Geometry Cumulative Review

Transcription

1 Geometry Cumulative Review 1. Bargain Bin sells jumbo size packages of hamburger patties and hamburger buns. The patties come in packages of 18 and the hamburger buns come in packages of 24. What is least amount of hamburgers you will have if you buy enough packages to make sure you do not have any leftovers? 2. Evaluate 15y + 24x z 3 for x = 7, y = 2, and z = The atomic weight of iron is The atomic weight of silver is How much more does silver weigh than iron? 4. Write an expression to represent the perimeter of the figure below. Simplify the expression by combining like terms. 8n 3n 5. Dianne ordered 39 daisies and 51 carnations. Let d represent the cost of each daisy and c represent the cost of each carnation. a. Write an algebraic expression to represent the total cost of the flowers. b. Use the Distributive Property to rewrite the expression by factoring out the greatest common factor. 6. Evaluate the following: a. 5 3 b. 2 5 c Jerry creates Jelly Bean Baskets for gift orders. The extra large basket contains 24 3 pounds of jelly beans. The suggested serving size is 3 of a pound. How 5 10 many servings are in the extra large basket? 8. Simplify the following expressions: a. 3 ( ) 8n 5m 2 5m 2 b ( ) c d (9 6.3) Which of the following are solutions to the inequality: n 15; {11, 8, 33, 28} NJ Center for Teaching and Learning ~ 1 ~

2 10. The students in Mrs. Carson s sixth grade class measured their heights in inches and organized the data into the following table Use the table to find the values: a. Mean b. Median c. Mode d. Range e. Maximum f. Minimum g. Lower Quartile h. Upper Quartile i. Interquartile Range j. Mean Absolute Deviation 11. Alan, Tara, and Dean are going to the arcade. They were able to buy 90 tokens for the games. They used 24 of tokens to play the free throw game. After the game, they decided to split the remaining tokens equally. Use parentheses to write an expression that represents the number of tokens each friend will get. 12. In a coordinate plane, if the x-coordinate is negative, the point to be plotted will be in which quadrant(s)? 13. Translate each set of words into algebraic expressions. a. 32 more than x b. The product of 18 and the quantity m less 45 c. The sum of eleven and w squared d. The difference of the quantity twenty-nine less than d and forty-three 14. Max s family went on a road trip to Florida. The first day they traveled for 6 ½ hours at a rate of 60 miles per hour. The second day they traveled for 8 ¼ hours at a rate of 50 miles per hour. Use the formula d = rt to find the distance traveled on both days. 15. Use the distributive property to rewrite the expressions without parentheses. a. 5(4m + 7n) b. 8(6x + 9y) c. 13(4g + 8h) d. 19(2r + 6s) 16. Simplify the expressions by combining the like terms. a. 5x + 11y 4 2x + 22xy + 8y 4 b. d 3c + 7d 2c 2 13c + 7c 2 c. 9(m + 3n) n m d. 2(a 3 + a) 4a 2 + 5a a 3 6a NJ Center for Teaching and Learning ~ 2 ~

3 17. The principal wants to put new tile floors in each classroom. Each classroom measures 16 feet by 28 feet. He wants to buy square tiles. What is the largest size square tile he can buy to fit the classroom floors? How many tiles will he need for each room? 18. Evaluate the expression: 5.3(3 + 7) A box of graham crackers weighs 44.1 oz. A recipe calls for 1.8 oz of crushed graham crackers. How many batches of the recipe can you make? 20. What two numbers have an absolute value of 17? 21. Peter and his family recycle all their aluminum cans. Peter decided to record the number of cans they recycle every week for 32 weeks. He created the dot plot below to show the data he collected. x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x Use the dot plot to answer the questions. a. What is the minimum number of cans Peter s family recycled? b. What is the maximum number of cans they recycled? c. What is the range? d. What is the mode? e. What is the median? 22. Which of the following are solutions to the inequality: x < 54; {51, 2, 54, 17, 58} 23. The current price of gold per ounce is $ If you have ounces of gold, how much is its exact worth? What is your answer rounded to the nearest hundredth? 24. Jill is the manager at Mr. and Mrs. Freeze s Ice Cream Shop. She ordered a small batch of the newest flavor, BananaRama. Before ordering enough for the summer, Jill gave out samples to her customers and asked them to rate the flavor from 1 to 10 with 10 being the highest. She created the following box-andwhisker plot using the data from the survey. NJ Center for Teaching and Learning ~ 3 ~

