XV. Mathematics, Grade 10

Transcription

1 XV. Mathematics, Grade 0

2 Grade 0 Mathematics Test The spring 0 grade 0 Mathematics test was based on standards in the 0 Massachusetts Curriculum Framework for Mathematics that match content in the grade 9 0 standards from the 000 Massachusetts Mathematics Curriculum Framework. The standards in the 0 Framework on the grade 0 test are organized under the five major conceptual categories listed below. Number and Quantit Algebra Functions Geometr Statistics and Probabilit The Massachusetts Curriculum Framework for Mathematics is available on the Department website at More information and a list of standards assessable on the spring 0 test are available at Mathematics test results for grade 0 are reported under four MCAS reporting categories, which are based on the five Framework conceptual categories listed above. The table at the conclusion of this chapter indicates each item s reporting categor, the 0 Framework standard it assesses, and the 000 Framework standard it assesses. The correct answers for multiplechoice and short-answer items are also displaed in the table. Test Sessions The grade 0 Mathematics test included two separate test sessions, which were administered on consecutive das. Each session included multiple-choice and open-response items. Session also included short-answer items. Reference Materials and Tools Each student taking the grade 0 Mathematics test was provided with a grade 0 Mathematics Reference Sheet. A cop of the reference sheet follows the final question in this chapter. During Session, each student had sole access to a calculator with at least four functions and a square root ke. Calculator use was not allowed during Session. During both Mathematics test sessions, the use of bilingual word-to-word dictionaries was allowed for current and former English language learner students onl. No other reference tools or materials were allowed.

3 Grade 0 Mathematics Session You ma use our reference sheet during this session. You ma not use a calculator during this session. DIRECTIONS This session contains fourteen multiple-choice questions, four short-answer questions, and three open-response questions. Mark our answers to these questions in the spaces provided in our Student Answer Booklet. ID:079 C Common The first five terms in a geometric sequence are shown below.,, 6, 08,,... What is the net term in the sequence? ID:999 WDN0_phi.eps B Common The length, in centimeters, of a rectangle is represented b an epression, as shown in the diagram below. A. B. 68 C. 97 D ID:880 A Common Which of the following is equivalent to the epression below? 7 60 A. ( )( ) B. ( 0)( 6) C. ( )( ) D. ( 0)( ) Based on the diagram, which of the following is closest to the length, in centimeters, of the rectangle? A. 8. B. 8.7 C. 9. D. 9.

4 Mathematics Session ID:080 CCF8_Laundr.eps [opt_a0 D Common Giselle surveed 0 students at random about the number of people in their household and the number of times laundr is washed in their household each week. The results of her surve are shown in the table below. Weekl Laundr Washes Number of People in Household Number of Washes 6 6 Which of the following scatterplots best represents the data in the table? A. Weekl Laundr Washes C. Weekl Laundr Washes 7 7 Number of Washes 6 Number of Washes Number of People in Household Number of People in Household B. Weekl Laundr Washes D. Weekl Laundr Washes 7 7 Number of Washes 6 Number of Washes Number of People in Household Number of People in Household

5 Mathematics Session ID:066 C Common What is the value of the epression below? A. 0 B. C. 60 D. 9 ( ) ( ) ID:080 C Common 6 What are the solutions of the equation below? ( ) ( 9) 0 A. ; 9 B. ; 9 C. ; 9 D. ; 9 ID:0876 NEE0_revised.eps B Common 7 The line plot below shows the fuel efficienc, in miles per gallon, for the vehicles owned b a rental car compan. X X X X X X X X X X X X X X X Fuel Efficienc (miles per gallon) Based on the line plot, what is the median fuel efficienc, in miles per gallon, for the vehicles? A. B. C. D.

6 Mathematics Session ID:88 B Common 8 Ja and Kalani graphed lines on a coordinate plane. Ja s line is represented b the equation below. Kalani s line is parallel to Ja s line. Which of the following could be an equation of Kalani s line? A. B. C. D. ID:87 A Common 0 Which of the following is equivalent to the epression below? 6 A. 8 B. 6 0 C. 0 0 D. 0 ID:90 B Common 9 The first,0 people to attend a baseball game received a free hat. A total of 9, people attended the game. Which of the following is closest to the fraction of people attending the game who received a free hat? A. 0 B. 8 C. D.

