CCA Ch 10: Solving Comple Equations Name Team # 10.1.1 What can I tell from a survey? Association in Two-Way Tables 10-1. a. c. d. d. 10-. a. Complete the following two-way table: Laptop No Laptop TOTAL π Phone 8 No π Phone 110 TOTAL 44 175 b. Similarities between Venn & Table: Differences between Venn & Table: c. i. Probability of π Phone OR Laptop? ii. Probability of π Phone AND Laptop?
10-3. Probability of a Laptop owner to own a π Phone: Probability of a non-laptop owner to own a π Phone: Is there an association between owning a Laptop and owning a π Phone? 10-4. a. Complete the following two-way table: Boys Girls TOTAL A s Not A s TOTAL b. Is it more likely for a boy to receive an A than a girl? c. Complete the following relative frequency table: Boys Girls A s Not A s 10-5. Two-Way Table: (# of people (in millions)) Relative Frequency Table: Has DapT Doesn t Have DapT Has DapT Doesn t Have DapT Type O 0.30 137 Type O Type A 0.8 131 Type B 0.07 31 Type AB 0.03 1 TOTAL Type A Type B Type AB
Is there an association between blood type and the presence of the DapT defect? 10-6. Age: Under 5 5 to 34 35 to 44 45 to 54 55 to 64 65 to 74 Over 75 TOTAL Living Alone (millions) Living with others (millions) TOTAL 1.45 4.16 3.55 5.57 6.69 4.81 6.50 109.67 37.41 36.8 38.37 30.8 16.59 11.6 a. Why is this called a two-way table? b. What is the probability of living alone? c. What is the probability of being 65 or over? d. What is the probability of being under 65? e. What is the probability of being under 35 AND living alone? f. What did Qui do wrong when calculating the probability of being under 35 OR living alone?
10-7. Relative Frequency Table: Age: Under 5 5 to 34 35 to 44 45 to 54 55 to 64 65 to 74 Over 75 Living Alone (millions) Living with others (millions) Is there an association between age and living alone? 10-8. a. Complete a two-way table: Eat 5 servings of Fruits & Vegetables Don t eat 5 servings of Fruits & Vegetables Eercise No Eercise TOTAL TOTAL b. Probability of Eercising AND Eating Fruits and Vegetables: c. Probability of Eercising OR Eating Fruits and Vegetables:
d. Complete a relative frequency table: Eat 5 servings of Fruits & Vegetables Don t eat 5 servings of Fruits & Vegetables Eercise No Eercise Is there an association between eercising and eating 5 servings of fruits and vegetables? 10-9. a. Two-Way Table: Relative Frequency Table: Early Curfew Late Curfew Early Curfew Late Curfew Chores 9 0 No Chores 9 9 TOTAL Chores No Chores b. Is there an association between curfew and chores? (Does having an early or late curfew affect whether or not a student does chores?) c. Two-Way Table: Relative Frequency Table: Chores No Chores Chores No Chores Early Curfew 9 9 Late Curfew 0 9 TOTAL Early Curfew Late Curfew Is there an association between chores and curfew? (Does having to do chores or not affect whether or not a student has an early or late curfew?)
Does changing the independent variable change your conclusions about association? d. Two-Way Table: Relative Frequency Table: Early Curfew Late Curfew Early Curfew Late Curfew Chores 6 3 No Chores 1 6 TOTAL Chores No Chores Is there an association between curfew and chores? (Does having an early or late curfew affect whether or not a student does chores?) Two-Way Table: Relative Frequency Table: Chores No Chores Chores No Chores Early Curfew 6 1 Late Curfew 3 6 TOTAL Early Curfew Late Curfew Is there an association between chores and curfew? (Does having to do chores or not affect whether or not a student has an early or late curfew?) e. What is interesting about the relative frequency tables that have no association?
10..1 How can I solve it? Solving by Rewriting 10-. a. What is Claudia talking about? Rewrite the equation so it has no decimals: b. Solve the new equation by factoring. Check your solutions. 10-3. SOLVING BY REWRITING a. 3 3 3 5 3 7 b. 9000 6000 15000 0 1 10 c. 3 3 3 d. 4.5 0
10-4. a. What were the boys thinking? Will both methods work? 4 b. 4 4 4 4 c. 5 3 9 10-5. a. 3 b. 3 3 1 3 c. 40 9 3 d. 70 8 10-6. a. Change your equation to a harder one. b. Verify that your harder equation gives you the same answer as your easier equation. c. Write your harder equation on the board. d. Copy down the equations generated by your class. You will need to solve these for homework.
