M.S. 181 PABLO CASALS CHRISTOPHER WARNOCK, PRINCIPAL 800 BAYCHESTER AVENUE, BRONX, NY 10475 PHONE: 718-904-5600 Conceive, it, Believe it, Achieve it! Winter-Break Packet 7 th grade mathematics Student: Class: Due Date: 01/05/15 There are 3 assignments in this packet. Winter Packet (Rational Numbers, Expressions and Ratios and Proportional Relationships) My Dream Car Homebuyer Checkpoint INSTRUCTIONS Required: Complete the first packet titled Winter Packet which includes multiple choice and short response questions Choice: Complete either the My Dream Car Task or the Homebuyer Checkpoint Task. Extra Credit: Complete both the My Dream Car Task and the Homebuyer Checkpoint Task SHOW ALL YOUR WORK WHERE REQUIRED
Directions: Write the letter of the best answer. 1. Daniel went bowling with $25 to spend. He rented shoes for $5.25 and paid $4.00 for each game. What was the greatest number of games Daniel could have played? a. 4 b. 5 c. 6 d. 7 2. Altitude above sea level is given in positive values and below sea level is given in negative values. Which situation describes a hiker in Death Valley stopping at an altitude of zero degrees? a. The hiker starts at -10 feet then increases altitude by 10 feet. b. The hiker starts at -10 feet then decreases altitude by 10 feet. c. The hiker starts at 10 feet then increases altitude by 10 feet. d. The hiker starts at 10 feet the decreases altitude by 10 feet. 3. Which expression is equivalent to (7x 5) (3x 2)? a. -4x 3 b. 10x 3 c. -10x 7 d. 4x 3 4. Yesterday the temperature change for a 5-hour period of time was -4/5 degree per hour. Which statement describes the change? a. The temperature rose by 5 0 b. The temperature rose by 4 1/5 degrees. c. The temperature fell by 4 0 d. The temperature fell by 5 4/5 degrees. 5. Solve for x in the equation 0.5x + 78.2 = 287 a. 208.8 b. 104.4 c. 417.60 d. 192.6 6. What is the value of the expression 4 ½ X 2 ¾? a. 8!! b. 12!! c. 12.3 d.!! 7. Jensen stopped at rest area A along the side of the highway. His map, shown below has a scale of 1 inch to 35 miles. HIGHWAY B 2.5 in A Jensen planned to stop at rest area B next. What is the actual distance, in miles, between the two rest areas? a. 87.5 inches b. 87.5 miles c. 5 inches d. 5 miles PAGE 1
8. The table below shows prices for shoe rental, games and snacks at the bowling alley. Gina rented shoes, bowled 3 games and bought 1 order of Nachos. She used a coupon for ½ off the price of her bowling game. What was Gina s total cost before tax was added? BOWLING ALLEY PRICES ITEM PRICE Shoe Rental $2.75 One Game of Bowling $2.50 Small Soda $0.95 Large Soda $1.50 Nachos $1.75 a. $12.00 b. $6.00 c. $8.25 d. None of the above 9. What is the value of the expression 3/8 + (- 4/5) + (- 3/8) + 5/4? a.! b.! c. (! ) d. All of the above 10. What is the value of the expression? 8/5 0.35 a..475 b. 4.57 c. 4.75 d..457 11. The relationship between the number of songs downloaded, x and the total cost, in dollars, of the downloads, y is represented by a graph drawn in an xy-plane. Point (1,3) and (4,12) lie on the graph. What does the ordered pair (4,12) indicate? a. 12 downloads that cost $4 each c. 12 downloads that cost a total of $4 b. 4 downloads that cost $12 each d. 4 downloads that cost a total of $12 12. Carmi paid an electrician x dollars per hour for a 5-hour job plus $70 for parts. The total charge was $320. Which equation can be used to determine how much the electrician charge per hour? a. 5x + 70 = 320 b. 320 + 70 = 5x c. 320 + 5x 70 d. All of the above 13. The number of students at a school who ate in the cafeteria yesterday can be represented by the expression! k, where k is the number of students in the school.! Which expression is equivalent to! k and shows the fraction of students who did! not eat in the cafeteria yesterday? a. 4k 5 b. 4 5k c. k 1/5 k d. 1 1/5 k PAGE 2
