6th Grade Practice Exam

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1 6th Grade Practice Exam Short Answer 1. The table gives the ratio of teachers to students at Jefferson Middle School. Jefferson Middle School Students Teachers At Hamilton Middle School, the ratio of teachers to students is 26 to 1. Write a statement taht correctly compares the ratio of teachers to students at the two schools? 2. Janet has a flower garden with 5 rose bushes, 7 lilac bushers, and 9 azaleas. Write a ratio of lilac bushes to the total number of plants in Janet s garden. 3. Which of the following numbers has a value between 0 and 1? 102% In the picture of 40 disks above, what percent of the disks are shaded? 5. On Friday, 65% of the students at Plainview Middle School bought a hot lunch in the cafeteria. What fractional part of the school did NOT buy a hot lunch in the cafeteria?. 6. About of all the freshwater in the United States is used for drinking, washing and other domestic puposes. What percent of our freshwater resources is that? 7. A certain shade of orange requires a 4:2 ratio of yellow to red paint. You have 6 gallons of red paint. How much yellow paint do you need?

2 8. This table contains x and y values in equivalent ratios. What is the missing value in the ratio table? x y 2 6 5? Davis runs at a speed of miles per hour. At this rate, how far can he run in hours? 10. Use the table to write the ratio of baseballs to the total number of balls in the store. Type of Ball Number of Balls Baseballs 61 Softballs 10 Footballs 80 Soccer Balls Robert paid $30.12 for 6 gallons of milk. What was the price per gallon of milk? 12. Which of the following is not an example of a proportion?. 13. Electric City is offering a 20% discount on all radios. Mark would like to buy a radio that was originally priced at $ What is the total cost after the discount 14. To find out which colors are popular for cars, a parking lot was sampled. The results are shown in the table. If there are k fewer green cars than blue cars, write an algebraic expression for the number of green cars. Color Number of Cars Black 38 Blue 19 Red 30 White 27 Other 32

3 15. Miguel s scooter can travel at a maximum speed of 45 miles per hour. Which inequality models all the speeds, s, at which Miguel s scooter can travel? 16. A box of cookies costs $4. Freeman has $34. The inequality below can be used to find the numbers of boxes of cookies, x, Freeman can buy with $34. 4x 34 Write an inequality statement describes all the possible numbers of boxes of cookies Freeman can buy with $34? 17. Graph the solutions to n 12 on a number line. 18. Solve the inequality x Graph the solutions on a number line. 19. Insert parenthesis to make this number sentence true x = Is v= 16 a solution to the equation 26 - v = 13? True or False 21. The expressions below differ by the positions of the parenthesis. Which expression has the greatest answer? x (12 4) c. 5 + (3 x 12 4) (5 + 3 x 12) 4 (5 + 3) x Which expression does not have a value of 5? 23. Evaluate the expression to find the missing values in the table. x x ? 24?

4 24. Aaron s class has collected 54 cans in a food drive. The class plans to sort the cans into n bags, with an equal number of cans in each bag. Write an expression to show how many cans will be in each bag. 25. Write 15 is 7 subtracted from d as an algebraic equation. Then find the solution. 26. Which expression does not equal 15? 3 + k for k = 12 3k for k = 5 for k = 60 k -10 for k = Twenty-six students will attend the field trip to the career center. The cost to attend the career center is $ x. Fifteen of these students will pay an additional $3 to attend the automotive class. Which expression represents the total cost? 15(x + 3) + 26x 26(x + 3) + 15x 26(x + 3) 15(x + 3) + 11x 28. If x = 9.7, what is the value of x? 29. If t = 1.8, what is the value of t? 30. At a hardware store the price of a rake, r, is one- third the price of a shovel, s. Write an equation represents the relationship between the price of the rake and the price of a shovel? 3r = s s = 3 + r 31. Doreen bought 5 cakes for $12 each and 3 cartons of milk for $2 each. Which expression shows how much Doreen spent in dollars? 5 x 12 x 3 x 2 (5 + 3) x (12 + 2) (5 + 2) x (12 + 3) 5 x x If 1.7n = 2.38 what is the value of n?

5 33. At the beginning of the year, Jason had $120 in his savings account. Each month, he added $15 to his account. Write an expression for the amount of money in Jason s savings account each month. Then use the expression to find the amount of money in his account at the end of the year. Month January February March m Amount $135 $150 $165 $? 34. If what is the value of x? 35. Tina wants to install a hot tub in her backyard. The backyard is 15 ft by 40 ft, and the hot tub will be 7 ft by 7 ft. What is the area of the backyard that will not be covered by the hot tub? 36. The algebraic expression 6x + 9x + 3 represents the area of a rectangle. What is the area of the rectangle when x = 4 feet? 37. A rectangular pool is 9 feet wide. The pool has an area of 108 square feet. What is the perimeter of the pool? 38. Find the length of side y if the perimeter is 15.5 cm. 3 cm y 2.5 cm 2.5 cm 2 cm 1.5 cm 39. Donny needs to put carpet in the hallway of his house, and drew the following diagram. All of the sides of the figure are 4 feet long, except for the two longer sides that are each 8 feet long. All angles in the figure are right angles. What is the area of Donny s hallway? 4 ft 4 ft 4 ft 4 ft 8 ft