10.. How can I solve it? Fraction Busters 10-34. a. Multiply each term in the equation by 6. 5 6 8 4 b. How can you change your equation from part (a) to eliminate all fractions? Do it and solve. What happened? Do any fractions remain? c/d. What could you have multiplied the original equation by to eliminate all the fractions all at once? Do it and solve. Do you get the same answer as part (b)? 10-35. a. Solve the equation by eliminating the fractions. 5 15 5 3 b. What number did you multiply by? How did you choose that number? Is it the smallest number that would eliminate all the fractions? Are there any other numbers that would work?
10-36. a. 3 4 6 b. 5 3 c. d. 1 3 3 7 8 3 5 10-37. Looking at the original problems in #10-36 parts (b) and (d), what values of cannot be allowed? 10-38. a. 50 00 150 a 9 a 3 b. 1
c. 1.m 0. 3.8 m d. 3 1 4 3 0 10..3 How can I solve it? Multiple Methods for Solving Equations 10-46. DIFFERENT METHODS TO SOLVE AN EQUATION Solve 4 3 0 Solve using a different method: 4 3 0 10-47. FURTHER GUIDANCE SOLVING BY REWRITING (Use this problem only if needed.) Solve by distributing the 4 first: 4 3 0 10-48. FURTHER GUIDANCE SOLVING BY UNDOING (Use this problem only if needed.) a. What can Juan do to remove the 4? b. Solve using Juan s method: 4 3 0 c. Why is it appropriate for this method to be called undoing?
10-49. FURTHER GUIDANCE SOLVING BY LOOKING INSIDE (Use this problem only if needed.) a. Why must the epression inside the parentheses equal 5? b. Write an equation comparing the inside epression = 5 then solve. 10-50. THE THREE METHODS a. Read the Math Notes on the net page with your team. b. Match the names of approaches with the eamples. 1. Rewriting. Looking Inside 3. Undoing 10-51. Which method (Rewriting, Looking Inside, or Undoing)? a. b. 8 10 6 4 3 9 c. 3 3 6 d. 7 7 3 3 e. 4 9 f. 3 9 6 10-5. a. Solve by rewriting: 7 9 Solve by Looking Inside: 7 9 Solve by Undoing: 7 9 b. Did you get the same solution from each method? If not, why not? c. Which method was the most efficient? Why?
10..4 How many solutions? Determining the Number of Solutions 10-60. THE NUMBER OF SOLUTIONS 7 5 a. 4 0 b. c. 3 49 d. 5 10 0 e. 10 f. 11 5 5 10-61. a. 5m 6 0 number of solutions: 10-6. 4 n 0 b. number of solutions: c. 11 7 number of solutions: a. 3 0 b. 1 c.
10-63. a. 9 4 6 y 3 b. 8 1 y 10-64. Use your graph and table in your graphing calculator to check your solutions to #6 part (a). 10-65. a. 5 9 b. c. 10-66. LEARNING LOG Number of Solutions
10..5 What kinds of numbers are there? Deriving the Quadratic Formula and the Number System 10-74. DERIVATION OF THE QUADRATIC FORMULA STEPS: Solve the equation a b c 0. REASONS: 1. a b c 1.. b c a a. 3. Draw a generic rectangle to complete the square: 3. 4. 5. b b c a 4a a b c b a a 4a 4. 5. 6. 7. b b c a 4a a b b 4ac Now solve for! a 4a 6. 7. 8. b b 4ac a 4a 8. 9. 4 b b ac a a 9. 10. 4 b b ac a a 10. 11. b b 4ac a 11. Simplify the result.
10-75. Use the Quadratic Formula to determine how many -intercepts. a. 8 14 15 y b. 8 0.5 y 3 c. 10 30 y d. 4 4 1 y 10-76. IMAGINARY NUMBERS a. Graph 0 1. How many solutions? c. Imaginary Numbers = b. Solve 0 1 algebraically. d. Solve 81 0 algebraically.