7 Mathematics Session ID:9676 CMC7_sales.eps C Common Salesperson s Monthl Commission (in dollars) The scatterplot below shows the relationship between the total monthl sales, in millions of dollars, at a retail store and the monthl commissions, in dollars, earned b one salesperson Retail Store Sales ID:79 B Common Which of the following is equivalent to the epression below? A. 0 B. C. D Total Monthl Sales (in millions of dollars) Based on the line of best fit for the scatterplot, which of the following is closest to the monthl commission that the salesperson could epect to make when the total monthl sales at the retail store are $0.8 million? A. $00 B. $00 C. $00 D. $600 6

8 Mathematics Session ID:068 D Common Da of Trip Miles Driven Leah took a -da car trip. The table below shows the number of miles she drove on each da of her trip. Leah s Car Trip ID:760 D Common Which of the following is equivalent to the epression below? A. 7 B. C. 7 D. 7 ( )( ) Of the total number of miles that Leah drove on her trip, which of the following is closest to the percentage she drove on da? A. % B. 0% C. % D. 0% 7

9 Mathematics Session Questions and 6 are short-answer questions. Write our answers to these questions in the boes provided in our Student Answer Booklet. Do not write our answers in this test booklet. You ma do our figuring in the test booklet. ID:008 ADJ_escalator.eps Common The diagram below shows a right triangle and some of its measurements. h 8 m 0 What is h, the height in meters of the triangle? ID:06777 NEE07.eps Common 6 A doctor recorded the resting heart rate, in beats per minute, of each of her patients. The distribution of the heart rates for this group of patients is shown in the bo-and-whisker plot below. Resting Heart Rate (beats per minute) Based on the bo-and-whisker plot, what was the median resting heart rate, in beats per minute, for this group of patients? 8

10 Mathematics Session Question 7 is an open-response question. BE SURE TO ANSWER AND LABEL ALL PARTS OF THE QUESTION. Show all our work (diagrams, tables, or computations) in our Student Answer Booklet. If ou do the work in our head, eplain in writing how ou did the work. Write our answer to question 7 in the space provided in our Student Answer Booklet. ID:067 Common 7 A student is approimating the locations of square roots and cube roots of integers on a number line. a. Between which two consecutive integers on the number line is located? Show or eplain how ou got our answer. b. What is the value of to the nearest tenth? Show or eplain how ou got our answer. The value of m, where m is an integer, is located between and on the number line. c. What could be the value of m? Show or eplain how ou got our answer. The value of number line. n, where n is an integer, is also located between and on the d. What could be the value of n? Show or eplain how ou got our answer. 9

11 Mathematics Session Questions 8 and 9 are short-answer questions. Write our answers to these questions in the boes provided in our Student Answer Booklet. Do not write our answers in this test booklet. You ma do our figuring in the test booklet. ID:907 Common 8 What is the value of the epression below? 0 ( ) ID:68 CMC6_slope.eps Common 9 What is the slope of the line graphed below? (0, ) (, ) (, )

12 Mathematics Session Questions 0 and are open-response questions. BE SURE TO ANSWER AND LABEL ALL PARTS OF EACH QUESTION. Show all our work (diagrams, tables, or computations) in our Student Answer Booklet. If ou do the work in our head, eplain in writing how ou did the work. Write our answer to question 0 in the space provided in our Student Answer Booklet. ID:90 CMC_puzzle.eps Common 0 A puzzle in the shape of a rectangle has si pieces. The puzzle and some of its dimensions are shown in the diagram below. 0 in. in. R B P in. 8 in. Y G O in. in. 8 in. a. What is the perimeter, in inches, of the puzzle? Show or eplain how ou got our answer. The shape of each piece of the puzzle is listed below. Pieces R and O are trapezoids. Pieces Y and G are rectangles. Piece B is a parallelogram. Piece P is a triangle. b. What is the area, in square inches, of piece B? Show or eplain how ou got our answer. c. What is the area, in square inches, of piece R? Show or eplain how ou got our answer. d. What is the area, in square inches, of piece P? Show or eplain how ou got our answer.

