PARCC Assessment Readiness

Transcription

1 UNIT 1 REVIEW/TEST PARCC Assessment Readiness Selected Response 1. A clock loses 5 minutes every day. How much time will it lose in hours? second 5 seconds 40 seconds 600 seconds. A statue is 8 feet tall. The display case for a model of the statue is 18 inches tall. Which scale allows for the tallest model of the statue that will fit in the display case? 1 inch : inches 1 inch : 7 inches 1 inch : 5 inches 1 inch : 10 inches 3. Mr. Phillips wants to install hardwood flooring in his den. The flooring costs $5.86 per square yard. The blueprint below shows his house. What other information do you need in order to find the total cost of the flooring? 0.5 in. 1 in. Den 1.8 in. 1.5 in. The lengths and widths of the adjoining rooms in the blueprint The total area of the blueprint The scale of inches in the blueprint to yards in the house The width of the den 4. Which two phrases are equivalent to the expression 7t? the product of 7 and t; 7 multiplied by t t subtracted from 7; t less than 7 t more than 7; t added to 7 the quotient of 7 and t; 7 divided by t 5. What is the solution of the equation f - 10 = 10? f = 0 f = -101 f = -0 f = 0 6. On her math test, Suki was asked to round the measurement meters to the nearest ten meters and underline the last significant digit. What should Suki write? 79 meters 70 meters 710 meters 78 meters 7. An architect built a scale model of a shopping mall. On the model, a circular fountain is 0 inches tall and.5 inches in diameter. The actual fountain is to be 8 feet tall. What will be the diameter of the fountain? 7.1 feet 9 feet 7 feet 10.5 feet 8. What is the solution of the equation 17a = 17? a = 1 a = 17 a = -17 a = Unit 1 Review/Test

2 9. Ramon drives his car 150 miles in 3 hours. What is the unit rate? 1 mile per 50 hours 50 miles per hour 30 miles per hour 150 miles per 3 hours 10. Which is the most precise measurement? 14 3 _ 4 ft 3 in. 4 ft _ in. 11. What is the solution of 3n = 4? n = 45 n = 39 n = 14 n = Which range of measurements is equivalent to 5 km ± 5%? 4.95 km km 3.75 km km 4.38 km km 0 km - 30 km 13. Isabel reads 15 books from the library each month for y months in a row. Which expression shows how many books Isabel read in all? 15 + y 15 - y 15y _ 15 y 14. If 8y = 3, what is the value of y? What is the value of the expression m + o when m = 9 and o = 7? If you are stuck on a problem, skip it and come back later. Another problem might remind you of something that will help. If you feel yourself become tense, take a few deep breaths to relax. 16. Melissa invested her savings in a retirement account that pays simple interest. A portion of her account record is shown below. What is the interest rate on Melissa s account? Date Transaction Amount Balance 8/1 Beginning deposit $ $ /31 Interest payment $19.00 $ /1 Withdrawal $ $ /30 Interest payment $ $ % 3.1% 0.3% 3.% 17. At :45 P.M. you are 11 miles from Dallas. You want to be in Dallas at 4:30 P.M. What is the average speed you must travel to be on time? 49.8 mi/h 51 mi/h 64 mi/h 89.6 mi/h 18. A cyclist travels 45 miles in 4 hours. What is her speed in feet per second? 16.5 ft/s 31 ft/s 66 ft/s 59,400 ft/s PARCC Assessment Readiness 55

