III. Mathematics Retest Mathematics Retest The Mathematics Retest was based on learning standards in the Massachusetts Mathematics Curriculum Framework (2000). The Framework identities five major content strands, listed below. * Number Sense and Operations * Patterns, Relations, and Algebra * Geometry * Measurement * Data Analysis, Statistics, and Probability The grades 9-10 learning standards for these strands appear on pages 72-75 of the Mathematics Curriculum Framework, which is available on the Department Web site at www.doe.mass.edu/frameworks/current.html. In Test Item Analysis Reports, Mathematics retest results are reported under five MCAS reporting categories, which are identical to the five Mathematics Curriculum Framework content strands listed above. Test Sessions The Mathematics Retest included two separate test sessions, which were administered on consecutive days. Each session included multiple-choice and open-response items. Session 1 also included short-answer questions. Reference Materials and Tools Each student taking the Mathematics Retest was provided with a Grade 10 Mathematics Reference Sheet and was allowed to refer to it at any time during testing. A copy of the reference sheet follows the final question in this chapter. During session 2, each student had sole access to a calculator with at least four functions and a square root key. Calculator use was not allowed during session 1. The use of bilingual word-to-word dictionaries was allowed for limited English proficient students only during both Mathematics retest sessions. No other reference tools or materials were allowed. Cross-Reference Information The table at the conclusion of this chapter indicates each item's reporting category and the Framework learning standard it assesses. The correct answers for multiple-choice and short-answer items are also displayed in the table. Mathematics SESSION 1 You may use your reference sheet during this session. You may not use a calculator during this session. [non calculator symbol] DIRECTIONS This session contains fourteen multiple-choice questions, four short-answer questions, and three open-response questions. Mark your answers to these questions in the spaces provided in your Student Answer Booklet. 1 What is the value of the expression below? [3 multiplied by the equation (4 to the second power subtracted by 2)] A. 18 B. 22 C. 42 D. 46 2 Jamison is taking a friend to the movies. He wants to estimate the amount of money he will need for tickets, large bags of popcorn, and large cups of soda. The prices are shown below. Ticket $7.75 Large bag of popcorn $3.85 Large cup of soda $2.65 Which of the following is closest to the amount of money Jamison will need for 2 tickets, 2 large bags of popcorn, and 2 large cups of soda? A. $34 B. $30 C. $24 D. $20 3 Which of the following is equivalent to the expression below? [x squared plus 3x subtracted by 5x squared plus 6] A. [negative 4x squared plus 3x plus 6] B. [4x squared plus 3x plus 6] C. [x squared subtracted by 2x plus 6] D. [x squared plus 2x plus 6] 4 Each week, Shanice deposits a total of $50 into her checking account and does not withdraw any money. Her account does not earn interest. At the end of 3 weeks, the total amount of money in Shanice's account was $170. Which of the following equations represents y, the total amount of money in Shanice's account at the end of x weeks? A. [y = 50x plus 20] B. [y = 20x plus 50] C. [y = 50x subtracted by 20] D. [y = 20x subtracted by 50] 5 Which of the following is closest to the value of [square root of 72] A. 8.1 B. 8.5 C. 8.9 D. 9.3 6 What is the value of x in the solution to the following system of equations? [x plus y = 5] [2x plus 6y = 22] A. x = 4 B. x = 3 C. x = 2 D. x = 1 7 Which of the following sets of data has a median of 17.5? A. {10.0, 17.5, 14.0, 16.0, 27.5} B. {12.5, 26.0, 17.5, 11.5, 10.5} C. {13.0, 17.5, 15.0, 15.5, 17.5} D. {14.5, 19.5, 16.0, 17.5, 24.0} 8 Which of the following equations best represents the line of best fit for the data shown in the scatterplot below? [Scatterplot graph displaying ascending plots] A. [y = negative 2.5x plus 1] B. [y = 2.5x plus 1] C. [y = negative 0.6x plus 1] D. [y = 0.6x plus 1] 9 Which of the following shows the expression below in factored form? [4y cubed plus 6y squared subtracted by 14y] A. [2y multiplied by (2y squared plus 3y subtracted by 7)] B. [4y multiplied by (y squared plus 2y subtracted by 10)] C. [2y squared multiplied by (2y plus 3 