13 Mathematics Session Write our answer to question in the space provided in our Student Answer Booklet. ID:966 CMC7_pentagons.eps Common The first five figures in a pattern are shown below. Figure Figure Figure Figure Figure The pattern continues. a. What is the number of pentagons in Figure 6? Show or eplain how ou got our answer. b. Write an epression that represents the number of pentagons in Figure n. Figure is one dot. Figure is composed of five dots connected b line segments. c. What is the number of dots in Figure 6? Show or eplain how ou got our answer. d. Eplain how the number of dots in Figure 8 and the number of dots in Figure 9 can be used to determine the number of dots in Figure 0.

14 Grade 0 Mathematics Session You ma use our reference sheet during this session. You ma use a calculator during this session. DIRECTIONS This session contains eighteen multiple-choice questions and three open-response questions. Mark our answers to these questions in the spaces provided in our Student Answer Booklet. ID:0898 C Common Ethan poured orange juice into each of four glasses and estimated that each glass contained 8 ounces, rounded to the nearest ounce. Based on Ethan s estimate, which of the following could be the actual total amount of orange juice in the four glasses? A. 8.0 ounces B. 9.6 ounces C..6 ounces D..0 ounces ID:087 NEE069.eps C Common Population The line graph below shows the change in the population of the state of Ohio, in twent-ear intervals, from 900 to 000.,000,000 0,000,000 8,000,000 6,000,000,000,000 Population of Ohio ,000,000 ID:068 B Common Four equations are shown below. e e f f e f f e f f f f e How man of the equations are true for all real values of e and f? A. B. C. D. e e e Year During which interval on the graph did the population of Ohio increase at the fastest rate? A. 900 to 90 B. 90 to 90 C. 90 to 960 D. 980 to 000

15 Mathematics Session ID:07988 NEE8.eps D Common A water tank in the shape of a right circular clinder has a height of 0 feet and a radius of feet, as shown in the diagram below. ID:087 NEE09_revised.eps A Common 6 The circle graph below represents the number of cars in a parking lot and their colors. Cars in Parking Lot 0 ft. Black 6 Gra Red 0 Other 8 White 0 Silver ft. Based on the diagram, what is the volume, in cubic feet, of the water tank? A. π B. 600π C. 00π D. 9000π If % of the cars in the parking lot are white, how man cars in the parking lot are silver? A. B. 6 C. D. 6

16 Mathematics Session ID:0870 NEE079_rev.eps [opt_a0, C Common 7 Which of the following scatterplots is most likel to have a line of best fit with a slope of? A ID:0967 A Common 8 Two families bu refreshments at a concession stand. Each drink costs d dollars. Each snack costs s dollars. The Blake famil bus drinks and snacks for $. The Reese famil bus drinks and snacks for $6. What is the cost of one drink at the concession stand? B. C A. $ B. $ C. $ D. $ ID:008 A Common 9 The first term in a sequence is. Each term in the sequence after the first term is equal to half the previous term, plus. Which of the following statements best describes the terms in the sequence as it progresses? A. The terms get closer to 8. D. B. The terms get closer to. C. The terms increase at a constant rate D. The terms decrease at a constant rate.

17 Mathematics Session ID:0889 D Common 0 Brandon plans to rent a truck. The cost to rent the truck is $0 for the first four hours plus $0 for each additional hour. He can spend no more than $60. What is the maimum number of hours for which Brandon can rent the truck? A. B. C. 6 D. 7 ID:08000 D Common A green can and a silver can are each in the shape of a right circular clinder. The cans have the same radius, but the height of the green can is times the height of the silver can. What is the ratio of the volume of the green can to the volume of the silver can? A. 7 : B. 9 : C. 6 : D. : ID:00 ADJ_amusement_park.eps B Common A student plotted point G(9, ) and point H(7, ) on a coordinate grid, as shown below H The student will plot point F so that the midpoint of GF is point H. What will be the coordinates of point F? A. (, ) B. (, 7) C. (8, ) D. (, ) G 6

18 Mathematics Session ID:06776 NEE06.eps C Common The bo-and-whisker plot below shows the distribution of the times, in seconds, that members of a soccer team took to run one lap around a field. Lap Times (in seconds) ID:0796 B Common Based on the bo-and-whisker plot, within which time interval did 0% of the members of the soccer team most likel run one lap around the field? A. 0 seconds to seconds B. seconds to 0 seconds C. seconds to seconds D. seconds to seconds What is the slope of the line represented b the equation below? 0 ID:00 MCE0_Congruent.eps C Common The diagram below shows LMN and its image, RST, after a series of transformations in the coordinate plane. T R S L M N 6 unit What is the length, in units, of RT? A. B.. C. D.. unit A. B. C. D. 7

