is also a real number. Every real number is also a rational number. A number can be both rational and irrational. 7

10 a = b a b a < b a > b a b a b

11 Write each sentence as a mathematical statement. Fifteen is greater than five. Five is greater than or equal to four. Fourteen is not equal to twelve. Absolute Value a 9

12 2 = = = 5 = 4 = 4 = 2 = 3 0 = 2.1 = 10

13 Insert <, >, or = to make a true statement

14 SECTION 1.3 Fractions and Mixed Numbers I. OBJECTIVES At the conclusion of this lesson you should be able to: 1. Write the prime factorization of a number. 2. Write equivalent fractions. 3. Write fractions in simplest forms. 4. Multiply and divide fractions. 5. Add and subtract fractions. 6. Perform operations on mixed numbers. II. PROCEDURE While watching the video, follow this study guide and take notes in the study guide as if you were sitting in a classroom. Stop or pause the video as needed to catch up or copy something down. Prime Number Composite Number Prime Factorization

15 Divisible by: IF: 2 The number ends in an even number ( 0, 2, 4, 6, 8) 3 The sum of the digits is divisible by 3. 4 The last two digits are divisible by 4. 5 The number ends in 0 or 5. 6 The number is divisible by both 2 and 3. Divisible by Divisible by

16 Divisible by Divisible by Divisible by

17 Fraction aa bb

18 aa 0 0 aa 16

19 Writing a Fraction in Lowest Terms (Reducing a Fraction)

20

21 Equivalent Fractions 19

22 Write 2 3 with a denominator of 36. Write 3 8 with a denominator of 48. Write 3 with a denominator of

23 Proper Fraction: Improper Fraction: Mixed Number: 21

24 Convert a Mixed Number to an Improper Fraction Convert an Improper Fraction to a Mixed Number

25 Adding and Subtracting Fractions Least Common Denominator (LCD)

26

27

28 Multiplication of Fractions a b c d = ac bd

29 Division of Fractions a b c d = a b d c = ad bc reciprocal reciprocal

30 Use subtraction to determine the unknown part of the circle.?

31 NOT ON THE VIDEO! Example 1 Add: The LCM/LCD of 12 and 4 and is 12. Get equivalent fractions with the common denominator of 12: = + = =. So, + = Add the numerators: = Reduce the result: Example 2 Subtract: The LCM/LCD of 8 and 12 is 24. Get equivalent fractions with the common denominator of 24: = + = + = = This fraction is already in lowest terms so: +. Example 3 Multiply: 3 1 Result: = = = 1 32 Example 4 Multiply: 5 4 Result: = 8 15 = = 1 6 Example 5 Divide: 5 3 Result: = = = 5 6 Example 6 Divide: 4 8 Result: = = =

32 SECTION 1.4 Exponents, Order of Operations, Variable Expressions and Equations I. OBJECTIVES At the conclusion of this lesson you should be able to: 1. Define and use exponents and the order of operations. 2. Evaluate algebraic expressions, given replacement values for variables. 3. Determine whether a number is a solution of a given equation. 4. Translate phrases into expressions and sentences into equations. II. PROCEDURE While watching the video, follow this study guide and take notes in the study guide as if you were sitting in a classroom. Stop or pause the video as needed to catch up or copy something down (1.2) 2 30

33 Order of Operations [66 + (55 22)] 31

34 (7 5) 22 (8 + 3) 32

35 (8 4) 6 33

36

37 6(5 + 1) 9(1 + 1) 5(8 4)

38 Algebraic Expression Evaluate an Algebraic Expression Evaluate: 2xx + 3yy 4 when xx = 4 and yy = 2 Evaluate: xxxx zz when xx = 4, yy = 8 and z= 16 36

39 Evaluate: 6xx 2 + yy 2 when xx = 2 and yy = 3 Evaluate: yy2 +xx xx 2 +3yy when xx = 12 and yy = 8 37

40 Expression: Equation: Is 6 a solution of = 3333? Is 10 a solution of xx + 66 = xx + 66? Is 6 a solution of = 88? 38

41 Converting/Translating Word Statements to Symbols Addition plus added to more than increased by sum total 39

42 Subtraction minus less less than difference decreased by subtracted from 40

43 Multiplication times multiply product twice Division divided by quotient ratio 41

44 is Write each phrase as an algebraic expression. Let x represent the unknown number. A number increased by 9. Five decreased by a number. Twice a number, decreased by 72. The ratio of a number and 4. Three times a number, increased by

45 SECTION 1.5 Adding Real Numbers I. OBJECTIVES At the conclusion of this lesson you should be able to: 1. Add real numbers. 2. Find the opposite of a number. 3. Evaluate algebraic expressions using real numbers. 4. Solve applications that involve addition of real numbers. II. PROCEDURE While watching the video, follow this study guide and take notes in the study guide as if you were sitting in a classroom. Stop or pause the video as needed to catch up or copy something down. Opposites or Additive Inverses The opposite of 1 is. The opposite of -1 is. The additive inverse of 2 is. The additive inverse of -2 is. 43

46 22 ( 22) Evaluate the following. (33) ( 33) If aa is a number, then ( aa) = aa. The sum of a number aa and its opposite aa is zero. aa + ( aa)=0 44

47 Adding Real numbers

48 Adding Real Numbers Like Signs Unlike signs ( 33) ( 1111)

49 ( )

50 ( 1111) 99 + ( 1111) ( 66) 48

51 On January 5 th the temperature was 6 at 6:30 a.m. The temperature increased by 41 over the next 5 hours. What was the temperature at 11:30 a.m.? The lowest elevation in the United States is 279 feet at Badwater Basin in Death Valley. If you are standing at a point 439 feet above Badwater Basin in Death Valley, what is your elevation? 49

52 NOT ON THE VIDEO! Example 1 Add: ( 4) + ( 9) The signs of the addends are the same. Add the absolute values of the numbers. 4 = 4, 9 = 9, = 13 The sum is negative.) ( 4) + ( 9) = 13 Example 2 Add: 6 + ( 13). Attach the sign of the addends. (Both addends are negative. The signs of the addends are different. Find the absolute values of the numbers: 6 = 6, 13 = 13 Subtract the smaller absolute value from the larger absolute: 13 6 = 7. Attach the sign of the number with the larger absolute value. Since 13 > 6, attach the negative sign: 6 + ( 13) = 7 50

