XIV. Mathematics, Grade 8


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1 XIV. Mathematics, Grade 8
2 Grade 8 Mathematics Test The spring 0 grade 8 Mathematics test was based on standards in the five domains for grade 8 in the Massachusetts Curriculum Framework for Mathematics (March 0). The grade 8 standards can be found on pages 6 69 in the Framework, and the five domains are listed below. The Number Sstem Epressions and Equations Functions Geometr Statistics and Probabilit The Curriculum Framework for Mathematics is available on the Department website at Mathematics test results are reported under five MCAS reporting categories, which are identical to the five framework domains listed above. Test Sessions The grade 8 Mathematics test included two separate test sessions. Each session included multiplechoice, shortanswer, and openresponse questions. Approimatel half of the common test items are shown on the following pages as the appeared in test booklets. Reference Materials and Tools Each student taking the grade 8 Mathematics test was provided with a plastic ruler and a grade 8 Mathematics Reference Sheet. A cop of the reference sheet follows the final question in this chapter. An image of the ruler is not reproduced in this publication. 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. The use of bilingual wordtoword dictionaries was allowed for current and former English language learner students onl, during both Mathematics test sessions. No other reference tools or materials were allowed. CrossReference Information The tables at the conclusion of this chapter indicate each released and unreleased common item s reporting categor and the framework standard it assesses. The correct answers for released multiplechoice and shortanswer questions are also displaed in the released item table. 0
3 Grade 8 Mathematics Session You ma use our reference sheet and MCAS ruler during this session. You ma not use a calculator during this session. DIRECTIONS This session contains eight multiplechoice questions, two shortanswer questions, and one openresponse question. Mark our answers to these questions in the spaces provided in our Student Answer Booklet. ID:877 C Common What is the value of the epression below? A. B. 6 C. 9 D. 8 ( 9) 0
4 Mathematics Session ID:767 cmh076_rotation.eps, [opt A Common Seth drew a figure on a coordinate grid and labeled one point P, as shown below. 0 P He then rotated the figure 80 clockwise around point P. Which of the following shows the figure after Seth rotated it? A. C. 0 P P 0 B. D. 0 P P 0
5 Mathematics Session ID:6070 CMH_opposite.eps [stem D Common Carmella graphed line p on the coordinate grid shown below. p 0 Which of the following lines appears to have the same slope as line p? A. C. 0 0 B. D. 0 0
6 Mathematics Session ID:967 LPW00_slope.eps [stem_0 B Common The total cost in dollars,, of a membership at each of four health clubs is represented below in terms of, the number of months of the membership. Health Club A: 60 Health Club B: 0 $ 0 $ $ $6 $8 ID:68 B Common In 00, the U.S. Mint in Denver produced Oregon state quarters. What is written in standard notation? A. 0,00,000 B. 0,000,000 C.,00,000,000 D. 0,00,000,000 Health Club C: Total Cost (in dollars) (, 70) (, 0) Number of Months Health Club D: A customer pas a onetime fee of $0 plus $0 each month for months. Which representation has the greatest rate of change? A. Health Club A B. Health Club B C. Health Club C D. Health Club D
7 Mathematics Session Question 6 is a shortanswer question. Write our answer to question 6 in the bo provided in our Student Answer Booklet. Do not write our answer in this test booklet. You ma do our figuring in the test booklet. ID:68 Common 6 What is the solution of the equation below? 7
8 Mathematics Session Mark our answers to multiplechoice questions 7 and 8 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:9679 D Common 7 Which of the following equations has infinitel man solutions? A. B. C. D. ID:696 D Common 8 Which of the following numbers is not a rational number? A. B..7 C. D. 6
