Winter Packet - AMC. Name: 6 th Grade American Math Date: Section: 1) Carissa drew the figures below on a sheet of paper.

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1 Winter Packet - AMC Name: 6 th Grade American Math Date: Section: 1) Carissa drew the figures below on a sheet of paper. Which of the following does not describe the figures Carissa drew? A. The ratio of circles to all figures is 3 to 9. B. The ratio of triangles to squares is 4 to 5. C. The ratio of squares to circles is 5 to 3. D. The ratio of all figures to squares is 12 to Joaquin created the figures below using design software on his computer. 4. A recipe for a mixed berry pie calls for 5 ounces of blackberries for every 9 ounces of raspberries. Which of the following statements is true? A. The recipe calls for 5/14 ounce of blackberries B. The recipe calls for 14/5 ounce of blackberries C. The recipe calls for 5/9 ounce of blackberries D. The recipe calls for 9/5 ounce of blackberries 5. Mariluz will be spending her vacation at her uncle's house in the mountains. She drove 582 kilometers from her home to her uncle's house in 6 hours. At what rate did Mariluz complete her trip? A km per hour B. 79 km per hour C. 97 km per hour D. 100 km per hour What is the ratio of quadrilaterals to all figures in simplest form? 3. Tito went to a concert given by a jazz band. The band had 5 saxophone players and 4 trumpet players. What was the ratio of trumpet players to saxophone players in the band? 6. Jackson analyzes polling results for elections across the country. Over the last 10 years, Jackson has correctly predicted the winner of an election 78% of the time. Which of the following statements best describes Jackson's results? A. For every 100 elections, Jackson has predicted the winner 78 times. B. For every 1,000 elections, Jackson has predicted the winner 78 times. C. Jackson has predicted the winner of 78 of the last 100 elections. D. Jackson has predicted the winner of the last 78 elections.

2 7. Yukiko plays on the soft ball team at her school. The team won 9 of its first 12 games. At that rate, how many games will Yukiko's team win if it plays 64 games in all? 8. John rode his mountain bike over some trails in a state park. He biked a total of 5 ½ miles. How many yards did John bike? There are 1,760 yards in a mile. 9. Jeffrey builds wooden decks for his clients' houses. His standard deck uses a fixed amount of lumber. The table below shows how much lumber Jeffrey needs to buy for different numbers of decks. LUMBER NEEDED NUMBER OF DECKS LUMBER (in ft²) 2 1, , , , ,156 7? Based on the data in the table, how much lumber would Jeffrey need to buy to build 7 standard decks? 10. At the local greenmarket, Debra bought 5 ounces of Chinese long beans for $ At that rate, how much would she pay for 8 ounces of Chinese long beans? 11. A recipe for salad dressing calls for fresh lime juice and honey. The ratio of tablespoons of honey to tablespoons of lime juice is 8:16. According to the recipe, how many tablespoons of honey are needed for every tablespoon of lime juice? Write your answer as a fraction in simplest form. 12. A carabiner is a key piece of equipment for a mountain climber. Ken's Mountain Adventures store is having a sale on carabiners. During the sale, you can buy 4 carabiners for $ What is the unit price of the carabiners? 13. Felipe makes salads at a restaurant. On average, Felipe can make 12 salads in 20 minutes. At that rate, how many salads could Felipe make in 45 minutes? 14. What is 45% of 120? 15. The students in Emily's school raised money to help the victims of a natural disaster in Asia. Emily's sixth grade class raised 40% of the total amount by the school. If Emily's class raised $580, how much money did the school raise in all?

3 16. An adult giraffe can have a mass of as much as 1,360 kilograms. What is 1,360 kilograms in grams? 1 kilogram = 1,000 grams. 20. Dora earns an annual salary of $85,608. How much does she earn every month? A. $6,144 B. $7,134 C. $7,144 D. $7, Which point is located at (-5, -6)? 21. Which of the following statements is NOT true? A. -11 is the opposite of 11. B. 0 is the opposite of 0. C. 5.3 is the opposite of 3.5. D. 21 is the opposite of Andie is taking a sewing class. Her first assignment is to stitch together 49 identical fabric rectangles from end to end to create a long banner. If each rectangle measures 8.3 centimeters long, what will be the length of the completed banner? 18. Naury has 4 cups of hot chocolate in her thermos. She offers 5/8 cups servings of hot chocolate to some close friends. What is the greatest number of friends Naury can offer hot chocolate to? 19. What is the absolute value of the number represented by the point on this number line? 23. Nisha is following a recipe for tomato sauce that calls for 1¾ teaspoons of oregano. She is using a measuring spoon that holds ⅛ teaspoon. How many times will she need to fill the measuring spoon with oregano to make the tomato sauce? 24. Sandy is putting 64 cookies and 40 chocolate truffles into gift boxes. Each box will have the same number of cookies and the same number of chocolate truffles. What is the greatest number of boxes Sandy can make with no cookies or chocolate truffles left over?