53 SECTION 1.6 Subtracting Real Numbers I. OBJECTIVES At the conclusion of this lesson you should be able to: 1. Subtract real numbers. 2. Add and subtract real numbers. 3. Evaluate algebraic expressions using real numbers. 4. Solve applications that involve subtraction of real numbers. II. PROCEDURE While watching the video, follow this study guide and take notes in the study guide as if you were sitting in a classroom. Stop or pause the video as needed to catch up or copy something down. Addition of Real Numbers Subtraction of Real Numbers 51

54 77 ( 33) ( 1111)

55

56 66 88 ( 1111) (55 11) 54

57 ( 66 55)

58 ( 1111)

59 Translate each phrase to an expression and simplify. Subtract -2 from 3. Subtract 9 from

60 Evaluate 9 xx yy+6 when xx = 5 and yy = 4. Evaluate xx ( 10) 2tt yy = 10. when xx = 5 and 58

61 SECTION 1.7 Multiplying and Dividing Real Numbers I. OBJECTIVES At the conclusion of this lesson you should be able to: 1. Multiply real numbers. 2. Find the reciprocal of a real number. 3. Divide real numbers. 4. Evaluate expressions using real numbers. 5. Determine whether a number is a solution of a given equation. 6. Solve applications that involve multiplication or division of real numbers. II. PROCEDURE While watching the video, follow this study guide and take notes in the study guide as if you were sitting in a classroom. Stop or pause the video as needed to catch up or copy something down. Multiplication Property of Zero 33(22) = 22(22) = 11(22) = 00(22) = 11(22) = 22(22) = 33(22) = a 0 = 0 a = 0 59

62 33( 22) = 22( 22) = 11( 22) = 00( 22) = 11( 22) = 22( 22) = 33( 22) = Multiplying Real/Signed Numbers pppppppppppppppp pppppppppppppppp = pppppppppppppppp nnnnnnnnnnnnnnnn = nnnnnnnnnnnnnnnn pppppppppppppppp = nnnnnnnnnnnnnnnn nnnnnnnnnnnnnnnn = 60

63 2( 8) 6(2) 4( 5) ( 2)( 3) ( 2)( 3)( 4) ( 2)( 3)( 4)( 1) When multiplying signed numbers we can count the number of negatives. Even Number of Negatives = Odd Number of Negatives = 61

64 ( 3) ( 2) ( 2) (nnnnnnnnnnnnnnnn) eeeeeeee = (nnnnnnnnnnnnnnnn) oooooo = 62

65 ( 4) ( 3) Dividing Real/Signed Numbers pppppppppppppppp pppppppppppppppp = pppppppppppppppp nnnnnnnnnnnnnnnn = nnnnnnnnnnnnnnnn pppppppppppppppp = nnnnnnnnnnnnnnnn nnnnnnnnnnnnnnnn = ( 4) 63

66

67

68 6 2( 3) 4 3( 2) 66

69 Evaluate 2xx 2 yy 2 when xx = 5 and yy = 3. 67

70 Evaluate 2xx 5 when xx = 5 and yy = 3. yy 2 68

71 Is 4 as solution of 2xx + 4 = xx + 8? Translate the phrase into an expression. Use x to represent a number. The difference of a number and

72 NOT ON THE VIDEO! Example 1 Multiply: ( 6)( 4) Find the product of their absolute values: 6 = 6, 4 = 4, 6 4 = 24. Since both numbers have the same sign, the product is positive: ( 6 )( 4) = 24. Example 2 Multiply: ( 6)( 4) Find the product of their absolute values: 6 = 6, 4 = 4, 6 4 = 24. Since the numbers have opposite signs, the product is negative: ( 6)( 4) = 24. Example 3 Multiply: ( 6)( 4)( 2) Find the product of their absolute values: 6 = 6, 4 = 4, 2 = 2, = 48. Since we are multiplying three negatives (odd number of negatives) the result is negative: =. ( )( )( ) 48 Example 4 Divide: ( 16) ( 4) 16 = 16, 4 = 4,16 4 = Find the division of their absolute values: 4. Since both numbers have the same sign, the division is positive: ( 16 ) ( 4) = 4. Example 5 Divide: ( 24 ) 4 Find the division of their absolute values: 24 = 24, 4 = 4, 24 4 = 6. Since the numbers have opposite signs, the division is negative: ( 24) 4 = Example 6 Divide: = = = 3 10 Result: 70

73 SECTION 1.8 Properties of Real Numbers I. OBJECTIVES At the conclusion of this lesson you should be able to: 1. Use the commutative properties. 2. Use the associative properties. 3. Use the identity properties. 4. Use the inverse properties. 5. Use the distributive property. II. PROCEDURE While watching the video, follow this study guide and take notes in the study guide as if you were sitting in a classroom. Stop or pause the video as needed to catch up or copy something down. Commutative Properties Commutative Property of Addition Commutative Property of Multiplication Associative Properties Associative Property of Addition Associative Property of Multiplication 71

74 Identity Properties Identity Property of Addition Identity Property of Multiplication Inverse Properties Additive Inverse/Inverse Property of Addition Multiplicative Inverse/Inverse Property of Multiplication 72

75 Use a commutative property to complete each statement yy = 2 xx = Use an associative property to complete each statement. 3 (xx yy) = (yy + 4) + zz = Use the commutative and associative properties to simplify each expression. 2(42xx) (rr + 3) rr 73

76 Distributive Property 7(aa + bb) 3(zz yy) 1 5 (15aa 30bb) 5(xx + 4mm + 2) (2xx 3yy) (3aa + 4bb) 74

77 Use the distributive property to rewrite each expression without parentheses. Then simplify the result. 2(2xx 3) 8 2(4xx + 5) + 7 3(2xx + 6) (4xx 5) 32 75

78 3(2xx 5) 21 2( 4xx 7) 11 1 (8xx + 6) 1 (9xx 12)