19 Mathematics Session Question 6 is an open-response question. BE SURE TO ANSWER AND LABEL ALL PARTS OF THE QUESTION. Show all our work (diagrams, tables, or computations) in our Student Answer Booklet. If ou do the work in our head, eplain in writing how ou did the work. Write our answer to question 6 in the space provided in our Student Answer Booklet. ID:8809 Common 6 The table below shows the numbers of students enrolled in different science classes at a high school. Number of Students Enrolled in Science Classes Science Class Number of Students biolog 0 environmental science 8 earth science 00 phsics 9 chemistr There are a total of 00 students enrolled in science classes at the high school. Each student is enrolled in onl one science class. a. What is the total number of students enrolled in chemistr class? Show or eplain how ou got our answer. b. What percent of the total number of students enrolled in science classes are enrolled in chemistr class? Show or eplain how ou got our answer. A guidance counselor at the high school made a circle graph based on the information in the table. The central angle of one sector of the circle graph measures 90. c. Which science class is represented b the sector of the circle graph that has a central angle that measures 90? Show or eplain how ou got our answer. d. What is the degree measure of the central angle of the sector of the circle graph that represents the number of students in biolog class? Show or eplain how ou got our answer. 8

20 Mathematics Session Mark our answers to multiple-choice questions 7 through 0 in the spaces provided in our Student Answer Booklet. Do not write our answers in this test booklet. You ma do our figuring in the test booklet. ID:87 CMC08_squaretriangle.eps B Common 7 The diagram below shows a trapezoid and its measurements. 6 cm 6 cm cm 0 cm The trapezoid has an area of 60 square centimeters. What is the value of? A. 0 B. C. 6 D. 8 ID:9999 C Common 8 A right circular cone has a volume of 9 cubic inches and a radius of inches. Which of the following is closest to the height of the cone? A. 0.7 inch B. 0.8 inch C. 6 inches D. 7 inches ID:08896 C Common 9 A computer software package is sold to small-business clients. The total cost of the software package is $00 for the first 0 computers on which the software is installed, plus $0 for installation on each additional computer. Which statement best describes the function that models the relationship between the number of computers on which the software is installed and the cost of the software? A. It is a constant linear function for 0 or fewer computers and an eponential function for more than 0 computers. B. It is an increasing linear function for 0 or fewer computers and an eponential function for more than 0 computers. C. It is a constant linear function for 0 or fewer computers and an increasing linear function for more than 0 computers. D. It is an increasing linear function for 0 or fewer computers and a constant linear function for more than 0 computers. 9

21 Mathematics Session ID:0877 MJB06_rhombus.eps [stem_ A Common 0 A parallelogram is graphed on the coordinate grid below. 0 The parallelogram will be rotated 90 clockwise about the origin. Which of the following shows the location of the parallelogram after the rotation? A. C. 0 0 B. D

22 Mathematics Session Questions and are open-response questions. BE SURE TO ANSWER AND LABEL ALL PARTS OF EACH QUESTION. Show all our work (diagrams, tables, or computations) in our Student Answer Booklet. If ou do the work in our head, eplain in writing how ou did the work. Write our answer to question in the space provided in our Student Answer Booklet. ID:067 Common The epression below can be used to calculate the balance in a savings account for which an initial deposit of P dollars has been compounded each ear for t ears at interest rate r. P( r) Elaine opened a savings account with a deposit of $000. The interest on her account is compounded each ear at a rate of %. Elaine will not make an additional deposits to or withdrawals from her account. a. What will be the balance in Elaine s account at the end of ear? Show or eplain how ou got our answer. b. What will be the balance in Elaine s account at the end of ears? Show or eplain how ou got our answer. Pavel opened a savings account with a deposit of $800. The interest on his account is compounded each ear at a rate of.%. Pavel will not make an additional deposits to or withdrawals from his account. c. Whose account, Elaine s or Pavel s, will have earned more interest at the end of ears? Show or eplain how ou got our answer. t 6

