Study Island Algebra 2 4/13/15

Transcription

1 Study Island Algebra 2 4/13/15 Scatter Plots 1. Fred graphed how long it takes to get through the grocery store line in relation to the number of registers that are open. What is the equation of the line of best fit above? Symbolic Algebra 2. Moore's law states that the number of transistors per integrated circuit, which indicates the processing power of a computer, doubles every year. The graph below shows information about the processing power of a computer by year.

2 Which equation below shows the processing power of a computer by year, where y is the number of transistors and x is the number of years since 1965? y = 60(2) x y = 60(2) -x y = 2(60) x y = 2 x Generalize Patterns 3. What is the recursive formula for this sequence? 15, 23, 39, 63, 95,... a 1 = 15, a n = a n-1 + 8(n) a 1 = 15, a n = a n a 1 = 15, a n = 8(a n-1 ) + (n-1) a 1 = 15, a n = a n-1 + 8(n-1) Algebraic Expressions 4. If x = 3 and y = 2, what is the value of the following expression?

3 Linear & Absolute Value Functions 5. Solve the following inequality for x. Algebraic Expressions 6. Rewrite the following expression with only positive exponents. x -4 y -6 z -12 x 4 y 12 z -6 1 x 8 y 18 z 18 1 y 6 z 6 z 6 x 8 y 18 1 x 8 y 18 z 6 Systems of Equations & Inequalities 7. Five pounds of cashews and seven pounds of peanuts cost $ Three pounds of cashews and nine pounds of peanuts cost $ Which system of equations can be used to determine the cost per pound of cashews, x, and the cost per pound of peanuts, y? 5x + 7y = x + 9y = x - 5y = x - 9y = y = 5x x + 9y = x + 7y = x + 3y = Symbolic Algebra

4 8. A ball is thrown straight down from the top of a building at a velocity of 16 ft/s. The building is 320 feet tall, and the acceleration due to gravity is 32 ft/s 2. This problem can be represented using the following equation. ( 1 / 2 )32t t = 320 How much time will the ball take to reach the ground? 8 seconds 5 seconds 4 seconds 10 seconds Symbolic Algebra 9. A rocket accelerates straight up from rest with a constant acceleration of 400 m/s 2. How long will it take the rocket to reach an altitude of 9,800 meters? This problem can be represented using the following equation. ( 1 / 2 )400t 2 = 9, seconds 7 seconds 5 seconds 9 seconds Generalize Patterns 10. What is the recursive formula for this sequence? 26, 22, 14, 2, -14,... a 1 = 26, a n = a n-1-4(n) a 1 = 26, a n = a n-1-4(n-1) a 1 = 26, a n = a n-1-4 a 1 = 26, a n = 4(a n-1 ) - (n-1) Generalize Patterns 11. What is the recursive formula for this sequence? 3, 6, 12, 21, 33,... a 1 = 3, a n = 3(a n-1 ) + (n-1) a 1 = 3, a n = a n-1 + 3(n) a 1 = 3, a n = a n-1 + 3(n-1) a 1 = 3, a n = a n-1 + 3

5 Systems of Equations & Inequalities x + 3y = -9-3x - 3y = 6 Find the solution to the system of equations shown above by graphing. x = 2, y = -3 x = 0.6, y = -2.6 x = -3, y = 3 x = -2, y = 2 Linear & Absolute Value Functions 13. Solve. Algebraic Expressions 14. Evaluate the expression below for x = 1 and y = Linear & Absolute Value Functions 15. Solve the following inequality for x. x > 4 x > x < -4.5x x < x < 4 Systems of Equations & Inequalities 16. Solve the following system of equations. x = 10, y = -4 x = -4, y = 10-2x + 4y = 48 x + 4y = 36 x = 2, y = 13 x = 8, y = 7

6 Scatter Plots 17. Choose the equation below which would be the line of best fit for the scatter plot. y = 4x y = 2x y = x y = 3x Algebraic Expressions 18. x 1/ 2 Which of the following expressions is equivalent to the expression above? (x) 1 / 2 x x -2 (x) Algebraic Expressions 19. Simplify the expression below.