79 Use the distributive property to rewrite each sum as a product. 9aa + 9bb ( 3)aa + ( 3)bb 11xx + 11yy yy 77

80 SECTION 2.1 Simplifying Algebraic Expressions I. OBJECTIVES At the conclusion of this lesson you should be able to: 1. Identify terms, like terms, and unlike terms. 2. Combine like terms. 3. Simplifying expressions containing parentheses. 4. Write word phrases as algebraic expressions. II. PROCEDURE While watching the video, follow this study guide and take notes in the study guide as if you were sitting in a classroom. Stop or pause the video as needed to catch up or copy something down. Variable Coefficient Constant 3xx

81 3 x + 4y + 6 Variables: Coefficients: Constant: Like Terms 3xx xx + 5 3xx 2 4xx xx 10 79

82 Combining Like Terms (Simplify) 3xx xx + 5 8xx + 4yy 3xx 12yy 3xx 2 4xx + 6xx 5xx 2 80

83 18 + 3(xx + 4) 18 3(xx + 4) 8 (xx + 4) 6 2(3aa + 4) 81

84 7 5 ( aa 15)

85 1 5 ( 9yy + 2) ( 2yy 1) 83

86 4(2xx 5) 4(3xx + 2) 7(2xx + 5) 4(xx + 2) 20xx 84

87 Write each of the following as an algebraic expression. Simplify if possible. Subtract 5mm 6 from mm 9 Add 3yy 5 to yy

88 Write each phrase as an algebraic expression and simplify if possible. Let x represent the unknown number. Eight more than triple a number. The sum of 3 times a number and 10, subtracted from 9 times the number. Double a number, minus the sum of the number and ten. 86

89 87 NOT ON THE VIDEO ( ) x x ( ) ( ) x x x x x x x x x

90 SECTION 2.2 The Addition and Multiplication Properties of Equality I. OBJECTIVES At the conclusion of this lesson you should be able to: 1. Use the addition property of equality to solve linear equations. 2. Use the multiplication property of equality to solve linear equations. 3. Use both the addition and multiplication properties of equality to solve linear equations. 4. Write word phrases as algebraic expressions. II. PROCEDURE While watching the video, follow this study guide and take notes in the study guide as if you were sitting in a classroom. Stop or pause the video as needed to catch up or copy something down. Linear Equation in One Variable Goal For Solving a Linear Equation in one Variable Addition Property of Equality 88

91 xx + 8 = 3 xx + 8 = 3 xx 8.4 = 3.2 xx 8.4 =

92 9xx = 8xx + 6 9xx = 8xx + 6 xx = aa means xx = aa 4(zz 3) = 2 3zz 90

93 (8rr 3) (7rr + 1) = 6 91

94 Multiplication Property of Equality Goal For Solving a Linear Equation in one Variable 4xx = 12 4xx = 12 92

95 2 3 xx = xx = 8 93

96 3 5 xx = xx = 18 xx 3 = 4 2xx 7 = 6 94

97 3xx 7xx = 8 2xx = 7 2 bb 4 5 = 2 6xx + 10 = 8 95

98 Solving Linear Equations 1. Simplify. Remove Parentheses, Brackets, Fractions, and combine like terms. 2. Get variables together on one side of the equal sign. To do this we have to add or subtract. 3. Get constants together on the opposite side of the equal sign of your variable. To do this we have to add or subtract. 4. Get a positive one coefficient on your variable. To do this we have to multiply or divide. 5. CHECK. 96

99 20 = 3(2xx + 1) + 7xx 97

100 3 = 5(4xx + 3) + 21xx 98

101 NOT ON THE VIDEO! Example 1: Solve + 4 = 11 k for k. k k + 4 = = 11 4 k = We need the k by itself. 2. Subtract 4 from both sides of the equation. 3. Since k has an understood positive one coefficient, we know that k=-15. Example 2: Solve a + 3 = 5 for a. Check your solution: a + 3 = 5 a = 5 3 a = 2 a + 3 = = 5 5 = 5 Example 3: Solve 5 x 2 = for x. Check your solution: x 2 = 5 x = x = 3 x 2 = = 5 5 = 5 Example 4: Solve 2 x = 18 for x. 2x = 18 2x 18 = 2 2 x = 9 1. We need a positive one coefficient on x. 2. Divide both sides by = Example 5: Solve 12 x for x. Check your solution: 3x = 12 3x 12 = 3 3 x = 4 3 3x = 12 ( 4) = = 12 99

102 1 2 Example 6: Solve 5 p = for p. Check your solution: 1 p = p = 2 2 p = 10 ( 5) ( 10) p = 5 = 5 5 = = 2 b for b. Example 7: Solve 7 5b 5b = = b = b + 2 = b = = b = 2 ( 5b) 1. We need to get the variable by itself and the constants together on the opposite side. 2. Add one-half to both sides. 3. Get a common denominator on the righthand side. 4. Simplify on the right-hand side of the equation. 5. We need a positive one coefficient on our variable. 6. Multiply both sides of the equation by the reciprocal of five which is one-fifth. 7. Simplify. 100

103 2 3 1 = 6 Example 8: Solve 3 b for b. Check your solution: b = b + = b = b = b = b = b = b = = = = = 3 Example 9: Solve = 1.3x x for x. 2.3x = 1.5x x 1.5x = 1.5x 1.5x x = x = x = x 16.6 = x = We need to get our x s together on one side of the equation. 2. Since 2.3 is larger than 1.5, subtract 1.5x from both sides of the equation. 3. With our variables together on one side of the equation, we need to get our constants together on the other side of the equation. 4. Subtract 13.7 from both sides of the equation. 5. We need a positive one coefficient on our x. 6. Divide both sides of the equation

104 SECTION 2.3 Solving Linear Equations I. OBJECTIVES At the conclusion of this lesson you should be able to: 1. Apply a general strategy for solving a linear equation. 2. Solve equations containing fractions and decimals. 3. Recognize identities and equations with no solution. II. PROCEDURE While watching the video, follow this study guide and take notes in the study guide as if you were sitting in a classroom. Stop or pause the video as needed to catch up or copy something down. Solving Linear Equations 1. Simplify. Remove Parentheses, Brackets, Fractions, and combine like terms. 2. Get variables together on one side of the equal sign. To do this we have to add or subtract. 3. Get constants together on the opposite side of the equal sign of your variable. To do this we have to add or subtract. 4. Get a positive one coefficient on your variable. To do this we have to multiply or divide. 5. CHECK. 102