10-77. Use the Quadratic Formula to solve k 10k 30. 10-78. Consider 7 5. How many solutions and what kind of solutions does this equation have? 10-79. a. Are the rational numbers a closed set under multiplication? (Is a rational number a rational number always = a rational number?) Are the rational numbers a closed set under addition? (Is a rational number + a rational number always = a rational number?) b. What is the area of the triangle? What is the perimeter of the triangle? c. Was the perimeter from (b) rational or irrational? How do you know?
d. If you multiply a rational number an irrational number, will the result be rational or irrational? How do you know? 10-80. LEARNING LOG The Number System Define the following in your own words: integer = rational numbers = irrational numbers = real numbers = imaginary numbers = 10..6 Which method is best? More Solving and an Application 10-88. Solve the equations. a. 4 0 8 b. 3 13 8
c. 4 14 d. 6 8 4 14 e. 3 1 7 f. 9 6 36 10-89. RUB A DUB DUB
10.3.1 Intercept or intersect? Intersection of Two Functions 10-97. a. Name all - and y-intercepts for the parabola. b. Name all the - and y-intercepts for the line. c. Where do the parabola and the line intersect? d. How are the words intersect and intercept alike? How are the words intersect and intercept different? 10-98. a. Intercept or Intersect? b. Intercept or Intersect? c. Intercept or Intersect? Why? Why? Why?
10-99. a. b. 10-100. Solve algebraically. Confirm by graphing on your graphing calculator: y 1 y 1 10-101. Solve algebraically. Confirm by graphing on your graphing calculator: y 1 y 4 5 10-10. LEARNING LOG Intercepts and Intersections
Eplain the difference between intercepts and intersections. Include a sketch or graph as an eample. 10-103. In problem #10-99, you already solved 3 10. How do the graphs of y 3 10 and y help ou find the solutions? Eplain. 10-104. Solve the system algebraically. y.6 0.45 y 1 Graph to confirm your solution(s). y 10-105.
Looking back at #10-104, what is the solution to 0.45 1? Verify by evaluating (not solving). 10-106. How many solutions are there to: 3 7 0.7 4 38 6? 4 Estimate the solution(s) using the graph. 10.3. How many points of intersection? Number of Parabola Intersections 10-10. Find the solution(s) to the system: y 3 y 1 10-11. How many different intersection points can a line and a parabola have? a. A line and a parabola that intersect twice. y How many intersection points can two parabolas have? Do two parabolas always intersect?
b. A line and a parabola that intersect once. c. A line and a parabola that intersect more than y twice. y d. Two parabolas that intersect twice. e. Two parabolas that have infinite intersection y points. y f. Two parabolas that never intersect. g. Two parabolas that intersect only once. y y 10-1. HOW MANY INTERSECTIONS?
Solve your system algebraically. 10-13. ALGEBRA COMES TO THE RESCUE! a. Help Darrel solve the system on your graphing y 5 calculator: y 4 3 b. Solve the system algebraically to be sure. How many solutions are there? 10.3.3 How can I solve the inequality? Solving Quadratic and Absolute Value Inequalities 10-131. a. Solve and graph 7 1. 10 9 8 7 6 5 4 3 1 0 1 3 4 5 6 7 8 9 10 What is the boundary point? Is it part of the solution? Why or why not?
b. In general, how do you find a boundary point? How do you find the solutions of an inequality after you have found the boundary point? 10-13. a. Solve and graph 3. 10 9 8 7 6 5 4 3 1 0 1 3 4 5 6 7 8 9 10 b. How was solving 3 different from solving 7 1? 10-133. FOG CITY 10-134.
a. 1 b. 1 0 10 9 8 7 6 5 4 3 1 0 1 3 4 5 6 7 8 9 10 10 9 8 7 6 5 4 3 1 0 1 3 4 5 6 7 8 9 10 c. 1 0 d. 9 4 6 10 9 8 7 6 5 4 3 1 0 1 3 4 5 6 7 8 9 10 10 9 8 7 6 5 4 3 1 0 1 3 4 5 6 7 8 9 10
e. 3 11 f. 7 10 9 8 7 6 5 4 3 1 0 1 3 4 5 6 7 8 9 10 10 9 8 7 6 5 4 3 1 0 1 3 4 5 6 7 8 9 10 10-135. PULLING IT TOGETHER Solve and graph 5 6 4 0 10 9 8 7 6 5 4 3 1 0 1 3 4 5 6 7 8 9 10 10-136. LEARNING LOG Solving Inequalities with Absolute Value