3 19. Julie s total cell phone bill consists of a monthly fee plus a charge per minute used. The expression that describes the total of Julie s cell phone bill is 0.07x What does the variable x represent? The number of months billed The total amount of the bill The number of minutes used The monthly fee 0. In a test, a hybrid car drove 619 yards on 1 ounce of gasoline. To the nearest tenth, what is this rate in miles per gallon? 7.5 miles/gallon 15.0 miles/gallon.5 miles/gallon 45.0 miles/gallon 1. Which equation has the solution x = -3? x = 6-9 = -3x -6 = x -18x = 6. In a scale model, a monument is 4.5 inches tall and.5 inches wide. The actual monument is 60 feet wide. How tall is the actual monument? 33 1 _ 3 feet 90 feet 108 feet 11 1 _ feet 3. A consultant charges for her services based on the number of hours worked. The expression that gives the total cost for h hours is 15h Which is the best interpretation of this expression? The consultant charges $150 per hour plus a fee of $15. The consultant charges $15 per hour plus a fee of $150. The consultant charges $75 per hour. The consultant s hourly charge varies from $15 to $150. Mini-Tasks 5. Triangles C and D are similar. The area of triangle C is 47.6 i n. The base of triangle D is 6.7 in. Each dimension of D is 6 the corresponding dimension 5 of C. What is the height of D? 6. A company sells furniture for home assembly. Their largest bookcase has shelves that should be 115 cm, with a tolerance of 0.6 cm. A set of six shelves had lengths of 115. cm, cm, cm, cm, cm, and cm. Which, if any, of the shelves are not within the specified tolerance? 7. A toy company s total payment for salaries for the first two months of 011 was $1,894. a. The total salaries for the first month of 011 were $10,05. Write an equation to find the total salaries for the second month. b. What were the total salaries for the second month? 8. A plane is cruising at an altitude of 4,000 feet. It begins to descend at a constant rate of 0 feet per second. a. Write an expression for the altitude of the plane after t seconds. b. What is the altitude of the plane after 5 min? 9. Juan scored 6 points in the first half of the basketball game, and he scored n points in the second half of the game. a. Write an expression to determine the number of points he scored in all. b. Juan scored 44 points in all. Find the number of points he scored in the second half of the game. 30. On a sunny day, a 5-foot red kangaroo casts a shadow that is 7 feet long. The shadow of a nearby eucalyptus tree is 35 feet long. a. Write a proportion to determine the height of the tree. b. What is the height of the tree? 31. A right triangle has legs 15 inches and 1 inches. Every dimension is multiplied by 1 to form a new 3 right triangle with legs 5 inches and 4 inches. How is the ratio of the areas of the two triangles related to the ratio of corresponding sides? 4. A rectangle has a length of 8 meters and a width of 3 meters. A larger, similar rectangle has a length of meters. What is the width of the larger rectangle? meters 8.5 meters 17 meters 9 meters 56 Unit 1 Review/Test

4 3. Let p represent the price of a pair of jeans. Miles has a coupon for $10 off each pair of jeans that he buys. a. Use the variable p to write an expression for Miles s cost of a pair of a jeans with his coupon. b. Miles decides to buy 4 identical pairs of jeans. Write an expression for the total cost. c. Miles also buys a pair of socks for $5. Write an expression for Miles s total cost. 33. One day, the exchange rate was 60 U.S. dollars for 50 euro. At this rate, about how many U.S. dollars would be equivalent to 70 euro? 34. A map has the scale 1 inch:10 miles. On this map, the area of a national park is about 1.5 square inches. What is the approximate area of the park in acres? (1 square mile = 640 acres) 35. The table shows the typing rates of four applicants for a typing job. Applicant Words Minute Ann 11 6 Theo 06 8 June Andy 10 5 a. Based on typing rates, which applicant is the best choice to hire? b. What other information besides typing rate might you want to consider when choosing an applicant? 36. A polygon has an area of 3 square feet. What is the area of the polygon in square inches? 37. In the 004 Olympics, the ratio of gold medals to silver medals won by the team from Hungary was 4:3. The ratio of silver medals to bronze medals won by the team was :1. The team won 3 bronze medals. How many gold medals did they win? Performance Tasks 38. Luke is buying food for a neighborhood block party. He has $139 to spend, and he has already spent $11. He wants to buy some bags of hamburger buns that cost $4 each. a. How much money does Luke have left to spend? b. Define a variable or variables needed to model this situation. c. Using the number you found in part a and the variable(s) defined in part b, write an equation to find the number of bags of hamburger buns Luke can buy. d. Luke wants to buy 6 bags of hamburger buns. Does he have enough money? Explain how you found your answer. 39. Suppose a report indicates that the surveyed distance between two points is 100 feet. a. If this is all of the information given about the surveyed distance, what might a reader think the measurement error is? Why? b. The error in the measurement is actually ± 0.1 feet. Explain how the distance might have been reported in a way that better indicates the true accuracy of the measurement. 40. To build an accurate scale model of the solar system, choose a diameter for the model of the Sun. Then other distances and sizes can be calculated proportionally. Sun Mars Pluto Diameter (mi) 865,000 4,00 1,500 Distance from Sun (million mi) ,670 a. Sara wants to draw a scale model of the solar system in which the diameter of the Sun is 1 inch. What should the diameter of Pluto be? b. Do you think it is reasonable for Sara to draw this model? Why or why not? my.hrw.com Online Assessment Go online for updated, PARCC-aligned assessment readiness. PARCC Assessment Readiness 57

