Big Bend Community College. Emporium Model Math Courses Workbook

Transcription

1 Name: Big Bend Community College Emporium Model Math Courses Workbook A workbook to supplement video lectures and online homework by: Tyler Wallace Salah Abed Sarah Adams Mariah Helvy April Mayer Michele Sherwood 1

2 This project was made possible in part by a federal STEM-HSI grant under Title III part F and by the generous support of Big Bend Community College and the Math Department. Copyright 2012, Some Rights Reserved CC-BY-NC-SA. This work is a combination of original work and a derivative of Prealgebra Workbook, Beginning Algebra Workbook, and Intermediate Algebra Workbook by Tyler Wallace, which all hold a CC-BY License. Cover art by Sarah Adams with CC-BY-NC-SA license. Emporium Model Math Courses Workbook by Wallace, Abed, Adams, Helvy, Mayer, Sherwood is licensed under a Creative Commons Attribution-NonCommercial- ShareAlike 3.0 Unported License ( You are free: To share: To copy, distribute and transmit the work To Remix: To adapt the work Under the following conditions: Attribution: You must attribute the work in the manner specified by the authors or licensor (but not in any way that suggests that they endorse you or your use of the work). Noncommercial: You may not use this work for commercial purposes. Share Alike: If you alter, transform, or build upon this work, you may distribute the resulting work only under the same or similar license to this one. With the understanding that: Waiver: Any of the above conditions can be waived if you get permission from the copyright holder Public Domain: Where the work or any of its elements is in the public domain under applicable law, that status is in no way affected by the license. Other rights: In no way are any of the following rights affected by the license: o Your fair dealing or fair use rights, or other applicable copyright exceptions and limitations; o The author s moral rights; o Rights other persons may have either in the work itself or in how the work is used, such as publicity or privacy rights 2

3 Conversion Factors LENGTH English 12 in = 1 ft 3 ft = 1 yd 1 mi = 5280 ft Metric (meter) 1000 mm = 1 m 100 cm = 1 m 10 dm = 1 m 1 dam = 10 m 1 hm = 100 m 1 km = 1000 m TEMPERATURE English to Metric 1 in = 2.54 cm VOLUME English Metric (liter) 8 fl oz = 1 cup (c) 2 cups (c) = 1 pint (pt) 2 pints (pt) = 1 quart (qt) 4 quarts (qt) = 1 gallon (gal) English to Metric 1 gallon (gal) = 3.79 liter (L) 1 in 3 = ml 1000 ml = 1 L 100 cl = 1 L 10 dl = 1 L 1 dal = 10 L 1 hl = 100 L 1 kl = 1000 L 1 ml = 1 cc = 1 cm 3 TIME 60 seconds (sec) = 1 minute (min) 60 minutes (min) = 1 hour (hr) 24 hours (hr) = 1 day 52 weeks = 1 year 365 days = 1 year English 16 oz = 1 pound (lb) 2,000 lb = 1 Ton (T) WEIGHT (MASS) English to Metric 2.20 lb = 1 kg Metric (gram) 1000 mg = 1 g 100 cg = 1 g 10 dg = 1 g 1 dag = 10 g 1 hg = 100 g 1 kg = 1000 g INTEREST Simple:. Continuous: A = Pe rt Compound:. Annual: n=1 Semiannual: n=2 Quarterly: n=4 3

4 Geometric Formulas Name Diagram Area Rectangle w A = lw P = 2l + 2w l Parallelogram b h A = bh Triangle h A = bh b a Trapezoid h A = h(a + b) b Circle d r A = πr 2 C = πd = 2πr Name Diagram Volume Rectangular Solid Right Circular Cylinder l r h h w V = lwh V = πr 2 h Right Circular Cone h r V = πr 2 h Sphere V = πr 3 r Right Triangle Pythagorean Theorem: a 2 + b 2 = c 2 a 4 c b

5 Table of Contents Unit 1: Integers and Algebraic Expressions Whole Numbers and Decimals Operations with Integers Exponents and Order of Operations Simplify Algebraic Expressions Unit 2: Fractions Prime Factorization Reduce Fractions Multiply and Divide Fractions Least Common Multiple Add and Subtract Fractions Order of Operations with Fractions Mixed Numbers Unit 3: Linear Equations One Step Equations Two Step Equations General Linear Equations Equations with Decimals and Fractions Unit 4: Stats, Graphing, Proportions, and Percents Averages Probability and Plotting Points Rates and Unit Rates Proportions and Applications Introduction to Percents Translate Percents and Applications Percents as Proportions and Applications Unit 5: Geometry and Intro to Polynomials Conversion Factors (Tear out copy) Convert Units Geometry Formulas Area, Volume, and Temperature Pythagorean Theorem

6 5.4 Introduction to Polynomials Scientific Notation Unit 6: Proficiency Exam # Unit 7: Linear Equations and Applications Order of Operations Evaluate and Simplify Algebraic Expressions Solve Linear Equations Formulas Word Problems Age Problems Distance, Rate, Time Problems Unit 8: Graphing Linear Equations and Solving Systems of Equations Slope Equations of Lines Parallel and Perpendicular Lines Systems by Graphing Systems by Substitution Systems by Elimination Unit 9: Polynomials Exponents Scientific Notation Add, Subtract, Multiply Polynomials Polynomial Long Division Unit 10: Factoring Factor Common Factors and Grouping Factor Trinomials Factoring Tricks Factoring Strategies Reduce Rational Expressions Solving Equations by Factoring Quadratic Formula Unit 11: Functions Evaluate Functions Exponential Equations Logarithms

7 11.4 Compound Interest Dimensional Analysis Unit 12: Proficiency Exam # Unit 13: Compound Inequalities Inequalities Compound Inequalities Absolute Value Equations Absolute Value Inequalities Unit 14: Systems of Equations Systems by Substitution and Addition/Elimination Systems with Three Variables Applications of Systems -Value Applications of Systems - Mixture Unit 15: Radicals Simplify Radicals Add, Subtract, and Multiply Radicals Rationalize Denominators Rational Exponents Radicals of Mixed Index Complex Numbers Complete the Square Quadratic Formula Unit 16: College Algebra Topics Multiply and Divide Rational Expressions Add and Subtract Rational Expressions Compound Fractions Rational Equations Equations with Radicals Equations with Exponents Rectangle Problems Work Problems Distance and Revenue Problems Unit 17: Functions Evaluate Functions Operations on Functions