subtracted by 7y)] D. [4y squared multiplied by (y plus 2 minus 10y)] 10 What is the value of the expression below? [4 multiplied by the absolute value of 3 subtracted by 5] A. [negative 32] B. [negative 8] C. 8 D. 32 11 What is the value of the expression below? [square root of 125 cubed cubed] A. 5 B. 25 C. 75 D. 125 12 The table below shows a relationship between values of x and y. x 1 2 3 4 y 3 10 29 66 Which of the following equations describes the relationship between x and y for the values in the table? A. [y = 3x] B. [y = 3x plus 4] C. [y = x squared plus 2] D. [y = x cubed plus 2] 13 Which of the following best represents the slope and y-intercept of the line on the coordinate grid below? [coordinate grid displaying a line with arrows at both ends on a slope and y-intercept] A. [slope = negative one-half; y-intercept = 2] B. [slope = one-half; y-intercept = 2] C. [slope = negative one-half; y-intercept = 4] D. [slope = one-half; y-intercept = 4] 14 If [x is greater than 0], which of the following is closest to the value of x that makes the equation below true? [2x squared = 40] A. 3.2 B. 4.5 C. 6.3 D. 8.9 Questions 15 and 16 are short-answer questions. Write your answers to these questions in the boxes provided in your Student Answer Booklet. Do not write your answers in this test booklet. You may do your figuring in the test booklet. 15 A box in the shape of a right rectangular prism has a volume of 60 cubic inches. The height of the box is 3 inches, and the width is 4 inches. What is the length, in inches, of the box? 16 Brian set up a birdhouse, a birdbath, and a bird feeder in his backyard. The vertices of the triangle shown below represent the locations of these three objects in his backyard. [Right triangle illustration of a Birdhouse and Birdbath sixty feet apart, Birdbath and Bird feeder eighty feet apart] Based on the distances shown, what is the distance, in feet, between the birdhouse and the bird feeder? Question 17 is an open-response question. * BE SURE TO ANSWER AND LABEL ALL PARTS OF THE QUESTION. * Show all your work (diagrams, tables, or computations) in your Student Answer Booklet. * If you do the work in your head, explain in writing how you did the work. Write your answer to question 17 in the space provided in your Student Answer Booklet. 17 Laurie's parents gave her $25 to open a checking account. At the end of each week after the account was opened, Laurie deposited $20 into her checking account. No other money was deposited into or withdrawn from the checking account. a. What was the total amount of money in Laurie's checking account at the end of week 5? Show or explain how you got your answer. b. On the grid in your Student Answer Booklet, plot six points with coordinates (x, y), in which x and y are defined as follows: * [x equals] the number of weeks since the account was opened (in whole numbers from 0 through 5), where x = 0 corresponds to the opening of the account * [y equals] the total amount of money in the account at the end of week x Be sure to label the x-axis and y-axis, indicate the scale on each axis, and include a title for your graph. c. Write an equation that represents the line that passes through all the points plotted in part (b). Show or explain how you determined your equation. d. For the line represented by your equation in part (c), explain the meaning of the y-intercept in the context of this problem. Questions 18 and 19 are short-answer questions. Write your answers to these questions in the boxes provided in your Student Answer Booklet. Do not write your answers in this test booklet. You may do your figuring in the test booklet. 18 What is the value of x that makes the linear equation below true? [3x subtracted by 5 = 2 multiplied by the equation (x plus 3)] 19 The diagram below shows a square in the interior of a rectangle. [Diagram showing a square that is 4 feet by 4 feet in the interior of a rectangle that is 12 feet by 10 feet] Based on the dimensions in the diagram, what is the area, in square feet, of the shaded region of the rectangle? Questions 20 and 21 are open-response questions. * BE SURE TO ANSWER AND LABEL ALL PARTS OF EACH QUESTION. * Show all your work (diagrams, tables, or computations) in your Student Answer Booklet. * If you do the work in your head, explain in writing how you did the work. Write your answer to question 20 in the space provided in your Student Answer Booklet. 