105 5(2mm + 3) 4mm = 8mm

106 6(2xx + 8) = 4(3xx 6) 104

107 3 5 tt 1 10 tt = tt

108 3(yy + 3) 5 = 2yy

109 5(xx 1) 4 = 3 (xx + 1) 2 107

110 xx 5 7 = xx

111 0.01(5xx + 4) = (xx + 4) 109

112 0.2xx 0.1 = 0.6xx

113 4(2 + xx) + 1 = 7xx 3(xx 2) 111

114 5(4yy 3) + 2 = 20yy

115 NOT ON THE VIDEO! Example 1: Solve = 1.3x x for x. 2.3x = 1.5x x 1.5x = 1.5x 1.5x x = x = x = x 16.6 = x = We need to get our x s together on one side of the equation. 2. Since 2.3 is larger than 1.5, subtract 1.5x from both sides of the equation. 3. With our variables together on one side of the equation, we need to get our constants together on the other side of the equation. 4. Subtract 13.7 from both sides of the equation. 5. We need a positive one coefficient on our x. 6. Divide both sides of the equation Example 2: Solve ( 4x 8) = ( x + 12) x 4 = x x 4 3 = 4 x Answer: ( 4x ) ( 8) = ( x) + ( 12) ( ) ( 2x ) 4( 4) = 4 x 4( 9) 8 x 16 = 3x x 3x 16 = 3x 3x x 16 = 36 5 x = x = x = 5 113

116 Example 3: Solve 2 ( ) = 3( x + 1) x for x. ( 5 + 3x) = 3( x + 1) x = 3x x = 3x x + 10 = 3x x 3x + 10 = 3x 3x x + 10 = 16 3x = x = 6 3x = 3 x = Apply the Distribute Property. 2. Simplify on the right-hand side. 3. Since 6 is larger than 3, we want to get our variables together on the lefthand side. 4. Subtract 3x from both sides. 5. Get your constants together on the left-hand side by subtracting 10 from both sides. 6. We need a positive one coefficient on x. Divide both sides by

117 SECTION 2.4 An Introduction to Problem Solving I. OBJECTIVES At the conclusion of this lesson you should be able to: 1. Solve problems involving direct translations. 2. Solve problems involving consecutive integers. II. PROCEDURE While watching the video, follow this study guide and take notes in the study guide as if you were sitting in a classroom. Stop or pause the video as needed to catch up or copy something down. Write each of the following as an equation. Then solve. The sum of 4 times a number and -2 is equal to the sum of 5 times the number and -2. Find the number. 115

118 Write each of the following as an equation. Then solve. Five times the sum of a number and -1 is the same as 6 times the number. Find the number. 116

119 Write each of the following as an equation. Then solve. If the difference of a number and four is doubled, the result is ¼ less than the number. Find the number. 117

120 A 25 inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece and the third piece is one inch more than five times the length of the first piece. Find the lengths of the pieces. 118

121 Consecutive Integers, -2, -1, 0,1, 2, 3,... = 1 st Consecutive Integer = 2 nd Consecutive Integer = 3 rd Consecutive Integer = 4 th Consecutive Integer The left and right page numbers of an open book are two consecutive integers whose sum is 447. Find the page numbers. 119

122 Consecutive Even Integers,-4,-2,0, 2,4,... = 1 st Consecutive Even Integer = 2 nd Consecutive Even Integer = 3 rd Consecutive Even Integer = 4 th Consecutive Even Integer The room numbers of two adjacent classrooms are two consecutive even numbers. If their sum is 370, find the classroom numbers. 120

123 Consecutive Odd Integers,-3,-1,1,3,... = 1 st Consecutive Odd Integer = 2 nd Consecutive Odd Integer = 3 rd Consecutive Odd Integer = 4 th Consecutive Odd Integer The room numbers of two adjacent classrooms are two consecutive odd numbers. If their sum is 424, find the classroom numbers. 121

124 NOT ON THE VIDEO! Example 1: Three less than seven times a certain number is 27 more than twice the number. Find the number. Let x represent the number. Three less than seven times a certain number is represented by 7x more than twice the number is represented by 2x Then, 7x 3 = 2x x = 30 x = 6 The number is 6. Example 2: Sixteen less than nine times a number is four times the sum of the number and six. Find the number. Let x represent the number. Sixteen less than nine times a number is represented by 9x 16. Four times the sum of the number and six is represented by 4(x + 6). Therefore, 9x 16 = 4(x + 6) 9x 16 = 4x x = 40 x = 8 The number is

125 SECTION 2.5 Formulas and Problem Solving I. OBJECTIVES At the conclusion of this lesson you should be able to: 1. Solve a formula for one variable given the value of the other variables. 2. Use a formula to solve an applied problem. 3. Solve a formula for a specified variable. II. PROCEDURE While watching the video, follow this study guide and take notes in the study guide as if you were sitting in a classroom. Stop or pause the video as needed to catch up or copy something down. Substitute the given values into each given formula and solve for the unknown variable. If necessary, round to one decimal place. Distance Formula dd = rrrr; d=420 miles, t=7 hours. 123

126 Substitute the given values into each given formula and solve for the unknown variable. If necessary, round to one decimal place. Area of a Trapezoid AA = 1 2 h (BB + bb); AA = 60, BB = 7, CC = 3 124

127 Substitute the given values into each given formula and solve for the unknown variable. If necessary, round to one decimal place. Circumference of a Circle CC = 2ππππ; CC = 62, ππ = 3.14 Area of a Circle AA = ππrr 2 ; rr = 3.8, ππ =

128 Substitute the given values into each given formula and solve for the unknown variable. If necessary, round to one decimal place. Simple Interest Formula II = PPPPPP; II = 2400, PP = 12000, RR =