8 17.3 Inverse Functions Graphs of Quadratic Functions Unit 18: Proficiency Exam #

9 Unit 1: Integers and Algebraic Expressions ID: 4422 To work through the unit you should: 1. Watch a video, as you watch, fill out the workbook (top and example sections). 2. Complete Q1 and Q2 in WAMAP, put your work in the bottom sections of the page. 3. Repeat #1 and #2 with each page until you reach. 4. Complete the homework assignment on your own paper. 5. Repeat #1-#4 until you reach the end of the unit. 6. Complete the practice test on your own paper. 7. Take the unit exam. 9

10 1.1a Adding and Subtracting Whole Numbers, Decimals, and Negatives Rounding Whole Numbers Whole numbers are: Place Value: 4, 2 8 7, Rounding: Look at the digit. Round up if it is and round down if it is Round 5,459,246 To the nearest thousand Round 5,459,246 To the nearest hundred-thousand 10

11 1.1b Adding and Subtracting Whole Numbers, Decimals, and Negatives Rounding Decimals Decimals are of the Place Value: Round To the nearest thousandth Round To the nearest hundredth 11

12 1.1c Adding and Subtracting Whole Numbers, Decimals, and Negatives Add Whole Numbers To add we place values and work to

13 1.1d Adding and Subtracting Whole Numbers, Decimals, and Negatives Add Decimals When adding decimals we must the Place decimal:

14 1.1e Adding and Subtracting Whole Numbers, Decimals, and Negatives Subtract Whole Numbers To subtract we place value and work to

15 1.1f Adding and Subtracting Whole Numbers, Decimals, and Negatives Subtract Decimals When subtracting decimals we must the Important: We may need additional to line up! Place decimal:

16 1.1g Adding and Subtracting Whole Numbers, Decimals, and Negatives Integers and Absolute Value Integers: Opposite means a over on the The symbol means, AND! Absolute Value is the from zero. It is always ( 6) (3) Example 3: 8 Example 4: 4 Example 5: 7 Example 6: 2 Q 3: Q 4: Q 5: Q 6: 16

17 1.1h Adding and Subtracting Whole Numbers, Decimals, and Negatives Add with the Same Sign Adding and Subtracting Integers: Keep the with the after it Rules for Dealing with Double Signs: Adding a negative, or subtracting a positive, is the same as simple Subtracting a negative is the same as 3 + ( 4) = 3 ( 4) = Visualize: 2 + ( 3): Add with the same sign: 7 + ( 4) ( 6) + ( 8) 17

18 1.1i Adding and Subtracting Whole Numbers, Decimals, and Negatives Add with Different Signs Visualize: Visualize: 1 + ( 3) Adding with different signs: 5 + ( 2) 9 ( 4) 18

19 1.1j Adding and Subtracting Whole Numbers, Decimals, and Negatives Add and Subtract Several Integers When adding and subtracting many integers we work to 5 + ( 2) ( 6) ( 3) ( 1) + 3 You have completed the videos for 1.1 Adding and Subtracting Whole Numbers, Decimals, and Negatives. On your own paper complete the homework assignment. 19

20 1.2a Multiplying and Dividing Whole Numbers, Decimals, and Negatives Multiply Whole Numbers Multiply the digits together Use to hold place value After multiplying we Different ways to show multiply : (48) 20

21 1.2b Multiplying and Dividing Whole Numbers, Decimals, and Negatives Multiply Decimals Place decimal: (3.52) 21

22 1.2c Multiplying and Dividing Whole Numbers, Decimals, and Negatives Divide Whole Numbers Long division places the number in front! The leftovers: Different ways to show divide :

23 1.2d Multiplying and Dividing Whole Numbers, Decimals, and Negatives Divide With Zero When dividing by zero, it helps to remember the of division. 6 3 implies how many of 3 I have. 0 4 implies how many of 4 I have. 6 0 implies how many groups of I have

24 1.2e Multiplying and Dividing Whole Numbers, Decimals, and Negatives Divide Decimals No decimals in the or Move the in both the and If you run out of digits you can Place decimal:

25 1.2f Multiplying and Dividing Whole Numbers, Decimals, and Negatives Multiply and Divide with Different Signs A pattern to multiplying: 2 2 = 2 1 = 2 0 = 2 ( 1) = Multiplying and dividing with a negative and a positive (or positive and negative) is a To remember: When things happen to people it is a thing To remember: When things happen to people it is a thing ( 8) 25

26 1.2g Multiplying and Dividing Whole Numbers, Decimals, and Negatives Multiply and Divide with the Same Sign A pattern to multiplying: 2 2 = 2 1 = 2 0 = 2 ( 1) = Multiplying and dividing a negative times a negative is a To remember: When things happen to people it is a thing 7( 4) 15 3 You have completed the videos for 1.2 Multiplying and Dividing Whole Numbers, Decimals, and Negatives. On your own paper complete the homework assignment. 26

27 1.3a Exponents and Order of Operations Exponents Exponents are 5 3 =

28 1.3b Exponents and Order of Operations Exponents on Negatives Exponents only effect what they are. ( 5) 2 = 5 2 = 3 4 ( 2) 6 28

29 1.3c Exponents and Order of Operations Order of Operations Why we need an order: 2 + 3(4) 2 + 3(4) The order: (4 7) (7 9) 29

30 1.3d Exponents and Order of Operations Order with Absolute Value Absolute values works just like but makes the number inside after it has been (2)

31 1.3e Exponents and Order of Operations Order with a fraction Simplify numerator Simplify denominator Last (32) 2( 1) You have completed the videos for 1.3 Exponents and Order of Operations. On your own paper complete the homework assignment. 31

32 1.4a Simplify Algebraic Expressions Substitute a Value I have a eggs means I have eggs. Variables are that represent amounts If we know the amount we can it in an expression Whenever we make a substitution or put it in Evaluate: x 2 7x 12 When x = 4 Evaluate: b 2 4ac When a = 2, b = 3, and c = 5 32

