Final Comprehensive

Transcription

1 Student Name: th Grade Math Final omprehensive raven ounty School istrict North arolina Published by TE21, Inc. January 2018 LL RIGHTS RESERVE This benchmark assessment is intended for use with students registered in your classroom this school year. Your right to use of this document is limited to its delivery in whole to your students as a formative assessment, and for review and instructional purposes for those registered students within your classroom in the year of assessment delivery. Please note the following restrictions regarding this benchmark assessment: No reproduction of the assessment in whole; No sharing with other classes or teachers; No dissection and reproduction of any individual questions; No distribution of or sharing of copies of the assessment in whole or any individual questions from the assessment; No preparation of derivative works of the assessment or the individual questions; No importing or otherwise loading the assessment in whole or any individual questions to any internal or external item bank or question data warehouse; No posting or uploading to any platform partner community board ; and No public displays of the assessment or individual questions outside your classroom.

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3 LULTOR INTIVE The items in this test are based on the ommon ore State Standards for Mathematics. IRETIONS FOR THE LULTOR INTIVE SETION OF THE TEST: alculators may not be used during this test. Read each problem carefully. hoose the best answer from the choices given. Fractions in some answer choices may have been simplified. heck each answer choice to see if this has been done. iagrams used in the test may not be drawn to scale. Stop when you see the words STOP. EN OF LULTOR INTIVE SETION. When you have completed the calculator inactive questions, read and follow the directions at the end of this section of the test. Page 1

4 1. Which equation demonstrates a correct product of two rational numbers? = = = = astor goes deep-sea diving. He starts at sea level and dives feet every minute for minutes. fter 21 2 minutes of diving, astor s speed slows down to 41 8 minute. feet every If astor continues to dive 4 1 feet every minute for 3 minutes, what is his depth at 8 the end of the last 3 minutes? feet below sea level 20 feet below sea level 28 feet below sea level feet below sea level 3. The table shows the cost of a taxi ride after a certain number of minutes. What is the cost of a 1-minute taxi ride? $0.75 $1.25 $1.75 $2.25 Minutes ost 3 $ $ $6.75 Page 2

5 4. Ms. avis asks four students to simplify the expression shows the response of each student. 8. The table 2 Student Response Gianna -22 Herbert -7 Riley 22 Taylor 7 Which student simplifies Ms. avis s expression correctly? Gianna Herbert Riley Taylor 5. middle school is selling candy bars to raise money for new calculators. The graph shows the number of candy bars sold, x, and the amount of money collected, y. Which equation represents this relationship? y = 0.5x y = 1.25x y = 2.5x y = 5x Page 3

6 6. The graph represents Willow s hourly earnings at her internship. Which statement about the coordinate pairs (0, 0) and (1, 4) is most accurate? The coordinate pair (0, 0) represents the fact that if Willow works zero hours, she earns zero dollars. The coordinate pair (1, 4) represents Willow s hourly unit rate of $2 per hour. The coordinate pair (0, 0) represents the fact that if Willow works zero hours, she earns zero dollars. The coordinate pair (1, 4) represents Willow s hourly unit rate of $4 per hour. The coordinate pair (0, 0) represents the starting day of Willow s internship. The coordinate pair (1, 4) represents Willow s hourly unit rate of 2 hours per dollar. The coordinate pair (0, 0) represents the starting day of Willow s internship. The coordinate pair (1, 4) represents Willow s hourly unit rate of 4 hours per dollar. Page 4

7 IRETIONS FOR THE GRIE RESPONSE SETION OF THE TEST: Questions 1 through 9 require you to write your answers in the boxes provided on the back of your answer document. Write only the number or symbol in each box, and fill in the circle in each column that matches what you have printed. Fill in only 1 circle in each column. 1. chef uses 1 2 cup of tomatoes for every 1 cup of onions to make salsa. How many 8 cups of onions will the chef need for 1 cup of tomatoes, written as a fraction? 2. Kendrick and Perla spend a total of $92 at an amusement park. They spend $28 on parking and lunch combined, and the rest on two admission tickets. How much does each admission ticket cost, in dollars? 3. The distance on a map between two locations is 2.25 inches. If 1 inch = 24 miles, what is the actual distance between the two locations, in miles? 4. scuba diver is at an elevation of 53 feet below sea level. hiker is at an elevation of 228 feet above sea level. What is the difference in elevation between the scuba diver and the hiker, in feet? Page 5

8 5. It takes a biker 1 3 hour to ride 8 3 miles. What is the biker s rate, in miles per hour? 6. ailey and Marcus buy a dog that weighs 18 pounds. The dog gains pounds each year. The dog now weighs pounds. How many years ago did ailey and Marcus buy the dog? 7. decorator hangs a picture on a wall that is 48 inches wide. The width of the picture is 17 1 inches. The decorator hangs the picture exactly in the middle of the wall, as 2 shown. What is the value of x, in inches, on each side of the picture, written as an improper fraction? Page 6