7 x 7 y 5 z -5 w -7 x 10 y -1 z -7 x17 y 13 z -12 w -7 w7 y 6 z 2 x 3 x-3 y 6 z 2 w 7 y6 z 2 w -7 x 3 Symbolic Algebra 20. The equation A = x(x - 4) describes the area, A, of a rectangular flower garden, where x is the width in feet. What would be the width in feet of the flower garden if the area is 21 square feet? Algebraic Expressions 21. Rewrite the following expression with only positive exponents. 2-4 x -2 y 2 z -4 z -4 y x 2 y2 z x 2 y x 2 z 8 y x 2 z 16 Systems of Equations & Inequalities 22. Chuck and Betsy are going on a trip to the state park. They want to be out there for no more than 8 hours, and they also want to travel at least 30 miles. They can hike at a rate of 3 mph, and they can canoe at a rate of 6 mph. If the solution region is the amount of time they spend hiking and canoeing so that they can meet their goals, which graph's shaded area represents the solution region?

8 W. X. Y. Z. Y X W Z Generalize Patterns 23. The first five terms of a sequence are given below. 28, 31, 34, 37, 40,... Determine which of the following formulas gives the n th term of this sequence. 30-2n n n 31-3n Systems of Equations & Inequalities 24. Mandy's Candies is most famous for their homemade fudge and homemade toffee. They make an average of 144 pounds of fudge and toffee combined each month. They sell a pound of fudge for $8.66 and a pound of

9 toffee for $7.24. Mandy's averages $1, each month in fudge and toffee sales. On average, how many pounds each of fudge and toffee does Mandy's Candies sell in one month? 66 fudge; 78 toffee 72 fudge; 72 toffee 69 fudge; 75 toffee 55 fudge; 89 toffee Linear & Absolute Value Functions 25. Solve for x. Scatter Plots 26. The graph above shows a line of best fit for data collected on the amount of student loans in relation to the number of years it takes to pay them back. What is the equation of the line of best fit? Systems of Equations & Inequalities 27. Find the solution to the system of equations given below using elimination by addition.

10 x = 7, y = 2 18x + 9y = 108 6x - 3y = 48 x = 10, y = 4 x = -7, y = 18 x = 7, y = -2 Linear & Absolute Value Functions 28. Solve for x. Scatter Plots 29. Choose the equation below which would be the line of best fit for the scatter plot. y = - 1 / 4 x + 6 y = - 1 / 2 x + 6 y = - 1 / 2 x + 5 y = - 1 / 4 x + 3 Generalize Patterns

11 30. Find the fifth term in the recursively defined sequence below if a 1 = 1. a n = 2 a n Scatter Plots 31. Cleaning Supplies, Inc., is a company that sells cleaning supplies to professional cleaning companies. The scatter plot below shows the profit of Cleaning Supplies, Inc., for each year over a nine-year period beginning in Which quadratic equation best represents the data? y = x x y = x x y = 11.42x x y = 11.15x x Scatter Plots

12 32. The graph above shows a line of best fit for the data collected at a batting cage for the number of hits in relation to the speed of the pitch. What is the equation of the line of best fit? Linear & Absolute Value Functions 33. Solve. 4 x - 6 = 16 { 6, 10 } { 2, 10 } { -4, 10 } { -10, -2 } Symbolic Algebra 34. John is 7 years older than Sam and the product of their ages is 260. How old is Sam? 13 years old 15 years old 12 years old 20 years old

13 Symbolic Algebra 35. On the Richter scale, the magnitude R of an earthquake of intensity I is given by R = log ( I ) I 0 where I 0 = 1 is the minimum intensity used for comparison. What would an earthquake with an intensity of 178,810,000 register on the Richter scale? Generalize Patterns 36. Define the sequence below recursively. a 1 = 1 a n = a n-1 + 1/3 a 1 = 1 a n = a n-1 + (1/3) n a 1 = 1 a n = 1 / 3 a n-1 a 1 = 1 a n = a n-1 + 1/3 n 1, 1 1 / 3, 1 2 / 3, 2, 2 1 / 3, 2 2 / 3, 3, 3 1 / 3...