5 UNIT REVIEW/TEST PARCC Assessment Readiness Selected Response 1. What value of n makes the equation below have no solution? x + = nx Which of the equations below represents the second step of the solution process? Step 1: 3 (5x - ) + 7 = -4 Step : Step 3: 15x + 1 = -4 Step 4: 15x = -45 Step 5: x = -3 3 (5x + 7) - = -4 3 (5x + 5) = -4 15x = -4 15x = Cass drove 3 miles to school, and then she drove m miles to a friend s house. The total mileage for these two trips was 8 miles. Which equation CANNOT be used to determine the number of miles Cass drove? 3 + m = m = = m 8 - m = 3 4. If _ 0 x = 4_, which of the following is a true x - 5 statement? x (x - 5) = 80 0x = 4 (x - 5) 0(x - 5) = 4x 4 = x A bike rental shop charges a one-time charge of $8 plus an hourly fee to rent a bike. Dan paid $4.50 to rent a bike for 5 1 hours. What is the bike shop s hourly fee in dollars? $3.00 $5.50 $4.45 $8 6. Which algebraic expression means 5 less than y? 5 - y y < y 5 y 7. If t + 8 =, find the value of t The length of the rectangle is (x + 1) meters and the perimeter is 60 meters. What is the length of the rectangle? 1 meters 6 meters 8 meters 56 meters 9. Samantha opened a bank account in June and deposited some money. She deposited twice that amount in August. At the end of August, Samantha had less than $600 in her account. If she made no other withdrawals or deposits, which inequality could be used to determine the maximum amount Samantha could have deposited in June? x < 600 x > 600 3x < 600 3x > (x + 1) 10. For which inequality is - a solution? x < -4 -x < 4 -x > -4 -x < Unit Review/Test

6 1. Which ordered pair is NOT a solution of the system graphed below? (0, 0) (0, 3) (1, 1) (, 1) y 0 -. The fare for a cab is $3.50 per trip plus $1.5 per mile. Which describes the cab fare in dollars as a function of miles traveled? f (x) = 3.5x f (x) = 3.5x f (x) = 1.5x f (x) = 1.5x Hillary needs markers and poster board for a project. The markers are $0.79 each and the poster board is $1.89 per sheet. She needs at least 4 sheets of poster board. Hillary has $15 to spend on project materials. Which system models this information? p m p m 1.89p 4p 15 4p 1.89 m + 4p 15 p + m m p 4 x Mini-Tasks 4. Alex buys 5 calendars to give as gifts. Each calendar has the same price. When the cashier rings up Alex s calendars, the total cost before tax is $ a. Write and solve an equation to find the cost of each calendar. b. The total cost of Alex s calendars after tax is $ Find the percent sales tax. Show your work and explain in words how you found your answer. 5. Write different inequalities that have the same solution as n > 3 such that a. the first inequality uses the symbol > and requires addition or subtraction to solve. b. the second inequality uses the symbol < and requires multiplication or division to solve. 6. Alison has twice as many video games as Kyle. Maurice has 5 more video games than Alison. The total number of video games is less than 40. a. Write an inequality to represent this situation. b. Solve the inequality to determine the greatest number of video games Maurice could have. Justify each step in your solution. 7. Donna s Deli delivers lunches for $7 per person plus a $35 delivery fee. Larry s Lunches delivers lunches for $11 per person. a. Write an expression to represent the cost of x lunches from Donna s Deli. Write an expression to represent the cost of ordering x lunches from Larry s Lunches. b. Write an inequality to determine the number of lunches for which the cost of Larry s Lunches is less than the cost of Donna s Deli. c. Solve the inequality and explain what the answer means. Which restaurant charges less for an order of 10 lunches? 8. Graph y > _ -x - 1 on a coordinate plane. Name 3 one point that is a solution of the inequality. 18 Unit Review/Test