33 1.4b Simplify Algebraic Expressions Is it a Solution? An equation is made up of two expressions A solution is the value of the that makes the equation Is x = 3 the solution to 2x + 7 = 1? Is x = 3 the solution to 2x 5 = 7x + 5? 33

34 1.4c Simplify Algebraic Expressions Combine Like Terms John has 5 cats and 3 dogs. Sue has 2 cats and 1 dog. Together they have cats and dogs. Terms are and that are together Like terms are terms that have matching and Combine like terms: the coefficients or from 9x + 2y 7x 5y + 2x 5x 2 2x 9 + 4x 7x

35 1.4d Simplify Algebraic Expressions Distributive Property Multiplication is 3(2x + 5) = Distributive Property: 3(2x + 5) 4(2x + 5y 7) 7(9x 2 7x + 8) 35

36 1.4e Simplify Algebraic Expressions Distribute and Combine Like Terms Order of operations states we before we Therefore we will first and then second 5(2x + 6y 2) 4(x + 3 6y) 2(4x 2 6x + 1) (x 2 + 5x + 3) 36

37 1.4f Simplify Algebraic Expressions Perimeter Problems Perimeter: Find the perimeter by the sides together 8 4x 3x x 9 2x 3 + x 5x x 6 4x You have completed the videos for 1.4 Simplify Algebraic Expressions. On your own paper complete the homework assignment. Congratulations! You made it through the material for Unit 1: Integers and Algebraic Expressions. It is time to prepare for your exam. On a separate sheet of paper complete the practice test. Once you have completed the practice test, ask your instructor to take the test. Good luck! 37

38 Unit 2: Fractions ID: 4423 To work through the unit you should: 1. Watch a video, as you watch, fill out the workbook (top and example sections). 2. Complete Q1 and Q2 in WAMAP, put your work in the bottom sections of the page. 3. Repeat #1 and #2 with each page until you reach. 4. Complete the homework assignment on your own paper. 5. Repeat #1-#4 until you reach the end of the unit. 6. Complete the practice test on your own paper. 7. Take the unit exam. 38

39 2.1a Prime Factorization Prime and Composite Prime numbers are divisible by and Examples of Primes: Composite numbers are divisible by Prime or Composite: 89 Prime or Composite:

40 2.1b Prime Factorization Divisibility Tests A number is divisible by a smaller number if the small number into the number Divisibility tests: 2: 3: 5: 7, 11, 13, 17, 19: 2730 is divisible by which prime numbers? 133 is divisible by which numbers? 40

41 2.1c Prime Factorization Prime Factorization Prime Factorization: a of numbers To find a prime factorization we divide by Find the prime factorization of 360 Find the prime factorization of 1224 You have completed the videos for 2.1 Prime Factorization. On your own paper complete the homework assignment. 41

42 2.2a Reduce Fractions Introduction to Fractions Fraction is a of a Example: 4 where the 4 is the, called the and the 5 is the called the 5 What fraction is shaded? What fraction is shaded? 42

43 2.2b Reduce Fractions Equivalent Fractions Equivalent fractions: To find an equivalent fraction the and by the Find three equivalent fractions: 3 7 Find three equivalent fractions:

44 2.2c Reduce Fractions Reduce with Prime Factorizations Reduced Fraction: The and have no common To reduce we find the and divide out

45 2.2d Reduce Fractions - Reduce Sometimes we can the common factors and

46 2.2e Reduce Fractions Reduce with Variables When reducing with variables, the variables that are in With exponents it may help to 4x 2 yz 10xy 3 27a 3 bc 9a 2 b 2 c 46

47 2.2f Reduce Fractions Convert Fractions to Decimals The fraction bar represents To convert a fraction to a decimal we To work through this process we will use If the decimal repeats we will use a Convert to decimal: 7 32 Convert to decimal:

48 2.2g Reduce Fractions Convert Decimals to Fractions To convert a decimal to a fraction we use of the last digit. Last check to see if the fraction can be Convert to a fraction: 0.43 Convert to a fraction: You have completed the videos for 2.2 Reduce Fractions. On your own paper complete the homework assignment. 48

49 2.3a Multiply and Divide Fractions Multiply with No Reducing Multiply the together and multiply the together

50 2.3b Multiply and Divide Fractions Multiply with Reducing Consider: = But if we factor each: = When we can a common factor from the and

51 2.3c Multiply and Divide Fractions Multiply with Variables With exponents on variables it may help to Remember, repeated is done with 6x 2 y 7 14y 3x 30a 3b 2 21ab 10 51

52 2.3d Multiply and Divide Fractions Multiply with Whole Numbers and Fractions Whole numbers can be made into fractions by putting them over

53 2.3e Multiply and Divide Fractions - Reciprocals Reciprocal: Reciprocals multiply to Find the reciprocal of 6 5 Find the reciprocal of 8 53

54 2.3f Multiply and Divide Fractions Divide Fractions Divide fractions by by the

55 2.3g Multiply and Divide Fractions Divide with Variables With exponents on variables it may help to Remember, repeated is done with 10x 3y xy 14m 3n 7 6m 2 n 55

56 2.3h Multiply and Divide Fractions Divide with Whole Numbers and Fractions Whole numbers can be made into fractions by putting them over You have completed the videos for 2.3 Multiply and Divide Fractions. On your own paper complete the homework assignment. 56

57 2.4a Least Common Multiple - Multiples Multiples are found by by other numbers Find the first three multiples of 8 Find the first three multiples of 7 57

58 2.4b Least Common Multiple LCM Using Mental Math Least Common Multiple (LCM): Multiples of 15: Multiples of 20: Common multiples of 15 and 20: Least common multiple of 15 and 20: Using mental math: Test of the number: Can it be divided by the Find the LCM of 12 and 9 Find the LCM of 20 and 4 58

59 2.4c Least Common Multiple LCM Using Prime Factorization To find an LCM of two larger numbers: 1. Find the of each 2. Use all the unique 3. Assign the to each factor Find the LCM of 24 and 36 Find the LCM of 54 and 90 59