14. What is the decimal equivalent of 7/8? a. 1.1 b. 0.1 c. 8.75 d. 0.875 15.What is the value of the expression below (- 5/8) x (3 ½)? a. (! ) b. -2 c. 2 R. 3 d. All of the above 16. A crew of highway workers paved 2/15 mile in 20 minutes. If they work at the same rate, what portion of a mile will they pave in one hour? a.!!! mile b. mile c. mile d. All of the above 17. Which expression is equivalent to 2(3n-4) 2(n-2)? a. 6n 4-2n 2 c. 6n 8 2n 4 b. 8n - 12 d. 4n 8 18. What is the value of the expression below? -11 5/6-8/9 + 5/3 a. 15!! b. 15! c. -15!! d. -15! 19. Which expression represents the sum of (2x-5y) and (x + y)? a. 3xy and xy b. 3xy + xy c. 3x + 4y d. 3x 4y 20. Katie bought 4 sweaters that each cost the same amount and 1 shirt that cost $20. The items she bought cost a total of $160 before tax was added. What was the cost of each sweater? a. $40 b. $8 c. $35 d. None of the above PAGE 3
21. Jeanette s rectangular backyard is 36 feet in length and 39 feet in width. She drew a model of the yard on a coordinate plane. Then she drew a rectangle to represent plans for a swimming pool she wants to put in. The coordinates of the corners of the pool are shown below. 18 12 9 6 0 3 6 9 12 15 18 21 24 27 30 33 If the pool is built as planned, what is the area, in square feet, that the pool will cover? a. 270 sq. in b. 30 sq in c. 270 sq. ft d. 270 sq. in 22. In which situation can a constant of proportionality be identified? a. Allison earns $8 per hour for h hours and an $8 bonus for each cellphone plans she sells. b. Ben buys x cans of dog food for $1.25 each and uses a coupon for $7.00 off his entire purchase. c. Claire orders b books online for $4.50 each plus shipping charges of $0.30 for each book. d. John runs 3 miles per day for m days in a week and bicycles 20 miles/day the remaining days in the week. 23. Gretchen makes pillows using 1 5/8 yards of fabric per pillow. She has 8 ¼ yards of fabric. What is the greatest number of pillows Gretchen can make? a. 5! b. 5! c. 5 d. 6 PAGE 4
24. Which steps can be used to solve the value of y? 2/3 (y + 57) = 178 a. Divide both sides by 2/3, then subtract 57 from both sides b. Subtract 57 from both sides, then divide both sides by 2/3 c. Multiply both sides by 2/3, then subtract 57 from both sides d. Subtract 2/3 from both sides, then subtract 57 from both sides. 25. The table shows that the number of miles driven by Sandra is directly proportional to the number of gallons used. What is the constant of proportionality for this relationship? a. 24.5 b. 25.4 c. 24.5 mi/gal d. 25.4 mi/gal 26. Francesca typed 496 words in 8 minutes. Which of the following is a correct understanding of this rate? a. At this rate, it takes 62 minutes for Francesca to type one word. b. At this rate, Francesca can type 62 words in 8 minutes. c. At this rate, Francesca can type 62 words in one minute. d. At this rate, Francesca can type 8 words in one minute. 27. A family went on a vacation and used 5.4 gallons of gasoline to travel 150 miles. How many total gallons of gasoline will they need to travel 200 more miles? a. 12.6 gallons c. 13.1 gallons b. 14.3 gallons d. 16.2 gallons 28. The speed limit on a highway is 70 miles per hour. About how fast is this in miles per minute? a. 4200 mi/min b. 11.7 mi/min c. 1.17 mi/min d. 0.117 mi/min PAGE 5
29. During a 3-hour period, 2,292 people rode the roller coaster at an amusement park. Which proportion can be used to find x, the number of people who rode the coaster during a 12-hour period, if the rate is the same? a.!!,! =! c. a.!! =!,! b a.!!,! =! d. a.!! =!,! 30. The table shows the prices of three boxes of cereal. Which box of cereal has the highest unit price? CEREAL BOX SIZE (OUNCES) PRICE($) 48 $5.45 32 $3.95 20 $3.10 a. the 20-ounce box c. the 32-ounce box b. the 48-ounce box d. All three boxes have the same unit price 31. CCSS 5.OA.B3 Angela started two patterns in the table below. Pattern A uses the rule Add 5. Pattern B uses the rule Add 10. Complete the table. Pattern A Pattern B 0 0 5 10 10 20 15 30 20 40 Write a rule that can be used to determine each term in Pattern B based on its corresponding term in Pattern A. Answer: Rule: PAGE 6