6 40. If the base of the right triangle below measures 24 centimeters, and its height measures 16 centimeters, what is the area of the triangle? 41. Find the area of the polygon. All angles in the figure are right angles. 3.5 ft 1 ft 2.5 ft 2 ft 1.5 ft 1.5 ft 42. A rectangle has a length of 8 inches. The table shows the area of the rectangle for different widths. Write an expression that can be used to find the area of the rectangle when its width is w inches. Length (in.) Width (in.) Area (in 2 ) w? 43. The school cafeteria is shaped like a rectangle with an area of 936 square feet. The length of the cafeteria is 39 feet. What is its width? 44. Samuel has a hamster cage that is a rectangular prism. It is 20 inches long, 12 inches deep and 10 inches tall. What is the volume, in cubic inchers of Samuel s hamster cage?

7 45. The two parallelograms are similar. Find the missing length x in parallelogram B. Parallelogram A Parallelogram B 4 in. 12 in. 7 in. x in. 46. Will walks his dog at a local dog park everyday after school. The park is located at (-4, -3) on the map. Each unit on the coordinate plane represents 1 block. What is the distance from Will s house to the park in blocks? y 6 Will's house x Both coordinates of a point in the coordinate plane are negative. In which quadrant is this point located? Quadrant I Quadrant III Quadrant II Quadrant IV 48. Which of the following coordinates is farthest to the right of the origin on a coordinate plane? (-17, 7) (4, 15) (7, 0) (0, 12)

8 49. Two of the vertices of a rectangle are plotted on the coordinate grid below. y x Which ordered pairs could be the other two vertices of the rectangle? 50. Amy used the coordinate grid shown below to plot her rectangular garden. She planted one-half vegetables and the other half flowers. y x A corner of the garden is at (1, -3) and the opposite corner is at (5, 3). In square units, what is the area of the vegetable portion of her garden?

9 Name Class Date UNIT 5 Math 6 Practice Exam: Constructed Response COMMON CORE Sweet Success? A youth group is raising money for a ski trip by baking and selling muffins on weekend mornings. The money raised will be distributed evenly among the group members, and the goal is to raise $65 per person. Will the group meet this goal? CC.6.RP.1 CC.6.RP.2 CC.6.RP.3a, b, c, d Pumpkin Muffins 4 cups white flour 4 cups wheat flour 4 tsp baking soda 2 tsp salt 4 tsp cinnamon 2 tsp ginger 1 tsp cloves 3 cups brown sugar 6 tsp molasses 1 cup oil 8 eggs 4 cups pumpkin 4 tsp vanilla 3 cups milk 1 Making Muffins Ruth volunteered to make pumpkin muffins for the sale. The ingredients used in Ruth s recipe are shown. A Write the ratio of total flour to sugar in three different ways. B Write the ratio of vanilla to molasses. Then write a ratio that is equivalent. Explain how you found the equivalent ratio. C At the grocery store, Ruth sees that a 15-ounce can of pumpkin costs $1.59 and a 29-ounce can of pumpkin costs $3.05. Which is the better buy?

10 D Ruth decides to make a larger batch of muffins for the bake sale by increasing the recipe. The increased recipe requires 6 teaspoons of cinnamon. Now Ruth must determine how many eggs she needs. What is the ratio of cinnamon to eggs in the original recipe? Use the table to help you find the number of eggs that Ruth needs. Cinnamon (tsp) 4 6 Eggs 8 Ruth needs eggs. 2 Preparing for the Sale Length 1 inch = 2.54 centimeters A The group has a 6-foot long table and a plastic tablecloth for the sale. The tablecloth s package states that the tablecloth is 180 centimeters long. Is the tablecloth long enough to cover the table? Explain. B Allison has painted a large Muffin Sale sign to display at the table. Chris wants to paint more signs. Allison made purple paint by mixing 3 parts red paint with 4 parts blue paint. Chris has 2 fluid ounces of blue paint. To match Allison s shade of purple, how much red paint should Chris mix with his blue paint? C The group members price the muffins at $15 per dozen. What is the price per muffin? 3 Sale Results A The table shows results after several weekends of sales. Muffins Dozens Dozens

11 Made Sold Pumpkin Blueberry Chocolate chip Banana nut What percent of the muffins made were pumpkin muffins? B Which type of muffin represents of the muffins made? Explain. C What percent of the muffins that youth group members made did NOT sell? Round your answer to the nearest percent. D Which type of muffin was most popular? Justify your answer. 4 Answer the Question A The treasurer of the youth group tracks the muffin sales for several weeks. Help her complete her spreadsheet. Type of Muffin Dozens Made Muffin Sales Dozens Sold Pumpkin Blueberry Number of Muffins Sold Income Sold

12 Chocolate chip Banana Total Income B After tallying the group members receipts for supplies, the treasurer has calculated that it cost the youth group $3.50 to bake a dozen muffins. How much has it cost the group to bake all of the muffins so far? C To find the group s profit, subtract cost from income. How much profit has the group earned from muffin sales so far? D The youth group divides the profit evenly between the 15 members. How much does each member now have toward the cost of the trip? Did the group meet its goal? E Ruth suggests raising the price per muffin by $0.25 in future sales, saying, If this had been the price from the beginning, we would have met our goal by now. Is Ruth correct? Explain.

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