129 Solve each formula for the specified variable. yy = mmmm + bb ffffff bb yy = mmmm + bb ffffff xx 127

130 Solve each formula for the specified variable. 3xx + yy = 4 ffffff yy AA = 1 bbh ffffff bb 2 128

131 Solve each formula for the specified variable. AA = PP + PPPPPP ffffff TT PP = aa + bb + cc ffffff bb 129

132 Solve each formula for the specified variable. SS = 4llll + 2wwh ffffff h Percent 130

133 Write each decimal as a percent

134 Write each percent as a decimal. 76% 119% 2% 0.7% 500% 132

135 NOT ON THE VIDEO! Example1: Solve y = mx + b for m. y = mx + b y b = mx + b b y b = mx y b mx = x x y b = m x We are asked to solve for m. We need to get m by itself on one side of the equation and everything else on the other side. 1. Subtract b from both sides of the equation. This will isolate the mx term. 2. We need a positive one coefficient on m. 3. Divide both sides by x. Example 2: Solve P 2 l + 2w P 2l 2 P 2l 2 = for w. P = 2l + 2w P 2l = 2l 2l + 2w P 2l = 2w 2w = 2 = w 133

136 Given the formula: 1 A bh 2 =, find b when A = 56 and h=8. 1 A = bh = b 2 56 = 4b 56 4b = 4 b 14 = b ( 8) Given the formula: P 2 l + 2w =, find l when P = 66 and w=8. P = 2l + 2w 66 = 2l = 2l = 2l 50 2l = = l 16 ( 8) 1. Substitute your values for P and w and simplify. 2. We now have a linear equation that we need to solve for l. 3. Subtract 16 from both sides. 4. Get a positive one coefficient on l by dividing both sides by

137 SECTION 2.6 Percent and Mixture Problem Solving I. OBJECTIVES At the conclusion of this lesson you should be able to: 1. Solve percent equations. 2. Solve discounts and mark-up problems. II. PROCEDURE While watching the video, follow this study guide and take notes in the study guide as if you were sitting in a classroom. Stop or pause the video as needed to catch up or copy something down. General Strategy for Problem Solving 1. UNDERSTAND the problem. During this step, become comfortable with the problem. Some ways of doing this are as follows: Read and reread the problem. Choose a variable to represent the unknown. Construct a drawing whenever possible. 2. TRANSLATE the problem into an equation. 3. SOLVE the equation. 4. INTERPRET the results: Check the proposed solution in the stated problem and state your conclusion. 135

138 Recall is means equal and of means times. Solve. If needed, round to one decimal place is what percent of 436? 136

139 Solve. If needed, round to one decimal place. 126 is 35% of what number? Find 40% of

140 Solve. If needed, round to one decimal place. 45% of what number is 270? The number 85 is what percent of 125? 138

141 Solve. If needed, round to one decimal place. Find 128% of 75. The number 38 is what percent of 24? 139

142 Discount dddddddddddddddd = pppppppppppppp oooooooooooooooo pppppppppp nnnnnn pppppppppp = oooooooooooooooo pppppppppp dddddddddddddddd Solve. Find the original price of a pair of shoes if the sale price is $68 after a 15% discount. 140

143 Solve. Find the original price of a dress if the sale price is $ after a 35% discount. 141

144 Mark-up mmmmmmmm-uuuu = pppppppppppppp oooooooooooooooo pppppppppp nnnnnn pppppppppp = oooooooooooooooo pppppppppp + mmmmmmmm-uuuu Solve. Find the original price of a pair pants if the increased price is $80 after a 25% increase. 142

145 Solve. Find last year s salary if, after a 5% pay raise, this year s salary is $68,

146 Solve. Find last year s salary if, after a 4% pay raise, this year s salary is $47,

147 NOT ON THE VIDEO! Example 1: A set of golf clubs costs $266 after a 30% discount. Find the original cost. Let x represent the original cost. The amount of the discount is 0.30x. (original cost) - (discount) = (sale price) Therefore, (x) (.30x) = x = x = = The original cost is $380. Example 2: Mary wrote a check for $88.20 for a new dress. The tax rate was 5%. Find the price of the dress. Let x represent the price of the dress. The amount of the tax is represented by.05x. (price of dress) + (amount of tax) = (amount written on check) Therefore, x +.05x = x = x = = The price of the dress is $84. Example 3: There are 32 candies in a bag. 12 of the candies are red. What percent are red? Understand 12 is what percent of 32? Translate 12 = P * 32 Solve 12/32 = P = P 37.5 % = P Interpret 37.5 % of the candies are red. Example 4: 80% of the concert tickets were sold. There were 700 concert tickets in all. How many tickets were sold? Understand: A is 80% of 700. Translate: A = Solve: A = 560 Interpret: 560 concert tickets were sold. 145

148 Example 5: There are 26 letters in our alphabet. 20 of the letters are consonants. What percent of the letters are vowels? Understand the problem: 6 is what percent of 26? (Notice, we are using the number of vowels (6) rather than the number of consonants given.) Translate: 6 = P * 26 Solve: 6/26 = P = P 23% = P Interpret: 23% of the letters are vowels. 146

149 SECTION 2.8 Solving Linear Inequalities I. OBJECTIVES At the conclusion of this lesson you should be able to: 1. Define linear inequality in one variable, graph solution sets on a number line, and use interval notation. 2. Solve linear inequalities. II. PROCEDURE While watching the video, follow this study guide and take notes in the study guide as if you were sitting in a classroom. Stop or pause the video as needed to catch up or copy something down. Inequalities < llllllll tthaaaa > ggggggaaaaaaaa tthaaaa llllllll tthaaaa oooo eeeeeeeeee tttt gggggggggggggg tthaaaa oooo eeeeeeeeee tttt Graphing Inequalities If there is an equal to such as or use brackets. If there is no equal to such as < or > use parentheses. 147

150 xx < xx

151 xx > xx

152 Graph each set of numbers given in interval notation. Then write an inequality statement in x describing the numbers graphed. (, 3] (, 4) 150

153 Graph each inequality on a number line. Then write the solutions in interval notation. xx > 2 3 xx 4 151

154 Multiplication Property of Inequality 1. If a, b, and c are real numbers, and c is positive, then aa < bb, aaaa < bbbb and aa < bb cc cc inequalities. 2. If a, b, and c are real numbers, and c is are equivalent negative, then aa < bb, aaaa > bbbb and aa cc > bb cc are equivalent inequalities. STEPS for Solving a Linear Inequality 1. Simplify on each side of the inequality sign. 2. Get the variables together on the left-hand side of the inequality sign. 3. Get the constants together on the right-hand side of the inequality sign. 4. Get a positive one coefficient on your variable. If you multiplied or divided by a negative, switch the inequality sign. 5. Graph. 6. Write the solution in interval notation. 152