60 2.4d Least Common Multiple LCM with Variables To find the LCM with variables: 1. Use all the unique 2. Assign the to each variable Find the LCM of a 3 b 2 c and a 2 b 7 d 2 Find the LCM of 6x 2 z and 8x 3 y 2 You have completed the videos for 2.4 Least Common Multiple. On your own paper complete the homework assignment. 60

61 2.5a Add and Subtract Fractions With Common Denominator Consider: = To add fractions that have the same denominator: numerators and denominators When adding fractions always check to at the of the problem

62 2.5b Add and Subtract Fractions With Different Denominators If the denominators don t match we will find the Multiply by missing factors. Then multiply the by the factors If you do not know the LCD you can always the two

63 2.5c Add and Subtract Fractions With Different Large Denominators We may have to use to find the LCD. To build up to the LCD we multiply by any factors You have completed the videos for 2.5 Add and Subtract Fractions. On your own paper complete the homework assignment. 63

64 2.6a Order of Operations with Fractions Exponents on Fractions Exponents mean ( 2 3 )2 = Or we could put the exponent on the and ( 3 2 ) 3 ( 7 4 ) 2 64

65 2.6b Order of Operations with Fractions Order of Operations with Fractions The order You may need some (5 2 ) 1 30 ( 8 5 )

66 You have completed the videos for 2.6 Order of Operations with Fractions. On your own paper complete the homework assignment. 66

67 2.7a Mixed Numbers Mixed Numbers and Conversions Mixed number: Change a mixed number to a fraction: the whole and and the Change a fraction to a mixed number:, the remainder is the new Convert 5 9 to a fraction Convert 73 to a mixed number

68 2.7b Mixed Numbers Add and Subtract Mixed Numbers To do math with mixed numbers it is easiest to to a When you have your answer,

69 2.7c Mixed Numbers Multiply and Divide Mixed Numbers To do math with mixed numbers it is easiest to to a When you have your answer, You have completed the videos for 2.7 Mixed Numbers. On your own paper complete the homework assignment. Congratulations! You made it through the material for Unit 2: Fractions. It is time to prepare for your exam. On a separate sheet of paper complete the practice test. Once you have completed the practice test, ask your instructor to take the test. Good luck! 69

70 Unit 3: Linear Equations ID: 4424 To work through the unit you should: 1. Watch a video, as you watch, fill out the workbook (top and example sections). 2. Complete Q1 and Q2 in WAMAP, put your work in the bottom sections of the page. 3. Repeat #1 and #2 with each page until you reach. 4. Complete the homework assignment on your own paper. 5. Repeat #1-#4 until you reach the end of the unit. 6. Complete the practice test on your own paper. 7. Take the unit exam. 70

71 3.1a One Step Equations Addition Principle A to an equation is the value for the that makes the equation We can anything to of the equation Addition Principle: To move a negative term we do the opposite and it to Very Important to your work! x 9 = 4 3 = 5 + x 71

72 3.1b One Step Equations Subtraction Principle We can anything to of the equation Subtraction Principle: To move a positive term we do the opposite and it from Very Important to your work! x + 8 = 4 3 = 7 + x 72

73 3.1c One Step Equations Division Principle We can anything to of the equation Division Principle: To undo multiplication of factors we do the opposite and it from Very Important to your work! 7x = 147 8x = 72 73

74 3.1d One Step Equations Multiplication Principle We can anything to of the equation Multiplication Principle: To clear division we do the opposite and it by Very Important to your work! x 7 = 4 5 = x 2 You have completed the videos for 3.1 One Step Equations. On your own paper complete the homework assignment. 74

75 3.2a Two Step Equations Two Steps Simplifying we use order of operations and we before we Solving we work and we before we 5x 7 = 8 9 = 5 2x 75

76 3.2b Two Step Equations Negative Variables If there is no number in front of a variable, we assume there is a in front This means x is the same as x + 8 = 5 4 = 6 x You have completed the videos for 3.2 Two Step Equations. On your own paper complete the homework assignment. 76

77 3.3a General Linear Equations Variable on Both Sides When solving an equation we want the variable on If the variable is on both sides we will the one by 5x + 7 = 9x 2 6x + 1 = 2x 12 77

78 3.3b General Linear Equations Combine Like Terms Before we solve we must the and sides One way to do this is 5x 3 2x = 7 + 8x x 2 = 3x x 78

79 3.3c General Linear Equations Distribute and Combine Before we solve we must the and sides One way to do this is 2(3x 1) = 4x + 6 x 3(2x + 1) 9x = 4(x + 6) 20 You have completed the videos for 3.3 General Linear Equations. On your own paper complete the homework assignment. 79

80 3.4a Equations with Decimals and Fractions Decimals When solving with decimals the pattern of solving is A may be helpful to speed up calculations 3.2x = (x 4.3) = 5.7x x 80

81 3.4b Equations with Decimals and Fractions Clear Fractions with LCD If the equation has fractions, we can clear the fractions by each term by the After multiplying we can to get an equation with no 5 6 x 1 3 = x = x You have completed the videos for 3.4 Equations with Decimals and Fractions. On your own paper complete the homework assignment. Congratulations! You made it through the material for Unit 3: Linear Equations. It is time to prepare for your exam. On a separate sheet of paper complete the practice test. Once you have completed the practice test, ask your instructor to take the test. Good luck! 81

82 Unit 4: Stats, Graphing, Proportions and Percents ID: 4425 (You may use a calculator on this unit) To work through the unit you should: 1. Watch a video, as you watch, fill out the workbook (top and example sections). 2. Complete Q1 and Q2 in WAMAP, put your work in the bottom sections of the page. 3. Repeat #1 and #2 with each page until you reach. 4. Complete the homework assignment on your own paper. 5. Repeat #1-#4 until you reach the end of the unit. 6. Complete the practice test on your own paper. 7. Take the unit exam. 82

83 4.1a Averages - Mean Mean: The average if all items were the or spread out To calculate the mean: Find the Mean: 5, 8, 6, 7, 9, 4, 8, 10 Find the Mean: 23, 26, 27, 21, 26, 22, 73, 24, 23 83