4 25. Find the quotient: 1, Plot and label the following 10 points on the graph provided. 29. Duke and Hilda went scuba diving to study migrating fish 41 feet beneath the ocean's surface. They returned to the surface after 15 minutes. Which integer best describes their location when they surfaced? A (-3, -1) B (5, -3) C (4, 2) D (-2, 6) E (6, 2) F (-4, 2) G (1, 5) H (2, -1) I (-1, -5) J (-4, -4) 27. Mack is working on his science project. He dropped a ball filled with sand from the balcony of a building 42 feet from the ground. Which of the following statements is true? A. Mack's ball traveled a distance of 42 feet because -42 is 42. B. Mack's ball traveled a distance of -42 feet because -42 is -42. C. Mack's ball traveled a distance of 0 feet because 0 is 0 and the ball ended at ground level. D. Mack's ball traveled a distance of 24 feet because -42 is Serena wants to buy reusable bamboo plates and cups for a barbecue. Plates are sold in packages of 8. Cups are sold in packages of 12. What is the least number of packages Serena can buy to have an equal number of plates and cups? Answer: packages of plates packages of cups 30. What quadrant is (-3, 8) located in? 31. Which of the following is equivalent to ? A. 4(6 + 3) B. 6(6 + 3) C. 6(8 + 3) D. 8(6 + 3) 32. Paul, Raul, and Saul had a competition to see who could pick the greatest amount of strawberries in three minutes. Paul picked 1⅝ pounds of strawberries, Raul 1¾ pounds, and Saul 1 11 / 16 pounds. Who came in second? Show your work. 33. Plot the points -3 and -8.1 on the number line below. Explain the position of -3 in relation to -8.1 on the number line. What does this mean?

5 Which verbal expression represents the algebraic expression 3(5 + 3)? A. 5 plus 3 times 3 B. 3 times 5 plus 3 C. 3 times the sum of 5 and 3 D. the product of 5 and Which expression is equivalent to b + b + b + b? A. 4b B. 4 + b C. b 4 D. 4(b + b) 35. Which is equivalent to 3 x 3 x 3 x 3 x 3? A. 3 x 5 B. 3³ C. 5 3 D Catya had $70 saved. She received some more money as a graduation gift. Now she has $150. Which equation could be used to determine how much money Catya received on her graduation? A = g B g = 150 C g = 70 D. g 70 = Which is equivalent to y 5? A. 5y B. y + 5 C. y y y y y D. y + y + y + y + y 41. Reina scored twice as many goals at her last field hockey game as she did during the first game of the season. If f represents the number of goals Reina scored during the first game, which expression represents the number of goals she scored during the last game? A. 2f B. 2 f C. 2 + f D. 2 f 42. Evaluate 6 3 2a for a = The formula for the volume of a cube is V = s 3. What is the volume of a cube with a side length, s, of 3 feet? 38. Which algebraic expression represents the verbal expression 7 decreased by m? A. m 7 B. 7m C. 7 m D. 7 + m 39. Which verbal expression represents the algebraic expression 3y? A. 3 increased by y B. the product of 3 and y C. y to the third power D. the quotient of 3 and y 44. Which expression is equivalent to 15x 6? A. 3(5x 2) B. 3(5x 6) C. 5(3x 6) D. 6(9x 1) 45. Which pair of expressions are equivalent? A. 20p 18 and 2(10p 16) B. g + g + g and g 3 C. 3z + 26 and 3z and 62 D. 8(2r + 3) and 16r + 24

6 46. The table shows the relationship between the number of smoothies, n, and the total cost in dollars of the smoothies, c, at Juicy's Smoothies. JUICY'S SMOOTHIES n c Write an equation to model the relationship between the cost and the number of smoothies. Which variable is the independent variable? Which variable is the dependent variable? 48. Andrea spent twice as many hours studying as Jonah this month. Jonah spent 7 fewer hours studying this month than last month. A. Let h represent the number of hours Jonah spent studying last month. Write an algebraic expression for the number of hours Andrea spent studying this month. B. Andrea used the difference of 2 times h and 7 to write the expression. Explain why she is correct or incorrect. 47. Carrie has 11 board games. This is 8 more board games than Marisol has. The equation 11 = m + 8 can be used to find the number of board games that Marisol has. How many board games does Marisol have? 49. Simplify the expression: 3x 2y + 5x + 3y 50. Simplify the expression: 2(s 5) + 12 s 51. Simplify the expression: 12m + 8m Solve for j: j 9.2 = 22.5