SUMMER PACKET Accelerated Algebra

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1 Acc Alg 1.5 Name SUMMER PACKET Accelerated Algebra Teacher: Mr. Tesoriero 1

2 Welcome to Accelerated Algebra 1.5! I. The problems in this packet are designed to help review the topics from previous mathematics courses that are important to your success in Accelerated Algebra 1.5. Please complete each problem, as they are topics you will need to know for the course. II. One resource you may use to help you is the online textbook. Focus on chapters 1-8. You can access the book at the web address below. III. Online resources you may use include, but are not limited to: Check out for videos that help review specific topics. Click on link and "browse the library" IV. You may questions to your teacher. will be checked weekly over the summer. V. Pacing: Below is a suggested time frame for completion. Please manage your time wisely. Fall Semester Pages #1-3 End of June Pages #4-5 End of July Pages #6-7 August VI. VII. Bring the completed summer packet to class on the first day of school, at which time the packet will be given credit. Within the first week of school a test will be given on the material from the packet. Be prepared! All math courses at the high school require the use of a graphing calculator. The teacher will model the use of the TI-83, TI-83+, TI-84, or TI-84+ model. You are free to purchase from a different company, or a different model. However, you will need to know how to use the brand you choose. 2

3 Solve each equation below. Show complete steps and write your answer in the blank at the right. 1. 3x 4 = 5x k + 3 4k + 7 = 2k p + 7 (-3) = p + (-2) (2x+5) = -2 + (x-3) (4y-17) + (-y) = (2y -1) (-y) 6. -3(2-c) = c (6x-5) = 4(7x-8) (7-9)x-6x=8(-6+2) Find the probability or odds for each problem below. Write your answers in the blanks provided. 9. A bowl contains 5 red chips, 7 blue chips, 6 yellow chips, and 10 green chips. One chip is randomly drawn. Find P(blue) Find P(not green) A weather forecast states that the probability of rain the next day is 40%. What are the odds that it will rain? 11. 3

4 12. The Uptown Deli offers a lunch special in which you can choose a sandwich, a side dish, and a beverage. If there are 10 different sandwiches, 12 different side dishes, and 7 different beverages from which to choose, how many different lunch specials can you order? The weather forecast for the weekend calls for a 40% chance of rain on Saturday and an 80% chance of rain on Sunday. What is the probability that it will rain on both Saturday and Sunday? A bag contains 8 red marbles, 9 yellow marbles, and 11 green marbles. Three marbles are randomly drawn from the bag and not replaced. Find the probability if the marbles are drawn in order. P(red, yellow, green) During a magic trick, a magician randomly draws one card from a standard deck of cards. What is the probability that the card drawn is a heart or a diamond? During a magic trick, a magician randomly draws one card from a standard deck of cards. What is the probability that the card drawn is a heart or a King? 16. Determine whether each relation is a function. Explain your answer. 17. {(-2, 6), (0, -2), (3, 6), (-2, 1)} x y

5 19. Use the vertical line test to determine if the following is a function. Then state the domain and range. 19. a) b) 20. If f(x) = -5x + 1, find each value. a) f(1) b) f(-2.5) c) f(5b) 20. a) b) c) 21. The number of miles traveled varies directly as the hours traveled. On a recent trip, Liz drove miles during the first 3.5 hours of her trip. If she maintains the same speed, how many miles will she travel during the next 6 hours of her trip? Water can be measured in liquid measure, in units such as gallons, and it can also be measured by volume, in units such as cubic inches. The number of cubic inches varies directly as the number of gallons of water. If a container of water measuring 693 cubic inches holds 3 gallons of water, how many cubic inches are needed for a container that holds 15 gallons? The number of painters needed to paint the Pioneer Inn, an apartment building for retired citizens, varies inversely as the number of days needed to complete the project. Suppose 3 painters can paint the building in 21 days. How many days will it take 6 painters to paint the building? Assume that they all work at the same rate In the formula d = rt, the time t varies inversely as the rate r. Two of the world s slowest creatures are spiders and chickens. Suppose a spider traveled at its maximum speed of 1.2 miles per hour for 3 hours. Find the maximum speed of a chicken if it traveled the same distance in 24 minutes at its maximum speed. 24.

6 Find slope for each problem below. 25. (2, 6) (3, 3) 26. (-6, -4) (-1, -4) 27. (1, -2) (6, 0) Write an equation in Point-Slope Form for each: 28. (5, 6), m = (-3, 1), m = (-4, 8), m = Write an equation in Slope-Intercept Form for each: 31. (1, 5) & (2, 8) 32. (3, 1) & (-7, 11) 33. (-4, 0) & (2, 3) A disk jockey notices that as the music gets faster, more people start dancing. Would a scatter plot showing speed of music and numbers of dancers have a positive relationship, negative relationship, or no relationship? EXPLAIN. 35. Determine the x-intercept and y-intercept of each equation. Then graph the line. a) x + 3 y = 6 6

7 b) 2 x y = Graph each line using the slope & y-intercept from the equation. a) y = x + 5 b) y = 2 x + 3 c) 2 x 4 y = Determine whether each pair of lines is Parallel, Perpendicular, or Neither. Explain why. 1 a) y = 4x + 9 & y = x 6 b) 2 x = y 3 & 2x 4 = y c) y 4 = x & 3x = y Write an equation in slope-intercept form of the line that is a. Parallel to the line y = 2 x + 5, and passes through the point (2, -3). Are these 2 lines a family? b. Perpendicular to the line y = 2 x + 5, and passes through the point (2, -3). Are these 2 lines a family? 7

8 39. Use the data below to draw a scatter plot. Label each axis. North Latitude January Low-mean temperature ( F ) a) Plot the data on the graph. b) Fit a line of best fit by sight. (use a ruler) c) Pick 2 points on your line. d) Use your 2 points to find the equation of your line. e) What is the January mean-low temperature for Acapulco, located at 17 degrees North Latitude. Simplify each of the following. Write your answer in the blank provided q r 41. m m 2 5 t t a 4 5a b 2 b 6 6 c x 10x 3 y 3 y 5 5 z h 3 25h k k

9 Use the Pythagorean Theorem to solve the following problems. Write your answers in the blanks provided. 45. Find the length of one leg of a right triangle if the length of the hypotenuse is 35 feet and the length of the other leg is 22 feet. Round to the nearest tenth Suppose a carpenter measures along one side of a deck, a distance of 9ft, and along the adjacent side, a distance of 12ft. The measure of the third side is 15ft. Is the corner of the deck square? When laying out a rectangular driveway, a concrete worker measures along one side a distance of 16ft and along the adjacent side a distance of 30ft. How could we determine if the corners of the driveway were square? Draw a picture & find this number TV sets are measured by the diagonal length of the screen. A 25-inch TV set has a diagonal that measures 25 inches. If the height of the screen is 15 inches, how wide is the screen? The radio tower shown is 130 meters tall. Four support wires are attached 10 meters from the top of the tower. The wires are attached to concrete anchors 50 meters from the base of the tower. How much wire is needed for all four support wires? 49. 9