84 4.1b Averages Missing Value The mean is when all the items are the or spread out If we know the mean and are missing a value, calculate the using the On three tests a student earns 83%, 71%, and 81%. What must she earn on her fourth test to raise her average of the four tests up to 80%? Another student has a goal of 90% on his four tests. On the first three tests he earned 92%, 75%, and 89%. Is it possible for him to reach his goal of 90%? What score would he have to earn? 84

85 4.1c Averages Weighted Mean Weighted average: Values that occur have a larger on the average (mean) To calculate the total we the by the In a survey, students were asked how many siblings they had. The results are below. Calculate the average number of siblings of the survey responders. Siblings Responses Grade Point Average (GPA) is calculated as a weighted average. The credits of a course are considered the frequency of the course. In this way, classes that are more credits have a larger effect on grade than classes with fewer credits. Calculate the GPA of the following report card: Class Credits Grade English Math History PE

86 4.1d Averages - Median Median: The average at which the data is and is To calculate the median: If two values are in the middle: Find the Median: 5, 8, 6, 7, 9, 4, 8, 10 Find the Median: 23, 26, 27, 21, 26, 22, 73, 24, 23 86

87 4.1e Averages - Mode Mode: the average or value that occurs It is possible to have modes or mode Find the Mode: 5, 8, 6, 7, 9, 4, 8, 10 Find the Mode: 23, 26, 27, 21, 26, 22, 73, 24, 23 You have completed the videos for 4.1 Averages. On your own paper complete the homework assignment. 87

88 4.2a Probability and Plotting Points Basic Probability Probability: Basic Probability Fraction: A bag contains 3 blue marbles, 2 red marbles and 1 green marble. If you were to draw one marble at random, what is the probability of drawing... 1) A blue marble? 2) A red marble? 3) A black marble? If you roll a standard six-sided die, what is the probability you roll 1) A three? 2) An even number? 3) A number smaller than three? 4) A seven? 88

89 4.2b Probability and Plotting Points Compound Events The probability of this OR that: we the individual probabilities The probability of this AND that: we the individual probabilities A bag contains 3 blue marbles, 2 red marbles and 1 green marble. If you were to draw one marble at random, what is the probability of drawing... 1) A blue or green marble? If you roll a standard six-sided die and then draw a marble out of a bag with 7 red and 3 black marbles, what is the probability you get 1) A three and a black? 2) A green or red marble? 2) An even and a red? 3) A blue or red or green marble? 89

90 4.2c Probability and Plotting Points Give Coordinate Coordinate Plane: x-axis: y-axis: Origin: Coordinate Point: Give the coordinates of points A, B, and C Give the coordinates of points E, F, and G A B E F C G 90

91 4.2d Probability and Plotting Points Plot Points To plot a point start at the and move then Negatives move the point Plot the points: A(2, 4), B( 3, 1), C(0,2), D( 3,4) Plot the points: E(1,2), F( 1,0), G(0,0) You have completed the videos for 4.2 Probability and Plotting Points. On your own paper complete the homework assignment. 91

92 4.3a Rates and Unit Rates Find Rates Rate: Amount per To set up, the word is the Rafael made $22,512 last year. What is his rate of pay per month? Giovanni covered his 2,500 square foot yard with 700 ounces of fertilizer. What is the rate of coverage the fertilizer can cover in ounces per square foot? 92

93 4.3b Rates and Unit Rates Find Unit Rate Unit Rate: Rate of per Use unit rates to identify the A 20 ounce bottle of soda sells for $1.99. What is the unit price? Lemon juice comes in a 24 oz bottle and a 32 oz bottle. The 24 oz bottle sells for $1.98 and the 32 oz bottle sells for $2.98. Which is the better deal and what is the unit price? You have completed the videos for 4.3 Rates and Unit Rates. On your own paper complete the homework assignment. 93

94 4.4a Proportions and Applications Solving Proportions To solve a proportion we both sides by the The quick method: Multiply by the 7 x = = x 3 94

95 4.4b Proportions and Applications Proportion Applications When solving applications we must first identify what we are Clearly label the and of the proportion A 65 inch tall man wants to determine how tall a large tree is. He noticed at a certain time his shadow was 14 inches long. When he measured the shadow of the tree he found it was 48 inches long. How tall is the tree? A manufacturer knows that out of every 300 parts the company ships, on average 18 are defective. If the company ships 5800 parts in a day, how many will be defective? You have completed the videos for 4.4 Proportions and Applications. On your own paper complete the homework assignment. 95

96 4.5a Introduction to Percents Convert Percents and Decimals Percent: To convert a decimal to a percent: Multiply by or move the decimal to the To convert a percent to a decimal: Divide by or move the decimal to the Convert to a percent Convert 145.6% to a decimal 96

97 4.5b Introduction to Percents Convert Percents and Fractions To convert a fraction to a percent: First then convert the to a To convert a percent to a fraction: Put the percent over and Convert 17 to a percent 20 Convert 32% to a fraction You have completed the videos for 4.5 Introduction to Percents. On your own paper complete the homework assignment. 97

98 4.6a Translate Percents and Applications Translate and Solve Key words to translate: What Is Of Percent What is 70% of 40? 45% of what is 70? 98

99 4.6b Translate Percents and Applications - Discount Discount Equation: A computer that normally costs $549 is on sale at 22% off. What is the new price of the computer? A desk that normally sells for $224 is on sale for $ What is the percent discount? 99

100 4.6c Translate Percents and Applications Sales Tax Sales Tax Equation: What is the sales tax on a $499 television if the tax rate is 8.5%? What would you pay for the TV? Marc purchased a $390 table and paid $25.35 in sales tax. What is the tax rate? 100

101 4.6d Translate Percents and Applications Commission Commission Equation: A cell phone company pays a 14% commission to its representatives. If an employee sells $23,000 worth of product in a month, how much will she be paid? A real estate agent sold $845,000 worth of properties and earned $16,900 in his commission. What is his commission rate? 101

102 4.6e Translate Percents and Applications Simple Interest Interest: Simple Interest Equation: Time must be in A bank account pays 2.1% simple interest on a certain account. If you invest $3500 for 4 years, how much will you earn in interest? A bank gives a loan with 4.5% simple interest for 9 months on a $12,000 loan. How much is owed back to the bank at the end of the loan? You have completed the videos for 4.6 Translate Percents and Applications. On your own paper complete the homework assignment. 102