155 Solve each inequality. Graph the solution set and write it in interval notation. 4xx 8 4xx 8 153

156 Solve each inequality. Graph the solution set and write it in interval notation. 4xx xx 9 154

157 Solve each inequality. Graph the solution set and write it in interval notation. xx + 4 > 2 3xx 5 < 2xx 8 155

158 Solve each inequality. Graph the solution set and write it in interval notation. 6xx + 2 > 2(5 xx) 156

159 Solve each inequality. Graph the solution set and write it in interval notation. 4(2xx + 1) < 4 157

160 Solve each inequality. Graph the solution set and write it in interval notation. 4(3xx 1) 5(2xx 4) 158

161 Solve each inequality. Graph the solution set and write it in interval notation. 7 9 ( xx 4) < 4 3 ( xx + 5) 159

162 Solve each inequality. Graph the solution set and write it in interval notation. 1 4 ( xx + 4) 1 5 ( 2xx + 3) 160

163 Solve each inequality. Graph the solution set and write it in interval notation. 3(xx + 2) 6 < 2(xx 3)

164 Solve each inequality. Graph the solution set and write it in interval notation. 2(xx 4) 3xx < (xx + 4) + 2xx 162

165 SECTION 9.1 Compound Inequalities I. OBJECTIVES At the conclusion of this lesson you should be able to: 1. Find the intersection and union of sets. 2. Graph the intersection and union of sets. 3. Solve a compound inequality. II. PROCEDURE SETS While watching the video, follow this study guide and take notes in the study guide as if you were sitting in a classroom. Stop or pause the video as needed to catch up or copy something down. Braces { } Intersection Union 163

166 If AA = { 2,0,2,4} and BB = {0,1,2,3,4,5}, list the elements of each set. AA BB AA BB If AA = { 1,1,3,5}, BB = { 2,0,2,4} and CC = { 1,0,1}, list the elements of each set. AA BB AA CC BB CC 164

167 If AA = {xx xx iiii aaaa eeeeeeee nnnnnnnnnnnn}, BB = {xx xx iiii aaaa oooooo nnnnnnnnnnnn}, CC = {2,3,4,5}, and DD = {4,5,6,7}, list the elements of each set. AA BB AA BB BB DD BB CC CC DD AA DD 165

168 Compound Inequalities and means intersection, or means union, xx < 4 aaaaaa xx > 1 1 < xx < 4 xx < 3 oooo xx > 4 166

169 Solve each compound inequality. Graph the solution set and write it in interval notation. xx < 1 aaaaaa xx 2 xx < 4 aaaaaa xx < 1 167

170 Solve each compound inequality. Graph the solution set and write it in interval notation. xx aaaaaa 2xx 4 xx < 3 oooo xx > 4 168

171 Solve each compound inequality. Graph the solution set and write it in interval notation. 5xx 10 oooo 3xx 5 1 2xx < 6 oooo xx 5 > 6 169

172 Solve each compound inequality. Write the solution in interval notation. 5 < xx 6 <

173 Solve each compound inequality. Write the solution in interval notation. 2 3xx

174 Solve each compound inequality. Write the solution in interval notation. 5 3xx

175 Solve each compound inequality. Write the solution in interval notation. 3(xx 1) < 12 oooo xx + 7 >

176 Solve each compound inequality. Write the solution in interval notation. 3 xx oooo 2xx <

177 Solve each compound inequality. Write the solution in interval notation. xx aaaaaa xx

178 Solve each compound inequality. Write the solution in interval notation. 6 < 3(xx 2) 8 176

179 Solve each compound inequality. Write the solution in interval notation. 2 3 < xx < 4 177

180 Solve each compound inequality. Write the solution in interval notation. 3xx oooo 7xx >

181 NOT ON THE VIDEO! 6 x 12 > 1 4 ( 6 x ) 12( 1) 4 > 24 4x > 12 4x > x > 12 4x 12 > 4 4 x < 3 or 6 x 12 < 1 6 ( 6 x ) < 12( 1) x < 12 6x < x < 48 6x 48 < 6 6 x > 8 Graph: ) ( 3 8 Interval Notation: (, 3) ( 8, ) Set Builder Notation: { x x < 3 or x > 8} 179

182 x < 2 Inequality Form Graph (,2) Interval Notation { x < 2} x Set Builder Notation x 2 Inequality Form Graph (,2] Interval Notation { x 2} x Set Builder Notation x > 2 Inequality Form Graph ( 2, ) Interval Notation { x > 2} x Set Builder Notation 180

183 x 2 Inequality Form Graph [ 2, ) Interval Notation { x 2} x Set Builder Notation 1 < x < 3 Inequality Form Graph ( 1,3) Interval Notation { 1 < x < 3} x Set Builder Notation 1 x 3 Inequality Form Graph [ 1,3] Interval Notation { 1 x 3} x Set Builder Notation 181

184 x < 1 or x > 3 Inequality Form ( 1) ( 3, ) Graph, Interval Notation { x < 1 or x > 3} x Set Builder Notation 1 or x 3 x Inequality Form ( 1] [ 3, ) Graph, Interval Notation { x 1 or x 3} x Set Builder Notation 182

185 SECTION 3.1 Reading Graphs and the Rectangular Coordinate System I. OBJECTIVES At the conclusion of this lesson you should be able to: 1. Read bar and line graphs. 2. Plot ordered pairs of numbers on the rectangular coordinate system. 3. Graph paired data to create a scatter diagram. 4. Find the missing coordinate of an ordered pair solution, given one coordinate of the pair. II. PROCEDURE While watching the video, follow this study guide and take notes in the study guide as if you were sitting in a classroom. Stop or pause the video as needed to catch up or copy something down. Rectangular Coordinate System 183