32. CCSS 6.EE.B.6 In the diagram of a quadrilateral below, the variables represent the lengths of the sides, in inches. k n n 2 k - n Part A: Write an expression using the variables n and k that could be used to find the perimeter of the quadrilateral. Part B: If n = 8 and k = 27, what is the perimeter of the quadrilateral? Show your work: 33. CCSS 6.NS.B.4 Part A: What is the greatest common factor of 28 and 63? Show your work: Part B: Using the greatest common factor, complete the equation below. 28 + 63 = ( + ) PAGE 7
34. CCSS 6.RP.A.3a Daniel needed 4 rectangle pieces of wood with the same ratio of length to width. The table below shows the measurements of 2 pieces that he cut and 2 more he needed to finish cutting. Complete the table. Length (Inches) Width (Inches) 5 4 9 6 21?? 22 Part A: What is the ratio of length to width expressed in simplest form. Show your work: Part B: Determine the two missing measurements in the table such that the third and fourth pieces have the same ratio of length to width. Answer: Width of 3 rd piece: Length of 4 th piece: 35. CCSS 6.EE.A.3 Four school groups were planning a field trip to a museum. Each group had one teacher and seven students. Leny used the expression 4(m+7r) to determine the total admission cost for all four groups, where m is the admission cost for each teacher and r is the admission cost for each student. Part A: Write an expression, without parenthesis, that is equivalent to Leny s expression. PAGE 8
Part B: Museum admission is $14 for each teacher and $9 for each student. How much will the field trip cost for one group? 36. CCSS 7.G.B.6 The area of a rectangular park is 3/5 square mile. The length of the park is 7/8 mile. What is the width of the park? Answer: 37. CCSS 6.RP.A.2 Miley s car used 12 gallons of gas to travel 456 miles. Part A: How many miles did her car travel per gallon of gas? Part B: It cost Miley $44.88 to buy 12 gallons of gas. What was the cost per gallon of gas? PAGE 9
38. CCSS 6>RP.A.3a Part A: Complete the table below to show the relationship between the lengths of the sides of equilateral triangles and their perimeter. EQUILATERAL TRIANGLES Side Lengths (in) Perimeter (in) 1?? 6 4?? 18 Part B: Create a graph by plotting the ordered pairs on the coordinate plane. Be sure to include all parts of the graph. 39. CCSS.EE.C.9 For each job, a plumbing services company charges a one-time service fee of $50 and a $125 per hour rate for labor. Let n be the total amount the company charges in dollars, for a job that takes b hours to complete. Write an equation that represents the relationship between n and b. Part A: What would the company charge for a job that takes 9 hours? Part B: If the total charge for a job was $425, how many hours did the job take? PAGE 10
40. Kimberly traveled to her friend s house and went 300 miles in 5 hours. On her way home she took a different route and traveled 420 miles in 7 hours. Are these ratios equivalent? Use proportion to show complete work. 41. On Monday Janine picked 20 tomatoes off 4 tomato plants. On Thursday she picked 15 tomatoes off 3 tomato plants. Determine whether the ratios are equivalent. Use proportion to show complete work to support your answer. 42. Daniel s basketball team won 23 games and lost 8 games. Write the ratio of wins to losses in simplest form. Show complete work to support your answer. 43. Mr. Jansen listened to 8 songs in 28 minutes. He later listened to 5 songs in 21 minutes. Determine whether the ratios are equivalent. Use proportion to show complete work. 44. A bakery sells 6 bagels for $2.99 and 4 muffins for $3.29. What is the total cost in dollars of 4 dozens bagels and 16 muffins, not including tax? 45. You can drive your car 21.7 miles with one gallon of gasoline. At that rate, how many miles can you drive with a3.2 gallons of gasoline? PAGE 11