103 4.7a Percents as Proportions and Applications Translate and Solve Percent Proportion: What percent of 25 is 16? 14 is 60% of what? 103

104 4.7b Percents as Proportions and Applications General Applications OF represents IS represents Among male smokers, the lifetime risk of developing lung cancer is 17.2%. According to the Washington State Department of Health, in 2011 the state had 760,000 smokers. How many are at risk of developing lung cancer in their lifetime? In 2010, women made up 58% of Big Bend Community College s students. If there were 1688 women enrolled in 2010, how many students were there total? 104

105 4.7c Percents as Proportions and Applications Percent Increase/Decrease Percent Increase/Decrease Proportions: The price of a sofa was $299. During a weekend sale the price was dropped to $179. What was the percent decrease? The population of a small town was 12,345 in This represents a decrease of 39.3% from What was the population in 1990? You have completed the videos for 4.7 Percents as Proportions and Applications. On your own paper complete the homework assignment. Congratulations! You made it through the material for Unit 4: Stats, Graphing, Proportions, and Percents. It is time to prepare for your exam. On a separate sheet of paper complete the practice test. Once you have completed the practice test, ask your instructor to take the test. Good luck! 105

106 Unit 5: Geometry and Intro to Polynomials ID: 4426 (You may use a calculator on this unit) To work through the unit you should: 1. Watch a video, as you watch, fill out the workbook (top and example sections). 2. Complete Q1 and Q2 in WAMAP, put your work in the bottom sections of the page. 3. Repeat #1 and #2 with each page until you reach. 4. Complete the homework assignment on your own paper. 5. Repeat #1-#4 until you reach the end of the unit. 6. Complete the practice test on your own paper. 7. Take the unit exam. 106

107 Conversion Factors LENGTH English 12 in = 1 ft 3 ft = 1 yd 1 mi = 5280 ft Metric (meter) 1000 mm = 1 m 100 cm = 1 m 10 dm = 1 m 1 dam = 10 m 1 hm = 100 m 1 km = 1000 m TEMPERATURE English to Metric 1 in = 2.54 cm VOLUME English Metric (liter) 8 fl oz = 1 cup (c) 2 cups (c) = 1 pint (pt) 2 pints (pt) = 1 quart (qt) 4 quarts (qt) = 1 gallon (gal) English to Metric 1 gallon (gal) = 3.79 liter (L) 1 in 3 = ml 1000 ml = 1 L 100 cl = 1 L 10 dl = 1 L 1 dal = 10 L 1 hl = 100 L 1 kl = 1000 L 1 ml = 1 cc = 1 cm 3 TIME 60 seconds (sec) = 1 minute (min) 60 minutes (min) = 1 hour (hr) 24 hours (hr) = 1 day 52 weeks = 1 year 365 days = 1 year English 16 oz = 1 pound (lb) 2,000 lb = 1 Ton (T) WEIGHT (MASS) English to Metric 2.20 lb = 1 kg Metric (gram) 1000 mg = 1 g 100 cg = 1 g 10 dg = 1 g 1 dag = 10 g 1 hg = 100 g 1 kg = 1000 g INTEREST Simple:. Continuous: A = Pe rt Compound:. Annual: n=1 Semiannual: n=2 Quarterly: n=4 107

108 Geometric Formulas Name Diagram Area Rectangle w A = lw P = 2l + 2w l Parallelogram b h A = bh Triangle h A = bh b a Trapezoid h A = h(a + b) b Circle d r A = πr 2 C = πd = 2πr Name Diagram Volume Rectangular Solid Right Circular Cylinder l r h h w V = lwh V = πr 2 h Right Circular Cone h r V = πr 2 h Sphere V = πr 3 r Right Triangle Pythagorean Theorem: a 2 + b 2 = c 2 a 108 c b

109 5.1a Convert Units One Step Conversions 57 in Consider: ( ) ( 1 ft ) = 1 12in Divide out units by placing them in the part of the fraction Conversion factor: Same in numerator and denominator, but different Dimensional analysis: Multiply by a to convert units 17.2 mi = km 88 lbs = kg 109

110 5.1b Convert Units Multi-Step Conversions If we do not have the correct conversion factor we can convert using conversion factors 365 g = lbs 5 gal = cups 110

111 5.1c Convert Units Dual Unit Conversions Dual Unit: Per is the With dual units we convert 35 mi per hr = ft per sec 45 oz per min = lbs per hr You have completed the videos for 5.1 Convert Units. On your own paper complete the homework assignment. 111

112 Geometric Formulas Name Diagram Area Rectangle w A = lw P = 2l + 2w l Parallelogram b h A = bh Triangle h A = bh b a Trapezoid h A = h(a + b) b Circle d r A = πr 2 C = πd = 2πr Name Diagram Volume Rectangular Solid Right Circular Cylinder l r h h w V = lwh V = πr 2 h Right Circular Cone h r V = πr 2 h Sphere V = πr 3 r Right Triangle Pythagorean Theorem: a 2 + b 2 = c 2 a 112 c b

113 5.2a Area, Volume, and Temperature Area of Rectangle and Parallelogram Area of a rectangle: Area of a parallelogram: Important: height must meet the base at a perfect angle Find the area: Find the area: 8 in 7 cm 9 cm 15 in 21 cm 113

114 5.2b Area, Volume, and Temperature Area of Triangle Area of a triangle: Important: height must meet the base at a perfect angle Find the area: Find the area: 5 ft 5 m 4.3 m 3 m 8 ft 6 m 114

115 5.2c Area, Volume, and Temperature Area of Trapezoid Area of a trapezoid: The bases (a and b) must be The connects the two Important: height must meet the base at a perfect angle Find the area: Find the area: 12 cm 5 in 5 cm 4 cm 5 cm 9 in 6 cm 2 in 4 in 115

116 5.2d Area, Volume, and Temperature Area of Circle Diameter: Radius: π = Area of a Circle: Find the area: Find the area: 12 cm 4 ft 116

117 5.2e Area, Volume, and Temperature Composition of Shapes If we do not have a formula for a shape we must Shapes attached to each other are Shapes cut out are Find the area: Find the area: 6 in 4 in 2 mm 9 in 117