4 Use the box-and-whisker plot to answer the questions. a. What is the minimum rating a customer gave the new flavor? b. What is the maximum rating? c. What is the median? d. What is the lower quartile? e. What is the upper quartile? f. What is the interquartile range? g. What percent of the customers rated the flavor 7 or greater? h. What percent of the customers rated the flavor 9 or less? i. Looking at the box-and-whisker plot, would you consider this flavor a good or bad flavor to order? Explain. 25. What numbers have 27 as their absolute value? 26. Use comparative symbols to compare the following pairs of rational numbers. a b c d Use the coordinate plane shown below to answer the following questions. a. List the coordinates of each point. b. Plot a point to create a parallelogram and provide its coordinates. c. What is the distance between points A and B? NJ Center for Teaching and Learning ~ 4 ~

5 28. Translate each statement into an inequality. a. 6 is greater than w b. The product of 12 and y is less than or equal to 30 c. 9 less m is greater than or equal to 4 d. Triple a number k is less than 183 e. 27 is greater than the difference of x and 14 f. Eleven less than n is less than Draw and label a coordinate plane. a. Plot the points X(-5, 4), Y(2, 4), and Z(2, -6). b. What is the distance of XY? c. Connect the points and identify the figure. 30. Solve the equations for the variable. a. g 13 = 46 b. 51 = 3x c. m + 29 = 114 a d. = Write the inequality for each of the graphs. Use the variable x. a. b. c. d. 32. Write the prime factorization of the following numbers in exponent form. a. 84 b. 256 c Graph the solution to the following inequalities on a number line. a. x > 7 b. x 4 c. x 5 d. x < Which of the following are solutions to the inequality: 7c > 40; {9, 2, 8, 5} NJ Center for Teaching and Learning ~ 5 ~

6 35. Tyra s test scores in science this marking period are 84, 93, 77, and 98. She wants to have an average of 98 in order to make high honor roll. What does she need on her fifth test in order to meet her goal? 36. On a coordinate plane, if the given point has a positive x-coordinate and a negative y-coordinate, in what quadrant is the point located? 37. Which of the following are solutions to the inequality: 11m 154; {10, 12, 14, 16} 38. Define a variable, write an inequality and graph the solution for each of the following: a. The speed limit by Thompson Elementary School is 25 miles per hour b. The Ice-Be-Gone sidewalk salt will melt all snow and ice in weather as cold as -30 F. c. The amount earned per hour by the wait staff at Dean s Diner if they earn $2 per hour and tips d. Laura works part-time and cannot exceed 40 hours of work a week. e. The Deep Ocean scuba tank is tested for use up to 50 feet below sea level. f. The minimum driving age in New York is A bag of Pop-errific Popcorn weighs 30 3 oz. There are 18 servings in a bag. How 8 many ounces does each serving weigh? 40. The atomic weight of lead is The atomic weight of gold is What is the difference in atomic weight between lead and gold? NJ Center for Teaching and Learning ~ 6 ~

7 1. 72 hamburgers m n 5. a. 39d + 51c b. 3(13d + 17c) 6. a. 125 b. 32 c servings 8. a b. 85 c. 5.1 d {11, 8, 33} 10. a b c. 62 d. 22 e. 68 f. 46 g h. 62 i. 9.5 j (90 24) 3 or (90 24) Quadrants II & III 13. a. x + 32 b. 18(m 45) c w 2 d. (d 29) ½ miles 15. a. 20m + 35n b. 48x + 72y c. 52g + 104h d. 38r + 114s 16. a. 3x + 19y xy Answer Key b. 16c + 5c 2 + 8d c. 3m + 40n 9 d. 4a + a a ft. x 4 ft.; 28 tiles batches and a. 1 b. 12 c. 11 d. 6, 8 e { 2, 17, 51} 23. $ ; $ a. 1 b. 10 c. 7 d. 4.5 e. 9 f. 4.5 g. 50% h. 75% i. It is a good flavor because most people gave it a high rating ; a. > b. < c. = d. < 27. a. A(-4, 2); B(-1, 2); C(-2, -3) b. (1, -3) or (-5, -3) c a. 6 > w b. 12y 30 c. 9 m 4 d. 3k < 183 e. 27 > x 14 f. n 11 < 55 NJ Center for Teaching and Learning ~ 7 ~

8 a. b. 7 c. Right triangle a. g = 59 b. x = 17 c. m = 85 d. a = 105 a. x 6 b. x < 9 c. x 2 d. x > 3 a. 2 x 2 x 3 x 7 = 2 2 x 3 x 7 b. 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 2 8 c. 3 x 3 x 5 x 7 = 3 2 x 5 x 7 a. b. c. d {2, 5} 36. Quadrant IV NJ Center for Teaching and Learning ~ 8 ~

9 37. {10, 12, 14} 38. a. x 25 b. x 30 c. x 2 d. x 40 e. x 50 f. x ounces NJ Center for Teaching and Learning ~ 9 ~