9 8. Last month, an investor s stock portfolio was worth $46,950. The value of the stock portfolio fell by $2, each week for 4 weeks. What is the value of the stock portfolio at the end of the 4 weeks, in dollars? 9. recipe for 45 biscuits uses 5 2 cup of flour? cups of flour. How many biscuits are made from each EN OF LULTOR INTIVE SETION IRETIONS: Look back over your answers for the calculator inactive questions. You will not be able to go back and work on these questions once you are given a calculator. Raise your hand to let your teacher know you are ready to begin the calculator active questions. o not begin work on the calculator active test questions until your teacher has given you a calculator. Turn your answer document over to the multiple choice side. When your teacher has given you a calculator, GO TO THE NEXT PGE, and EGIN the calculator active questions. Stop when you see the words STOP. EN OF MTH TEST. Page 7

10 7. Which expression is equivalent to 5(x ) 1 (12x 52)? 4 2x 11 2x 9 2x x basketball coach determines the team has a 1 probability of winning a 32 tournament. Which choice describes the probability of the coach s basketball team winning the tournament most accurately? certain impossible likely unlikely 9. onsider the diagram. What is the value of n? Page 8

11 10. Tom borrows $2,000 at an 11.5% simple interest rate for 5 years. What is the total amount Tom will have paid back at the end of 5 years? $1,150 $2,050 $2,230 $3, Mr. and Mrs. arnes budget to spend $350 on a coat, shoes, and a television at a department store. The table shows how much Mr. and Mrs. arnes would spend if they buy all the items. Item mount Spent coat 55% off of $180 shoes 1 2 off of $150 television $240 Which statement about Mr. and Mrs. arnes s budget is true? Mr. and Mrs. arnes are over their budget by $46. Mr. and Mrs. arnes are over their budget by $64. Mr. and Mrs. arnes are under their budget by $46. Mr. and Mrs. arnes are under their budget by $ raig and Madison spend d dollars on dinner and then tip the server 18%. Which expression represents the total cost of raig and Madison s dinner? 1.82d 1.18d 0.82d 0.18d Page 9

12 13. The dimensions of a rectangular prism are shown in the table. Length Width Height 10 in. 12 in. 16 in. What is the surface area of the rectangular prism? 3,840 in. 2 1,920 in in in aleb makes a map with distances from his home to four different locations. The scale factor he uses is 1 in. = 1 2 mile. Location city hall gym post office school istance from Home 3 inches 5.5 inches 6.5 inches 12 inches ccording to aleb s map, which location is 6 miles from his house? city hall gym post office school Page 10

13 15. Which graph displays the solution to the inequality -6x 72 > 24 correctly? ounce box of cereal costs $4.80. Which equation relates the price, p, to the weight, w, in ounces, of the cereal correctly? w = 0.4p w = 0.25p p = 0.4w p = 0.25w Page 11

14 17. Wendy and Yosef draw a figure in the shape of a rectangle with two semicircles at the ends of the sides, where the diameter of each semicircle is 4 cm. What is the area of the figure? (Use 3.14 as an approximation of pi.) cm cm cm cm student spends 12% of his or her money on a book. fter buying the book, the student has $ left. How much money did the student have before buying the book? $ $ $ $ Page 12

15 19. The table shows the different choices for making a stuffed animal at a toy store. Maya and Kyle will randomly select one animal type, one shirt color, and one pants color. nimal Type Shirt olor Pants olor bear blue black cat green white dog red What is the probability that Maya will make a stuffed animal that is a dog wearing a green shirt and white pants? Jaden and Monica go to the mall. Jaden brings $120, and Monica brings $144. Jaden spends 80% of his money. Monica spends 3 4 of her money. Which statement is true? Jaden spends $12 more than Monica because Jaden spends $36, and Monica spends $24. Jaden spends $12 more than Monica because Jaden spends $108, and Monica spends $96. Monica spends $12 more than Jaden because Monica spends $36, and Jaden spends $24. Monica spends $12 more than Jaden because Monica spends $108, and Jaden spends $96. Page 13

16 21. doctor randomly samples male and female weights for a study. The results of the doctor s study are shown. Male Weights in Pounds Female Weights in Pounds ased on the data, which statement about male and female weights is true? The range of female weights is 20 pounds greater than the range of male weights, but the mean weights of females and males are the same. The range of male weights is 20 pounds greater than the range of female weights, but the mean weights of females and males are the same. The mean weight of males is 20 pounds greater than the mean weight of females, but the range of weights of females and males is the same. The mean weight of females is 20 pounds greater than the mean weight of males, but the range of weights of females and males is the same. 22. Norah was 45 inches tall when she started kindergarten. She grew an average of 2.5 inches every year. Norah is now 62.5 inches tall. Which equation can be used to find how many years ago Norah started kindergarten, and how many years ago was it? ( ) 2.5 = x 7 years 2.5x + 45 = years ( ) 2.5 = x 43 years 2.5x + 45 = years Page 14