186 Ordered Pair (xx, yy) Plotting Ordered Pairs (2, 5) ( 8,4) (7, 6) ( 6, 8) 184

187 (0, 0) (0, 5) (0, 4) ( 6, 0) (5, 0) Find the x- and y-coordinates of each labeled point. A D A B E C C B D E 185

188 Determine whether each ordered pair is a solution of the given linear equation. 2xx yy = 6 (3,0), (4,3), ( 2, 10) 186

189 Determine whether each ordered pair is a solution of the given linear equation. yy = 2 (2,3), (4,2), ( 2,2) Complete each ordered pair so that it is a solution of the given linear equation. xx 2yy = 6 (4, ), (,1) 187

190 Complete each ordered pair so that it is a solution of the given linear equation. yy = 1 3 xx 2 ( 6, ), (,1) 188

191 Complete the table of ordered pairs for each linear equation. yy = 1 2 xx xx yy

192 Complete the table of ordered pairs for each linear equation. xx + 3yy = 6 xx 0 yy

193 Hamburger Eaters in Millions Hamburger Eaters The line graph above shows the number of hamburger eaters in the U.S. Use this graph to answer the following. 1. Approximate the number of hamburger eaters in Approximate the number of hamburger eaters in Between what years shown did the greatest decrease in hamburger eaters occur? 4. What was the first year shown that the number of hamburger eaters increased by 1.2? 5. During what period was the number of hamburger eaters at 3.2? 191

194 SECTION 3.2 Graphing Linear Equations I. OBJECTIVES At the conclusion of this lesson you should be able to: 1. Graph linear equations by finding and plotting ordered pair solutions. II. PROCEDURE While watching the video, follow this study guide and take notes in the study guide as if you were sitting in a classroom. Stop or pause the video as needed to catch up or copy something down. Linear Equations in Two Variables AAAA + BBBB = CC yy = mmmm + bb 192

195 For each equation, find three ordered pair solutions by completing the table. Then use the ordered pairs to graph the equation. 2xx + 3yy = 6 xx 6 0 yy 0 193

196 For each equation, find three ordered pair solutions by completing the table. Then use the ordered pairs to graph the equation. yy = 1 2 xx + 3 xx 2 0 yy 0 194

197 Graph each linear equation. xx + 2yy = 6 195

198 Graph each linear equation. yy = 2xx

199 Graph each linear equation. yy = 1 3 xx 2 197

200 Graph each linear equation. xx = 3yy 198

201 Graph each linear equation. yy = 6 Graph each linear equation. xx = 6 199

202 SECTION 3.3 Intercepts I. OBJECTIVES At the conclusion of this lesson you should be able to: 1. Identify intercepts of a graph. 2. Graph a linear equation by finding and plotting intercept points. 3. Identify and graph vertical and horizontal lines. II. PROCEDURE While watching the video, follow this study guide and take notes in the study guide as if you were sitting in a classroom. Stop or pause the video as needed to catch up or copy something down. (5, 0) ( 8,0) (9, 0) ( 4, 0) 200

203 (0, 5) (0, 8) (0, 9) (0, 6) 201

204 x-intercept(s) y-intercept(s) 202

205 x-intercept(s) y-intercept(s) 203

206 x-intercept y-intercept 204

207 2xx + 4yy = 8 205

208 yy = 3xx

209 yy = 3xx 207

210 yy + 5 = 0 208

211 xx 4 = 0 209

212 NOT ON THE VIDEO! y 5 = x x 3 5 y x-intercept 5 0 = x = x = 3 x 3 3 = 5x 3 = x 5 ( ) x-intercept y-intercept y-intercept y y = 5 3 = 1 ( 0) + 1 y y 5 = 3 = 5 +1 y y = 6 5 = 3 = 5 +1 y y = 4 ( 3) + 1 ( 3)

213 SECTION 3.4 Slope and Rate of Change I. OBJECTIVES At the conclusion of this lesson you should be able to: 1. Find the slope of a line given two points of the line. 2. Find the slope of a line given its equation. 3. Find the slopes of horizontal and vertical lines. II. PROCEDURE While watching the video, follow this study guide and take notes in the study guide as if you were sitting in a classroom. Stop or pause the video as needed to catch up or copy something down. (4,6) (1,2) 211

214 Slope Formula mm = yy 2 yy 1 xx 2 xx 1 PP 1 (xx 1, yy 1 ) PP 2 (xx 2, yy 2 ) Find the slope of the line that passes through the given points. (2, 3) and (2,5) (4, 3) and (6, 3) 212

215 Find the slope of the line that passes through the given points. (2, 8) and ( 5,4) 213

216 Positive Slope Negative Slope mm > 0 mm < 0 No Slope Slope of Zero Undefined Slope mm = 0 214

217 Find the slope of each line if exists. 215

218 Determine whether a line with the given slope is upward, downward, horizontal or vertical. mm = 4 mm = 3 mm = 0 mm = undefined mm =

219 Equations of Lines in Two Variables Standard Form: AAAA + BBBB = CC Slope Intercept Form: yy = mmmm + bb Slope Intercept Form of a line yy = mmmm + bb Find the slope of each line. yy = 2 xx + 2 yy = 0.3xx

220 Find the slope of each line. 3xx yy = 2 3xx + 4yy = 12 xx + 3yy = 6 2xx 6yy =

221 Horizontal Line Vertical Line y = a x = a Slope = 0 Slope = Undefined Find the slope of each line. yy = 6 xx = 6 219

222 SECTION 5.1 Exponents I. OBJECTIVES At the conclusion of this lesson you should be able to: 1. Evaluate exponential expressions. 2. Use the product rule for exponents. 3. Use the power rule for exponents. 4. Use the power rules for products and quotients. 5. Use the quotient rule for exponents, and define a number raised to the 0 power. 6. Decide which rules to use to simplify an expression. II. PROCEDURE While watching the video, follow this study guide and take notes in the study guide as if you were sitting in a classroom. Stop or pause the video as needed to catch up or copy something down. xx 4 (2xx) 3 2xx 3 Base Base Exponent Exponent Recall (nnnnnnnnnnnnnnnn) eeeeeeee = pppppppppppppppp (nnnnnnnnnnnnnnnn) oooooo = nnnnnnnnnnnnnnnn 220