20 The dots shown below represent the first four figures in a quadratic pattern. [Four figures of dots representing the first four figures in a quadratic pattern] The table below shows the number of dots needed for each of Figures 1 through 4. Number of Dots per Figure Figure Number 1 2 3 4 5 6 7 8 Number of 1 4 9 16 Dots a. Copy the table into your Student Answer Booklet. Complete your table by writing the number of dots needed for each of Figures 5 through 8. Show or explain how you got each of your answers. b. Based on the pattern, what number of dots will be needed for Figure n? Show or explain how you got your answer. c. What number of dots will be needed for Figure 20? Show or explain how you got your answer. d. If Figure n has exactly 225 dots, what is the value of n? Explain your reasoning. Write your answer to question 21 in the space provided in your Student Answer Booklet. 21 Triangle ABC and the coordinates of each vertex of the triangle are shown on the coordinate grid below. [Coordinate grid showing triangle ABC with coordinates of each vertex: A(negative 5, 2), B(3,6), C(1, negative 2)] a. Let M be the midpoint of [line AC]. What are the coordinates of M? Show your work. b. Let N be the midpoint of [line BC]. What are the coordinates of N? Show your work. c. What is the length of [line MN]? Show your work. (You may leave your answer as a square root of a number.) d. What is the slope of the line that contains both point M and point N? Show your work. e. Write an equation representing the line that contains both point M and point N. Show your work. Mathematics SESSION 2 You may use your reference sheet during this session. You may use a calculator during this session. [calculator symbol] DIRECTIONS This session contains eighteen multiple-choice questions and three open-response questions. Mark your answers to these questions in the spaces provided in your Student Answer Booklet. 22 The number of hours Nadia spent painting each day during a one-week period are shown below. 1.5, 4.25, 1.0, 3.75, 6.0, 0.75, 0.25 What is the mean number of hours per day that Nadia spent painting for this week? A. 1.5 B. 2.5 C. 3.75 D. 5.75 23 A stadium has seats that are arranged into sections. In each section, the seats are arranged into rows. There are 11 sections, 7 rows in each section, and 10 seats in each row. At a baseball game in the stadium, all of the seats are occupied. A seat will be chosen at random, and a prize will be awarded to the person sitting in that seat. If Hoda is sitting in one of the seats, what is the probability that she will win the prize? A. [1 over 770] B. [3 over 770] C. [1 over 28] D. [3 over 28] 24 A candle in the shape of a right circular cylinder is pictured below. [circular cylinder 23 cm high and 14.8 cm wide] Based on the dimensions shown in the picture, which of the following is closest to the lateral surface area of the candle? A. 46 cm^2 B. 170 cm^2 C. 1100 cm^2 D. 4000 cm^2 25 If [x does not equal 0], which of the following expressions belongs in the box below to make the equation true? (-2x) [multiplied by question mark in box] = 1 A. [negative 1 over 2x] B. [negative x over 2] C. [2 over x] D. [2x] 26 Hector made a scale drawing of the front of a building. * The front of the actual building is in the shape of a rectangle with a height of 21 feet and a width of 15 feet. * The height of the building in Hector's drawing is 3.5 inches, and the width is 2.5 inches. What scale factor did Hector use in his scale drawing? A. 1 inch : 2 feet B. 1 inch : 4.3 feet C. 1 inch : 6 feet D. 1 inch : 8.4 feet 27 Which of the following figures appears to have 2 lines of symmetry? A. [pentagon] B. [trapezoid] C. [geometric figure] D. [geometric figure] 28 The diagram below represents five of Gina's classrooms and the paths between them. The classrooms are labeled P, Q, R, S, and T. The length, in yards, of each path is shown. [Diagram labeled P, Q, R, S, and T. P to Q 25 yards, Q to R 12 yards, Q to S 20 yards, R to S 10 yards, S to T 12 yards, R to T 11 yards, T to P 8 yards] Gina needs to pick up homework assignments from each of the five classrooms. She begins at classroom P. What is the minimum distance she can walk along the paths so that she stops once at each of the remaining four classrooms without taking any path more than once? A. 31 yards B. 42 yards C. 49 yards D. 59 yards 29 Which of the following is equivalent to the expression below? [(3x plus 2)(x plus 1)] A. [3x squared plus 2] B. [4x squared plus 3] C. [3x squared plus 5x plus 2] D. [4x squared plus 5x plus 2] 30 Which of the following is closest to the area of a circle that has a diameter of 8 centimeters? A. 12.56 cm^2 B. 25.12 cm^2 C. 50.24 cm^2 D. 200.96 cm^2 Question 31 is an open-response question. * BE SURE TO ANSWER AND LABEL ALL PARTS OF THE QUESTION. * Show all your work (diagrams, tables, or computations) in your Student Answer Booklet. * If you do the work in your head, explain in writing how you did the work. Write your answer to question 31 in the space provided in your Student Answer Booklet. 