9 Mathematics Session Question 9 is a shortanswer question. Write our answer to question 9 in the bo provided in our Student Answer Booklet. Do not write our answer in this test booklet. You ma do our figuring in the test booklet. ID:970 LW88007_rectangle.eps Common 9 The students in a science club planted a rectangular flower garden in front of their school. The garden is 6 feet wide and has a diagonal length of 0 feet. 6 feet 0 feet What is, the length in feet of the garden? 7
10 Mathematics Session Mark our answer to multiplechoice question 0 in the space provided in our Student Answer Booklet. Do not write our answer in this test booklet. You ma do our figuring in the test booklet. ID:87 B Common 0 What is the value of the epression below? A. 6 B. C. D. 6 ( ) ( ) 8
11 Mathematics Session Question is an openresponse 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 in the space provided in our Student Answer Booklet. ID:980 CMC_compan.eps Common Ton collected data on the ears of emploment and the annual salaries of the salespeople at Compan Z. He made a scatterplot and drew a trend line that approimated the line of best fit for the data, as shown below. Salaries of Salespeople at Compan Z $70,000 $60,000 (9, $,000) Salar $0,000 $0,000 $0, Years of Emploment a. Based on the trend line drawn for the data, what is the salar a salesperson with ears of emploment at Compan Z can epect to earn? Show or eplain how ou got our answer. b. What is the slope of the trend line that Ton drew? Show or eplain how ou got our answer. c. What does the slope mean in this situation? Ton epects his salar to be about $70,000 after he has been emploed as a salesperson at Compan Z for ears. d. Use the trend line and our answer from part (b) to eplain wh Ton s salar epectation is reasonable. 9
12 Grade 8 Mathematics Session You ma use our reference sheet and MCAS ruler during this session. You ma use a calculator during this session. DIRECTIONS This session contains eight multiplechoice questions, one shortanswer question, and one openresponse question. Mark our answers to these questions in the spaces provided in our Student Answer Booklet. ID:7 CMH070_triangles.eps A Common 6 cm A mathematical puzzle uses four triangles with the dimensions shown below. P 8 cm 6 cm 6 cm Q 8 cm 6 cm ID:998 C Common A cand is in the shape of a sphere. The cand has a radius of. centimeters. Which of the following is closest to the volume of the cand? (Use. for π.) A. cm B. 9 cm C. cm D. cm 9 cm R 9 cm cm S cm cm cm Which of the following triangles are congruent? A. P and Q B. Q and R C. R and S D. S and P 0
13 Mathematics Session ID:9897 CMC_pq.eps C Common The sstem of equations represented b lines p and q is shown on the graph below q 6 p ID:07 A Common Barb purchased a loaf of bread for $ and p pounds of sliced ham at $ per pound for a total of $.. The relationship between what she purchased and her total purchase price is represented b the equation below. p. What was the total number of pounds of ham that Barb purchased? A.. pounds B..6 pounds C..0 pounds D..6 pounds Based on the graph, what is the solution of the sstem of equations? A. (0, 0) B. (0, ) C. (, ) D. (, )
14 Mathematics Session ID:67 CMC0_triangles.eps C Common 6 Triangle EFG is similar to triangle TUV, as shown below. E 6 cm 0 0 cm G 8 8 F T 8 cm cm V U Based on the measurements of the triangles, what is the measure of angle U? A. B. 8 C. 8 D.
15 Mathematics Session Question 7 is a shortanswer question. Write our answer to question 7 in the bo provided in our Student Answer Booklet. Do not write our answer in this test booklet. You ma do our figuring in the test booklet. ID:99 Common 7 A mailing tube in the shape of a clinder has a height of inches and a radius of inches. What is the volume, in cubic inches, of the mailing tube? (Use. for p.)
16 Mathematics Session Mark our answers to multiplechoice questions 8 and 9 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:9767 CMC0_function.eps [opt_ C Common 8 Which of the following tables does not represent a function? ID:6787 CMC9_lines_mn.eps B Common 9 Amanda graphed line m and line n on a coordinate plane, as shown below. A m n B C. 0 D Which of the following statements is true? A. The slope of line m is greater than the slope of line n. B. The slope of line n is greater than the slope of line m. C. The intercept of line m is greater than the intercept of line n. D. The intercept of line n is greater than the intercept of line m.