223 Evaluate each expression. ( 2) xx 2 xx 4 Product Rule xx mm xx nn = xx mm+nn aa mm aa nn = aa mm+nn 221

224 Use the product rule to simplify each expression. Write the results using exponents. xx 4 xx 5 xx 7 xx 3 xx 2 ( 2) 6 ( 2) 4 (3xx 3 ) (2xx 5 ) (xx 3 yy 2 ) (xx 4 yy 6 ) 222

225 Use the product rule to simplify each expression. Write the results using exponents. (3aabb 2 ) ( 2aa 2 bb 4 ) ( 4aa 3 bb 2 cc) ( 3aabb 4 ) (3bb 2 ) ( 4bb 4 ) (bb 3 ) 223

226 (3 3 ) 2 (xx 4 ) 3 Power Rule (aa mm ) nn = aa mm nn Product Rule aa mm aa nn = aa mm+nn Use the power rule to simplify each expression. Write the results using exponents. (xx 2 ) 3 (2 3 ) 2 (xx 5 ) 3 224

227 (xx 2 yy 3 ) 3 (aa mm bb nn ) pp = aa mmmm bb nnnn Product Rule aa mm aa nn = aa mm+nn aa mmmm bb nnnn Power Rule (aa mm ) nn = aa mm nn (aaaa) nn = aa nn bb nn (aa mm bb nn ) pp = aamm bb nn pp = aammmm bb nnnn 225

228 Use the power rule to simplify each expression. Write the results using exponents. (2xx 2 ) 4 ( 3xx 3 ) 2 ( 3xx 5 yyzz 2 ) 3 3xx2 3 yy 2aa2 2 bb 4 226

229 xx 4 xx xx 8 xx 5 xx 4 xx 4 Quotient Rule aa mm aann = aamm nn xx 4 xx 4 aa 0 = = 1 (2aa) 0 = 1 227

230 Use the quotient rule to simplify each expression. Write the results using exponents. xx 6 yy 9 xx 2 yy 7 xx 16 yy 8 xx 12 yy 2 6aa 10 bb 8 3aa 2 bb 228

231 Simplify each expression (2xx 6 yy 2 ) 5 32xx 20 yy

232 Simplify each expression. ( 6xxxxxx 3 ) 2 3yy5 2 6xx 4 230

233 Rules To REMEMBER Product Rule Power Rule a m n m+ n = ( m ) n m n a = a a a m m m ( ab ) = a b ( m n ) p mp np a b = a b a b m = a b m m ( b 0) Division Rule a a m n = a m n a b m n p = a b mp np Zero Power Rule, a 0 = 1, a 0 ( negative) even = positive ( negative) odd = negative 231

234 232 NOT ON THE VIDEO! ( ) n m n m a a = Example: ( ) = = ( ) n n n b a ab = Example: ( ) x x x = = ( ) np mp p n m b a b a = Example: ( ) b a b a b a = = n n n b a b a = Example: x x x = = np mp p n m b a b a = Example: z y x z y x z y x = = n m n m a a a = Example: z y x z y x z xy z y x = =

235 SECTION 5.2 Polynomial Functions and Adding and Subtracting Polynomials I. OBJECTIVES At the conclusion of this lesson you should be able to: 1. Define term and coefficient of a term. 2. Define polynomial, monomial, binomial, trinomial, and degree. 3. Evaluate polynomials for given replacement values. 4. Simplify a polynomial by combining like terms. 5. Simplify a polynomial in several variables. 6. Write a polynomial in descending powers of the variable and with no missing powers of the variable. II. PROCEDURE While watching the video, follow this study guide and take notes in the study guide as if you were sitting in a classroom. Stop or pause the video as needed to catch up or copy something down. 2xx + 4 3xx 2 Expression Terms xx, 4 33xx yy 22 3xx 2, 4xxxx, 6yy 2 22xx 33 2xx

236 Polynomial A polynomial in x is a finite sum of terms of the form aaxx nn, where a is a real number and n is a whole number. 4xx 3 + 3xx 2 2xx + 6 2xx 4 + 4xx 3 + 5xx 9 Descending Order 4xx 3 + 3xx 2 2xx + 6 3xx 2 4xxxx + 6yy 2 3yy 2 4xxxx + 6xx 2 234

237 Write the following polynomial in descending order. 6aa 2 4aa 3 + 6aa aa Polynomials Monomial: Binomial: Trinomial: 235

238 Degree of a Term 3, 3xx, 3xx 2, 3xxxx, 3xx 2 yy, 3xx 2 yy 2 Degree of a Polynomial 4xx 3 + 3xx 2 2xx + 6 6xx 3 8xx 2 + 8xx 4 + 9xx 236

239 Find the degree of each of the following polynomials and determine whether it is a monomial, binomial, trinomial, or none of these. 4xx 3 yy 4 4xx 3 +3yy 4 3xx 2 6xx xx 5 yy 6xx 3 yy 2 + 8xx 2 yy 6 237

240 Simplify each of the following by combining like terms. 6xx 2 4xx yy 2 1.2yy

241 Simplify each of the following by combining like terms. 1 6 xx4 1 7 xx xx4 3 7 xx

242 Perform the indicated operations. (3xx 2 6xx + 8) + (2xx 2 4xx 10) (xx 2 4xx 6) (2xx 2 4xx 8) 240

243 Perform the indicated operations. ( 8xx 4 + 7xx) + ( 8xx 4 + xx + 9) 3tt tt

244 Perform the indicated operations. 4zz 2 8zz + 3 (6zz 2 + 8zz 3) (3xx 2 + 5xx 8) + (5xx 2 + 9xx + 12) (xx 2 14) 242

245 243 NOT ON THE VIDEO! Simplify: ( ) ( ) x x x x x x ( ) ( ) x x x x x x x x x x x x x x x Simplify: ( ) ( ) x x x x ( ) ( ) x x x x x x x x x x x Simplify: ( ) ( ) x x x x x x ( ) ( ) x x x x x x x x x x x x x x x 1. Remove the parentheses. 2. Combine like terms and write in descending order. 1. Remove the parentheses. 2. Combine like terms and write in descending order. 1. Remove the parentheses. 2. Combine like terms and write in descending order.