31 Aimee, Darlene, Percy, and Sinclair went bowling. Their scores for 4 games are shown in the table below. Bowling Scores Scores Name Game 1 Game 2 Game 3 Game 4 Aimee 165 140 170 130 Darlene 120 140 125 140 Percy 115 130 160 160 Sinclair 150 150 150 165 a. What is the range of Aimee's scores for the 4 games? Show or explain how you got your answer. b. Who had the greatest median score for the 4 games? Show or explain how you got your answer. c. Who had the greatest mean score for the 4 games? Show or explain how you got your answer. d. After Darlene bowled 2 more games, her mean score for all 6 games was 135. What could her scores for each of those 2 games have been? Show or explain how you got your answer. Mark your answers to multiple-choice questions 32 through 40 in the spaces provided in your Student Answer Booklet. Do not write your answers in this test booklet. You may do your figuring in the test booklet. 32 In the figure below, [line PQ is parallel to line SR], and [line PR] and [line QS] intersect at point T. [figure with points labeled PQSR and intersection at point T. Angle Q is 62° and angle R is 40°] Based on the angle measures in the figure, what is the measure of [angle STR]? A. 62° B. 78° C. 102° D. 118° 33 A right square pyramid and its dimensions are shown below. [illustration of a 6 cm by 5 cm by 4 cm right square pyramid] What is the volume of the right square pyramid? A. 40 cm^3 B. 48 cm^3 C. 60 cm^3 D. 144 cm^63 34 A researcher collected data on the final heights of corn plants. The data were collected from one farm over four growing seasons. He drew box-and-whisker plots to represent the data he collected for each growing season. Which of the following box-and-whisker plots shows the greatest median final height? A. [box-and-whisker plot with plot between 1 and 2.1] B. [box-and-whisker plot with plots between 0.9 and 2.2] C. [box-and-whisker plot with plots at 0.7 and 2.2] D. [box-and-whisker plot with plots at 0.7 and 2.1] 35 Which of the following is the solution to the inequality below? [3 subtracted by 2x is less than or equal to 7] A. [x is less than or equal to negative 2] B. [x is greater than or equal to negative 2] C. [x is less than or equal to negative 5] D. [x is greater than or equal to negative 5] 36 Martin uses a ramp to practice skateboarding. The ramp leans against a wall. The right triangle formed by the ramp, the wall, and the ground is represented by the diagram below. [right triangle] The measure of the angle formed by the wall and the ramp is 57°. What is the measure of the angle formed by the ramp and the ground? A. 33° B. 43° C. 93° D. 123° 37 Elaine's summer job earnings were $1275. She spent $40 of her earnings per week during the school year. Which of the following equations represents the amount of money, m, that was remaining from Elaine's summer job earnings after w weeks of school? A. [m = negative 1275 plus 40w] B. [m = negative 40 plus 1275w] C. [m = 40 subtracted by 1275w] D. [m = 1275 subtracted by 40w] 38 Greta is making soup and needs to buy broth. She is able to buy cans of broth in the four different sizes listed below. * Can A costs $3.84 for 32 ounces. * Can B costs $1.40 for 14 ounces. * Can C costs $3.96 for 49.5 ounces. * Can D costs $1.60 for 14.5 ounces. Which can costs the least per ounce? A. Can A B. Can B C. Can C D. Can D 39 Jacob made the stem-and-leaf plot below to show the number of minutes per day he spent playing video games over a 10-day period. [stem-and-leaf plot] What is the mean of the set of data in the stem-and-leaf plot? A. 81 B. 82 C. 83 D. 85 40 The annual salaries, in millions of dollars, of 10 professional baseball players are shown below. 2.4 0.9 10.1 5.5 13.0 15.6 12.0 10.5 0.7 11.5 What is the range of the 10 annual salaries, in millions of dollars? A. 8.2 B. 9.1 C. 10.3 D. 14.9 Questions 41 and 42 are open-response questions. * BE SURE TO ANSWER AND LABEL ALL PARTS OF EACH QUESTION. * Show all your work (diagrams, tables, or computations) in your Student Answer Booklet. * If you do the work in your head, explain in writing how you did the work. Write your answer to question 41 in the space provided in your Student Answer Booklet. 