118 5.2f Area, Volume, and Temperature Volume of a Rectangular Solid Volume of rectangular solid: Find the volume: 14 3 ft On Southwest Airlines, the maximum size of a carryon bag is a length of 24 inches, a width of 10 inches and a height of 16 inches. How much is packed in this maximum sized bag? 24 7 ft 3 2 ft 118

119 5.2g Area, Volume, and Temperature Volume of a Cylinder Volume of a cylinder: Find the volume: 6 ft A can of soda is about 5 inches tall with a diameter of 2.5 inches. How much soda can fit into the can? 8 ft 119

120 5.2h Area, Volume, and Temperature Volume of a Cone Volume of a cone: Find the volume: How much ice cream can fit inside a cone that is 5 cm tall and 3 cm wide? 24 ft 2 ft 120

121 5.2i Area, Volume, and Temperature Volume of a Sphere Volume of a sphere: Find the volume: Find the volume of the planet Pluto if the radius is approximately 1195 km. 9 ft 121

122 5.2j Area, Volume, and Temperature Composition of Solids If we do not have a formula for a shape we must Find the volume 4 ft 10 ft Q 1: 122

123 5.2k Area, Volume, and Temperature Convert Temperature Formulas to convert temperature: C = F = 98.6ᵒ F is body temperature. Find body temperature in degrees Celsius. 100ᵒ C is the boiling point of water. Find at what temperature water boils in degrees Fahrenheit. You have completed the videos for 5.2 Area, Volume, and Temperature. On your own paper complete the homework assignment. 123

124 5.3a Pythagorean Theorem Square Roots Square root asks the question what number is the inside number? 25 = On calculator use the button (may have to use the or button first)

125 5.3b Pythagorean Theorem Find Missing Side Name the sides of the right triangle: Pythagorean Theorem: C is always the When finding a leg with the Pythagorean theorem, first then Find the missing side: Find the missing side: 4 cm 7 yds 8 cm 2 yds 125

126 5.3c Pythagorean Theorem Applications With applications it is always helpful to The base of a ladder is four feet from a building. The top of the ladder is eight feet up the building. How long is the ladder? A young boy is flying a kite. He let out 21 meters of string until the kite was flying over the head of his sister who was 9 meters away. How high is the kite? You have completed the videos for 5.3 Pythagorean Theorem. On your own paper complete the homework assignment. 126

127 5.4a Introduction to Polynomials Add Polynomials Term: Monomial: Binomial: Trinomial: Polynomial: Adding Polynomials: the (4x 3 2x 2 + x) + ( 3x 2 5x + 7) (3ab 3 2a 2 b + ab) + (4a 2 b 2ab 3 + 4ab) 127

128 5.4b Introduction to Polynomials Subtract Polynomials First the. Then (3x 2 7x + 8) (2x 2 + 9x 4) (2x 8y + 6) ( 3y 7 + 5x) 128

129 5.4c Introduction to Polynomials Multiply Monomials Consider a 3 a 2 = When multiplying variables we the exponents If there is no exponent, then we assume the exponent is a (4x 3 y 2 z)(2x 7 yz 4 ) 7a 3 b 2 c 4 2ab 8 c 4 129

130 5.4d Introduction to Polynomials Multiply a Monomial by a Polynomial Consider: 5(3x 6) = When multiplying a monomial by a polynomial we 5x 3 (3x 2 4x + 2) 2a 3 b(5ab 4 6a 2 b 7 + 2a 4 ) You have completed the videos for 5.4 Introduction to Polynomials. On your own paper complete the homework assignment. 130

131 5.5a Scientific Notation Convert Scientific Notation to Standard Notation Scientific Notation: a 10 b a is greater than or equal to but less than. This means the decimal is always after the digit b tells us how many times to the decimal If b is negative, then standard notation is. If b is positive, then standard notation is Convert to standard notation: Convert to standard notation:

132 5.5b Scientific Notation Convert Standard Notation to Scientific Notation To convert to scientific notation the number of times the must move If standard notation is small then the exponent is if it is big then the exponent is When converting we will the extra Convert to scientific notation: 48,100,000,000 Convert to scientific notation You have completed the videos for 5.5 Scientific Notation. On your own paper complete the homework assignment. Congratulations! You made it through the material for Unit 5: Geometry and Intro to Polynomials. It is time to prepare for your exam. On a separate sheet of paper complete the practice test. Once you have completed the practice test, ask your instructor to take the test. Good luck! 132

133 Unit 6: Proficiency Exam #1 ID: 4427 To work through this unit you should: 1. Complete the practice tests on your own paper. NOTE: There are three parts to the practice test Part A, B, and C. 2. Take the (three part) unit exam. 133

134 Unit 7: Linear Equations and Applications ID: 8107 To work through the unit you should: 1. Watch a video, as you watch, fill out the workbook (top and example sections). 2. Complete Q1 and Q2 in WAMAP, put your work in the bottom sections of the page. 3. Repeat #1 and #2 with each page until you reach. 4. Complete the homework assignment on your own paper. 5. Repeat #1-#4 until you reach the end of the unit. 6. Complete the practice test on your own paper. 7. Take the unit exam. 134

135 7.1a Order of Operations The Order The Order: To remember: 5 3( ) 30 5( 2) + (4 7) 2 135

136 7.1b Order of Operations Lots of Parentheses Different types of parenthesis: Always do first! (4 + 2) [5 2 (2 + 3)] 7{2 + 2[20 (4 + 6)]} 136

137 7.1c Order of Operations Fractions When simplifying fractions, always simplify and first Only reduce after the rest has been (4 + 5)(2 9) 2 3 ( ) 4 2 ( ) 5 + 3(5 4) 137

138 7.1d Order of Operations Absolute Value Absolute values works just like but makes the number inside after it has been (5 + 4) ( ) You have completed the videos for 7.1 Order of Operations. On your own paper complete the homework assignment. 138

139 7.2a Evaluate and Simplify Algebraic Expressions Substitute a Value Replace the with what it Whenever we make a substitution or put it in Evaluate 4x 2 3x + 2 When x = 3 Evaluate 4b(2x + 3y) When b = 2, x = 5, y = 7 139