17 Mathematics Session Question 0 is an openresponse 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 0 in the space provided in our Student Answer Booklet. ID:8769 Common 0 Some of the students from Eastwood School are taking a trip to a museum. In all, fewer than 60 students will go on the trip. The cost for food and admission to the museum is $8 per student. a. What is the total cost for food and admission to the museum for students? Show or eplain how ou got our answer. The students will travel on one bus to the museum. The cost of the bus is $800. b. In our Student Answer Booklet, cop and complete the table below to show the total cost for food, admission, and the bus for different numbers of students to go to the museum. Show or eplain how ou got our answers. Number of Students Student Trip to the Museum Total Cost for Food, Admission, and the Bus 0 $ $ c. Write an epression that can be used to find the total cost for food, admission, and the bus for n students from Eastwood School to go to the museum. d. A total of students go to the museum. What is the total cost, for food, admission, and the bus, per student to go to the museum? Show or eplain how ou got our answer.
18 Mathematics Session Mark our answer to multiplechoice question in the space provided in our Student Answer Booklet. Do not write our answer in this test booklet. You ma do our figuring in the test booklet. ID:9767 CMC0_MN.eps D Common Right triangle LMN is shown on the coordinate grid below. 8 M(, 7) 7 6 L(, ) N(, ) unit 8 unit Which of the following is the length, in units, of line segment MN? A. 8 B. 8 C. D. 6
19 Massachusetts Comprehensive Assessment Sstem Grade 8 Mathematics Reference Sheet PERIMETER FORMULAS square P s rectangle P b h OR P l w triangle P a b c AREA FORMULAS square A s rectangle A bh OR A lw parallelogram..... A bh triangle A bh trapezoid A h( b b ) VOLUME FORMULAS rectangular prism V lwh OR V Bh (B = area of a base) cube V s (s length of an edge) clinder V sphere V CIRCLE FORMULAS C C A πr OR πd πr πr h PYTHAGOREAN THEOREM πr circle A πr TOTAL SURFACE AREA FORMULAS a c rectangular prism.. SA ( lw) ( hw) ( lh) clinder SA πr πrh sphere SA πr b a b c 7
20 Grade 8 Mathematics Spring 0 Released Items: Reporting Categories, Standards, and Correct Answers* Item No. Page No. Reporting Categor Standard Correct Answer (MC/SA)* Epressions and Equations EE. C Geometr G. A Functions F. D Functions F. B Epressions and Equations EE. B 6 Epressions and Equations EE.7 = 7 6 Epressions and Equations EE.7 D 8 6 The Number Sstem NS. D 9 7 Geometr G.7 8 feet 0 8 Epressions and Equations EE. B 9 Statistics and Probabilit SP. 0 Geometr G. A 0 Geometr G.9 C Epressions and Equations EE.8 C Epressions and Equations EE.7 A 6 Geometr G. C 7 Geometr G cubic inches 8 Functions F. C 9 Epressions and Equations EE. B 0 Functions F. 6 Geometr G.8 D * Answers are provided here for multiplechoice and shortanswer items onl. Sample responses and scoring guidelines for openresponse items, which are indicated b the shaded cells, will be posted to the Department s website later this ear. 8
21 Grade 8 Mathematics Spring 0 Unreleased Common Items: Reporting Categories and Standards Item No. Reporting Categor Standard Geometr G.9 Statistics and Probabilit SP. Functions F. Functions F. 6 Epressions and Equations EE. 7 Epressions and Equations EE. 8 Epressions and Equations EE. 9 The Number Sstem NS. 0 Epressions and Equations EE.8 The Number Sstem NS. Functions F. Geometr G.7 Functions F. Functions F. 6 Statistics and Probabilit SP. 7 Epressions and Equations EE.8 8 Geometr G.8 9 Geometr G. 0 Functions F. Geometr G. Geometr G. 9
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