41 Steve completed his research for a term paper and started writing a first draft. He asked Luisa to proofread the first draft. a. Steve wrote 720 words of his first draft in 3 hours. What was the rate, in words per hour, at which Steve wrote? Show or explain how you got your answer. b. Luisa can proofread 1200 words per hour. At this rate, what was the time, in hours, it took her to proofread 720 words? Show your work. Steve's completed term paper has 6000 words on 20 pages. Each page contains an equal number of words. c. Using your answer from part (a), what was the time, in hours, it took Steve to write 1 page? Show your work. d. Luisa proofread all 20 pages of Steve's completed term paper at a rate of 1200 words per hour. What is this rate in pages per hour? Show your work. Write your answer to question 42 in the space provided in your Student Answer Booklet. 42 Ethan wants to build a backgammon game board. A diagram of the game board, its dimensions, and a detailed view of two triangles are shown below. [Backgammon Game Board 18 inches long by 20 inches wide, black and white triangles 8 inches long by 1.5 inches wide] To make the board, Ethan will begin with a rectangular piece of wood that has a length of 20 inches and a width of 18 inches. He will then glue congruent triangles of black plastic and white plastic onto the rectangular piece of wood. The table below shows the price per square inch of each material Ethan will use. Prices of Backgammon Game Board Materials Material Wood Black plastic White plastic Price (per square inch) $0.20 $0.50 $0.50 a. What is the area, in square inches, of 1 black triangle? Show your work. b. Using your answer from part (a), what is the cost of the amount of black plastic needed to make 1 black triangle? Show your work. c. What is the cost of the amount of white plastic needed to make all of the white triangles? Show your work. d. What will be the total cost of the materials Ethan uses to build the game board, not including the glue? Show your work. [MCAS logo] [Massachusetts Comprehensive Assessment System Grade 10 Mathematics Reference Sheet] Mathematics Retest November 2007 Released Items: Reporting Categories, Standards, and Correct Answers* Item No. Page No. Reporting Category Standard Correct Answer (MC/SA)* 1 41 Number Sense and Operations 10.N.2 C 2 41 Number Sense and Operations 10.N.4 B 3 42 Patterns, Relations, and Algebra 10.P.4 A 4 42 Patterns, Relations, and Algebra 10.P.7 A 5 42 Number Sense and Operations 10.N.3 B 6 42 Patterns, Relations, and Algebra 10.P.8 C 7 43 Data Analysis, Statistics, and Probability 10.D.1 D 8 43 Data Analysis, Statistics, and Probability 10.D.2 B 9 43 Patterns, Relations, and Algebra 10.P.4 A 10 43 Number Sense and Operations 10.N.2 C 11 44 Number Sense and Operations 10.N.1 D 12 44 Patterns, Relations, and Algebra 10.P.1 D 13 44 Patterns, Relations, and Algebra 10.P.2 A 14 44 Number Sense and Operations 10.N.3 B 15 45 Measurement 10.M.2 5 inches 16 45 Geometry 10.G.5 100 feet 17 46 Patterns, Relations, and Algebra 10.P.2 18 47 Patterns, Relations, and Algebra 10.P.6 11 19 47 Measurement 10.M.1 104 square feet 20 48 Patterns, Relations, and Algebra 10.P.1 21 49 Geometry 10.G.7 22 50 Data Analysis, Statistics, and Probability 10.D.1 B 23 50 Data Analysis, Statistics, and Probability 8.D.4 A 24 51 Measurement 10.M.2 C 25 51 Number Sense and Operations 10.N.1 A 26 51 Geometry 10.G.9 C 27 52 Geometry 10.G.1 C 28 52 Geometry 10.G.11 B 29 53 Patterns, Relations, and Algebra 10.P.3 C 30 53 Measurement 10.M.1 C 31 54 Data Analysis, Statistics, and Probability 10.D.1 32 55 Geometry 10.G.3 B 33 55 Measurement 10.M.2 B 34 56 Data Analysis, Statistics, and Probability 10.D.1 A 35 57 Patterns, Relations, and Algebra 10.P.6 B 36 57 Geometry 10.G.5 A 37 57 Patterns, Relations, and Algebra 10.P.7 D 38 57 Number Sense and Operations 8.N.3 C 39 58 Data Analysis, Statistics, and Probability 10.D.1 A 40 58 Data Analysis, Statistics, and Probability 10.D.1 D 41 59 Number Sense and Operations 8.N.3 42 60 Measurement 10.M.1 * Answers are provided here for multiple-choice items and short-answer items only. Each open-response item has its own set of scoring guidelines, which allow for valid alternate interpretations and responses.