140 7.2b Evaluate and Simplify Algebraic Expressions Combine Like Terms Terms are and that are together Like terms are terms that have matching and Combine like terms: the coefficients from the. 4x 3 2x 2 + 5x 3 + 2x 4x 2 6x 4y 2x + 5 6y + 7y 9 140

141 7.2c Evaluate and Simplify Algebraic Expressions Distributive Property Distributive Property: a(b + c) = 2(5x 4y + 3) 4(7x 2 6x + 1) 141

142 7.2d Evaluate and Simplify Algebraic Expressions Distribute and Combine Like Terms Order of operations states we before we Therefore we will first and then second 4(3x 7) 7(2x 1) 2(7x 3) (8x + 9) You have completed the videos for 7.2 Evaluate and Simplify Algebraic Expressions. On your own paper complete the homework assignment. 142

143 7.3a Solve Linear Equations Variable on Both Sides Move the variable to one side by Solve remaining two step equation by first and second. 3x + 4 = 16 8x 2x 7 = 8x 9 143

144 7.3b Solve Linear Equations Simplify First The first step of solving is to each side We can simplify by and 3(2x 6) + 8 = 17 12x 5(3x 1) = 4 + 3(2x + 1) 144

145 7.3c Solve Linear Equations - Fractions Clear fractions by by the Be sure to multiply term on sides 3 4 x 1 2 = x 7 10 = x 145

146 7.3d Solve Linear Equations Special Cases Sometimes the variable! This means there is either or 2x + 5 = 2x 1 3x 9 = 3(x 3) Example 3: 6x + 2 = 3(2x + 1) Example 4: 4x + 1 = 2(2x + 3) 5 You have completed the videos for 7.3 Solve Linear Equations. On your own paper complete the homework assignment. 146

147 7.4a Formulas Two Step Formulas Solving formulas: Treat other variables like Final answer is an Example: 3x = 15 and wx = y Solve wx + b = y for x Solve ab + 5y = wx + y for b 147

148 7.4b Formulas Multi-Step Formulas Strategy: IMPORTANT: Terms reduce Solve a(3x + b) = by for x Solve 3(a + 2b) + 5b = 2a + b for a 148

149 7.4c Formulas Fractions and Formulas Clear fractions by Solve 5 x + 4a = b x for x Solve A = 1 2 hb hb 2 for b 1 You have completed the videos for 7.4 Formulas. On your own paper complete the homework assignment. 149

150 7.5a Word Problems - Number Translate: Is/Were/Was/Will Be: More than: Subtracted from/less than: Five less than three times a number is nineteen. What is the number? Seven more than twice a number is six less than three times the same number. What is the number? 150

151 7.5b Word Problems Consecutive Integers Consecutive Numbers: First: Second: Third: Find three consecutive numbers whose sum is 543. Find four consecutive integers whose sum is

152 7.5c Word Problems Consecutive Even/Odd Integers Consecutive Even: First: Second: Third: Find three consecutive even integers whose sum is 84 Consecutive Odd: First: Second: Third: Find four consecutive odd integers whose sum is

153 7.5d Word Problems - Triangles The angles of a triangle add to Two angles of a triangle are the same measure. The third angle is 30 degrees less than the first. Find the three angles. The second angle of a triangle measures twice the first. The third angle is 30 degrees more than the second. Find the three angles. 153

154 7.5e Word Problems - Perimeter Formula for perimeter of a rectangle: Width is the side A rectangle is three times as long as it is wide. If the perimeter is 112 cm, what is the length? The width of a rectangle is 6 cm less than the length. If the perimeter is 52 cm, what is the width? You have completed the videos for 7.5 Word Problems. On your own paper complete the homework assignment. 154

155 7.6a Age Problems Unknown Now Table: Equation is always for the Alexis is five years younger than Brian. In seven years the sum of their ages will be 49 years. How old is each now? Maria is ten years older than Sonia. Eight years ago Maria was three times Sonia s age. How old is each now? 155

156 7.6b Age Problems Given the Sum Now Consider: Sum of 8.. When we have the sum now, for the first box we use and the second we use The sum of the ages of a man and his son is 82 years. How old is each if 11 years ago, the man was twice his son s age? The sum of the ages of a woman and her daughter is 38 years. How old is each if the woman will be triple her daughter s age in 9 years? 156

157 7.6c Age Problems Unknown Time If we don t know the time: A man is 23 years old. His sister is 11 years old. How many years ago was the man triple his sister s age? A woman is 11 years old. Her cousin is 32 years old. How many years until her cousin is double her age? You have completed the videos for 7.6 Age Problems. On your own paper complete the homework assignment. 157

158 7.7a Distance, Rate, Time Problems Opposite Directions The distance equation: Opposite directions: OR Brian and Jennifer both leave the convention at the same time, traveling in opposite directions. Brian drove 35 mph and Jennifer drove 50 mph. After how much time were they 340 miles apart? Maria and Tristan are 126 miles apart biking towards each other. If Maria bikes 6 mph faster than Tristan and they meet after 3 hours, how fast did each ride? 158

159 7.7b Distance, Rate, Time Problems Catch Up the head start to the of the person with the head start Catch up: Raquel left the party traveling 5 mph. Four hours later Nick left to catch up with her, traveling 7 mph. How long will it take him to catch up with her? Trey left on a trip traveling 20 mph. Julian left 2 hours later, traveling in the same direction at 30 mph. After how many hours does Julian pass Trey? 159

160 7.7c Distance, Rate, Time Problems Total Time Consider: Total time of 8.. When we have the total time, we use for the first time and for the second Lupe rode into the forest at 10 mph, turned around and returned by the same route traveling 15 mph. If her trip took 5 hours, how long did she travel at each rate? Ian went on a 230 mile trip. He started driving 45 mph. However, due to construction on the second leg of the trip, he had to slow down to 25 mph. If the trip took 6 hours, how long did he drive at each speed? You have completed the videos for 7.7 Distance, Rate, Time Problems. On your own paper complete the homework assignment. Congratulations! You made it through the material for Unit 7: Linear Equations and Applications. It is time to prepare for your exam. On a separate sheet of paper complete the practice test. Once you have completed the practice test, ask your instructor to take the test. Good luck! 160