7 11. Which graph shows the solutions of - (1 - x) < 3 (x - )? Which compound inequality has no solution? x > 1 OR x < - x < 1 AND x > - x < 1 OR x < - x > 1 AND x < Which inequality has the same solutions as p <-? p + 1 < - p + 4 < p + 1 < -4 3p < What is the greatest integer solution of 5-3m > 11? The sum of the measures of any two sides of a triangle must be greater than the measure of the third side. What is the greatest possible integer value for x? 16. For which inequality is 3 a solution? x 5 > x x x Which of the problems below could be solved by finding the solution of this system? x + y = 56 y = 1 _ 3 x The area of a rectangle is 56 square units. The width is one-third the length. Find the length of the rectangle. The area of a rectangle is 56 square units. The length is one-third the perimeter. Find the length of the rectangle. The perimeter of a rectangle is 56 units. The length is one-third more than the width. Find the length of the rectangle. The perimeter of a rectangle is 56 units. The width is one-third the length. Find the length of the rectangle. 18. What is the slope of a line perpendicular to a line that passes through (3, 8) and (1, -4)? - 1 _ 6-1 _ 19. Which inequality is graphed below? y 4 6 x 15 x x > -3 x < -6 -y > -3 3y < 9 0. A chemist has a bottle of a 10% acid solution and a bottle of a 30% acid solution. He mixes the solutions together to get 500 ml of a 5% acid solution. How much of the 30% solution did he use? 15 ml 375 ml 150 ml 450 ml PARCC Assessment Readiness 181

8 9. Marc and his brother Ty start saving money at the same time. Marc has $145 and will add $10 to his savings every week. Ty has $0 and will add $15 to his savings every week. After how many weeks will Marc and Ty have the same amount saved? What is that amount? Show your work. 30. A movie producer is looking for extras to act as office employees in his next movie. The producer needs extras that are at least 40 years old but less than 70 years old. They should be at least 60 inches tall but less than 75 inches tall. Graph all the possible combinations of ages and heights for extras that match the producer s needs. Let x represent age and y represent height. Show your work. Performance Tasks 31. Korena is laying out a flower garden in her front yard. The garden will be 6 feet wide, and one side will be flush against her house. She wants to add a decorative border around the other three sides, and she has feet of decorative border. She also needs the garden to have an area of at least 50 square feet to fit all of her plants. Garden 6 ft House 3. Serena wants to use the interest earned for one year from her college savings to update the software on her computer. She can invest up to $10,000, and she needs at least $300 for the software. She wants to put part of this amount into a money market account that earns.5% simple interest per year. She puts the other part in a certificate of deposit (CD), which earns 4% simple interest per year. a. Use x to represent the money invested in the CD and y to represent the money invested in the money market account. Write an inequality to represent the amount of money she can invest. b. Using the same variables as in part a, write an inequality to represent the amount of interest she needs to earn in one year. c. Graph the system of inequalities. Identify a solution that meets Serena s requirements, and calculate how much money she will earn on interest with that solution. d. Serena wants to put as little money in the CD as possible, because unlike the money market account, she can t withdraw any money from the CD until the end of the year. What is the least amount of money Serena can put in the CD and still earn enough interest? Round to the nearest whole dollar, and explain how you found your answer. a. Write formulas for the area of the garden and for the length of the decorative border. Write both formulas in terms of length l and width w. b. Solve both formulas from part a for l. c. Use your formulas to find out if there is a length l that satisfies Korena s requirement for the area and fits the amount of border she has. Explain your reasoning. d. Describe one way Korena could change her plans so that she has the materials she needs to make her garden. Explain your reasoning and detail your changes. my.hrw.com Online Assessment Go online for updated, PARCC-aligned assessment readiness. PARCC Assessment Readiness 183