23 Mathematics Session Write our answer to question in the space provided in our Student Answer Booklet. ID:99 CMC_parallel_lines.eps Common Parallel lines q and m are cut b transversal lines j and k. The lines, and the measures of some of the angles created b the intersections of the lines, are shown in the diagram below. j k q m a. What is the measure, in degrees, of? Show or eplain how ou got our answer. b. What is the measure, in degrees, of? Show or eplain how ou got our answer. c. What is the measure, in degrees, of? Show or eplain how ou got our answer. d. What is the measure, in degrees, of 6? Show or eplain how ou got our answer. 6

24 Massachusetts Comprehensive Assessment Sstem Grade 0 Mathematics Reference Sheet AREA FORMULAS square... A = s rectangle... A = bh parallelogram... A = bh triangle... A = bh VOLUME FORMULAS cube...v = s (s = length of an edge) right rectangular prism...v = lwh OR V = Bh (B = area of a base) trapezoid... A = h(b + b ) circle... A = pr LATERAL SURFACE AREA FORMULAS right rectangular prism... LA = (hw)+(lh) sphere...v = pr right circular clinder...v = pr h right circular cone...v = pr h right square pramid...v = s h right circular clinder... LA = prh right circular cone... LA = pr ( = slant height) right square pramid... LA = s ( = slant height) CIRCLE FORMULAS C = pr A = pr TOTAL SURFACE AREA FORMULAS SPECIAL RIGHT TRIANGLES cube... SA = 6s right rectangular prism... SA = (lw) +(hw)+(lh) sphere... SA = pr right circular clinder... SA = pr + prh right circular cone... SA = pr +pr ( = slant height) right square pramid... SA = s + s ( = slant height)

25 Grade 0 Mathematics Spring 0 Released Items: Reporting Categories, Standards, and Correct Answers Item No. Page No. Reporting Categor Standard Correct Answer 000 (MC/SA) Standard Algebra and Functions F-BF. C 0.P. Algebra and Functions A-SSE. A 0.P. Number and Quantit 8.NS. B 0.N. Statistics and Probabilit S-ID.6 D 0.D. Number and Quantit 7.EE. C 0.N. 6 Algebra and Functions A-REI. C 0.P. 7 Statistics and Probabilit S-ID. B 0.D. 8 Geometr G-GPE. B 0.G.8 9 Number and Quantit 7.EE. B 0.N. 0 Number and Quantit 7.EE. A 0.N. 6 Statistics and Probabilit S-ID.6 C 0.D. 6 Number and Quantit 7.NS. B 0.N. 7 Number and Quantit 7.EE. D 0.N. 7 Algebra and Functions A-APR. D 0.P. 8 Geometr G-SRT.6 9 meters 0.G Statistics and Probabilit S-ID. 80 beats per minute 0.D. 7 9 Number and Quantit 8.NS. 0.N. 8 0 Number and Quantit 7.EE. 0.N. 9 0 Algebra and Functions 8.F. 0.P. 0 Geometr 7.G.6 0.M. Algebra and Functions F-BF. 0.P. Number and Quantit N-Q. C 0.M. Number and Quantit 7.EE. B 0.N. Statistics and Probabilit S-ID.7 C 0.D. Geometr G-GMD. D 0.M. 6 Statistics and Probabilit 6.SP. A 0.D. 7 Statistics and Probabilit S-ID.6 C 0.D. 8 Algebra and Functions A-REI.6 A 0.P.8 9 Algebra and Functions F-BF. A 0.P. 0 6 Algebra and Functions A-CED. D 0.P.7 6 Geometr G-GMD. D 0.M. 6 Geometr G-GPE.6 B 0.G.7 7 Statistics and Probabilit S-ID. C 0.D. 7 Algebra and Functions 8.F. B 0.P. 7 Geometr G-SRT. C 0.G. 6 8 Statistics and Probabilit 6.SP. 0.D. 7 9 Geometr 7.G.6 B 0.M. 8 9 Geometr G-GMD. C 0.M. 9 9 Algebra and Functions F-LE. C 0.P Geometr G-CO. A 0.G.9 6 Algebra and Functions A-CED. 0.P.7 6 Geometr 8.G. 0.G. The Reporting Categor and Standard columns refer to the current (0) Massachusetts Curriculum Framework for Mathematics. More information about reporting categories for Mathematics is available on the Department s website at Answers are provided here for multiple-choice and short-answer items onl. Sample responses and scoring guidelines for open-response items, which are indicated b the shaded cells, will be posted to the Department s website later this ear. The Department is providing the standard from the previous (000) curriculum framework for Mathematics for reference purposes. 6