17 23. Mr. Smith places 10 cards labeled 1, 5, 8, 9, 11, 19, 21, 23, 28, and 30 in a bowl. He will randomly select one card from the bowl without looking. What is the probability that Mr. Smith will select a card with a two-digit number? teacher asks four students to write three side lengths that will not make a triangle and describe why. The table shows the students responses. Student adence Enrique Jocelyn Myron Response 2 cm, 8 cm, 8 cm will not make a triangle because = 10, and 10 > 8. 2 cm, 3 cm, 6 cm will not make a triangle because = 5, and 5 < 6. 4 cm, 5 cm, 7 cm will not make a triangle because 5 4 = 1, and 1 < 7. 5 cm, 6 cm, 9 cm will not make a triangle because 9 6 = 3, and 5 > 3. Which student is correct? adence Enrique Jocelyn Myron Page 15

18 25. onsider the expression. 5(x + 2) 7(x + 2) Which choice simplifies the expression correctly? 12x x 4-2x x contractor fills up a foundation hole in the shape of a cube with cement before starting to build a house. One side of the foundation hole measures meters. pproximately how much cement does the contractor need to fill the foundation hole completely? 14,706 cubic meters 13,824 cubic meters 600 cubic meters 196 cubic meters 27. Eileen purchases a laptop for $1,530 with her credit card. If Eileen does not pay off the full amount charged each month, the credit card company charges an 11% fee on the remaining balance. If Eileen can pay only $750 when she receives her first credit card statement, how much will the company charge in fees for the second month? $82.50 $85.80 $95.24 $ Page 16

19 28. contractor is cutting a circular hole from a square piece of plywood to create an opening for a sink. The piece of plywood is 4 feet by 4 feet. If the contractor cuts a circular hole with a diameter of 2 1 feet, approximately how 2 much plywood is left over? (Use 3.14 as an approximation for π.) 4 square feet 5 square feet 11 square feet 20 square feet 29. Joy and Tyler conduct a survey on the favorite video games of all middle school-aged students. Which population sample produces the most valid results for the survey? surveying all 7 th grade boys surveying every 5 th student who walks into school in the morning surveying every girl on the volleyball team surveying every other student in the eighth grade lunch line Page 17

20 30. Nancy and Fabian s dinner bill at a restaurant is $28 before tax. The tax on their meal is 2.5%. How much is Nancy and Fabian s final bill after tax is added? $21.00 $27.30 $28.70 $ Four tables are shown. Table 1 Table 2 Table 3 Table 4 x y x y x y x y Which table represents a proportional relationship? Table 1 Table 2 Table 3 Table Two random samples of students are asked which types of music they prefer. The table shows the results. Student Sample ountry Pop Rap Total # # ccording to the survey, which statement is true? The majority of the students prefer to listen to pop music. The majority of the students prefer to listen to rap music. From both samples combined, 55% of the students prefer to listen to rap music. From both samples combined, 25% of the students prefer to listen to country music. Page 18

21 33. The image shows one of the walls of a house that includes both a rectangular and triangular region. What is the entire area of the wall? 110 ft ft ft ft lifeguard earns $12 per hour working during the summer. The lifeguard works a total of 52 hours and spends 80% of the money earned on a video game system. Which statement is true? The lifeguard has about $500 left after earning $624 and spending about $125 of that on the video game system. The lifeguard has about $500 left after earning $624 and spending about $499 of that on the video game system. The lifeguard has about $125 left after earning $624 and spending about $125 of that on the video game system. The lifeguard has about $125 left after earning $624 and spending about $499 of that on the video game system. Page 19

22 35. carpenter inscribes a circle within a square. The carpenter shades in the area of the square outside of the circle. The circumference of the circle is inches. What is the approximate area of the shaded part of the carpenter s figure? (Use 3.14 as an approximation of pi.) square inches square inches square inches square inches 36. right rectangular prism is sliced at an angle, as shown. What must be true about the shape created when the right rectangular prism is sliced at the angle shown? The shape is always a kite. The shape is always a parallelogram. The shape is always a square. The shape is always a triangle. Page 20

23 37. onsider the image. Which equation demonstrates how to solve for x, and what is the value of x? The equation x = 180 demonstrates one way to solve for x, and x = 38. The equation x = 90 demonstrates one way to solve for x, and x = 52. The equation y = 90 demonstrates one way to solve for y, and y = 52. Since x + y = 180, x = 128. The equation y = 180 demonstrates one way to solve for y, and y = 38. Since x + y = 180, x = eline and iego are both playing a game. The table shows their scores, in points, at the end of each round of the game. Round eline iego What is the difference between eline s and iego s average scores? 3.6 points 4.6 points 18 points 21 points Page 21

24 39. cashier s weekly pay increases from $80 to $100. What is the percent increase in the cashier s weekly pay? 10% 20% 25% 40% 40. The temperature in a town starts at -6 elsius at 7:00 a.m. and rises 3 elsius every hour. Which inequality shows the number of hours, x, past 7:00 a.m. it will take for the temperature to be more than 3 elsius? x < 1 x > 1 x < 3 x > student simplifies an expression as -12z 72 correctly. Which expression could the student have simplified? -6(2z + 12) -4(3z 68) 6(-2z 72) 12(-z + 6) Page 22 STOP. EN OF MTH TEST.

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