MCAS Prep Grade 7 Mathematics

Transcription

1 MCAS Prep Grade 7 Mathematics by Jonathan D. Kantrowitz Edited by Philip W. Sedelnik and Ralph R. Kantrowitz Item Code RAS3031 Copyright 2008 Queue, Inc. All rights reserved. No part of the material protected by this copyright may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system. Printed in the United States of America. Queue, Inc. 1 Controls Drive Shelton, CT (800) Fax: (800)

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3 Table of Contents Massachusetts Grade 7 Mathematics Standards Pages/ Problem # s Number Sense and Operations Pages N.1 7.N.2 7.N.3 7.N.4 7.N.5 7.N.6 7.N.7 7.N.8 7.N.9 Compare, order, estimate, and translate among integers, fractions and mixed numbers (i.e., rational numbers), decimals, and percents. Use ratios and proportions in the solution of problems involving unit rates, scale drawings, and reading of maps. Represent numbers in scientific notation (positive powers of ten only) and use that notation in problem situations. Demonstrate an understanding of absolute value. Apply the rules of positive integer exponents to the solution of problems. Extend the order of operations to include positive integer exponents. Use the inverse relationships of addition and subtraction, and of multiplication and division, to simplify computations and solve problems. Estimate and compute with fractions (including simplification of fractions), integers, decimals, and percents (including those greater than 100 and less than 1). Determine when an estimate rather than an exact answer is appropriate and apply in problem situations. Select and use appropriate operations addition, subtraction, multiplication, division, and positive integer exponents to solve problems with rational numbers (including negatives)

4 Patterns, Relations, and Algebra Pages P.1 7.P.2 7.P.3 7.P.4 7.P.5 7.P.6 Geometry 7.G.1 7.G.2 7.G.3 7.G.4 7.G.5 7.G.6 Extend, represent, analyze, and generalize a variety of patterns with tables, graphs, words, and when possible, symbolic expressions. Include arithmetic and geometric progressions. Evaluate simple algebraic expressions for given variable values. Create and use symbolic expressions for linear relationships and relate them to verbal, tabular, and graphical representations. Solve linear equations using tables, graphs, models, and algebraic methods. Identify, describe, and analyze linear relationships between two variables. Compare positive rate of change to negative rate of change. Use linear equations to model and analyze problems involving proportional relationships. Analyze, apply, and explain the relationship between the number of sides and the sums of the interior angle measures of polygons. Classify figures in terms of congruence and similarity, and apply these relationships to the solution of problems. Demonstrate an understanding of the relationships of angles formed by intersecting lines, including parallel lines cut by a transversal. Graph points and identify coordinates of points on the Cartesian coordinate plane (all four quadrants). Use a ruler, protractor, and compass to draw polygons and circles. Predict the results of translations and reflections of figures on unmarked or coordinate planes and draw the transformed figure Pages

5 7.G.7 Identify three-dimensional figures by their physical appearance, distinguishing attributes, and spatial relationships such as parallel faces Measurement Pages M.1 7.M.2 7.M.3 Select, convert (within the same system of measurement), and use appropriate units of measurement or scale. Given the formulas, convert from one system of measurement to another. Demonstrate an understanding of the concepts and apply formulas and procedures for determining measures, including those of area and perimeter/circumference of parallelograms, trapezoids, and circles. Given the formulas, determine the surface area and volume of rectangular prisms and cylinders Data Analysis, Statistics, and Probability Pages D.1 7.D.2 7.D.3 Select, create, interpret, and utilize the following tabular and graphical representations of data: circle graphs, Venn diagrams, stem-and-leaf plots, tables, and charts. Find, describe, and interpret appropriate measures of central tendency (mean, median, and mode) and spread (range) that represent a set of data. Use these notions to compare different sets of data. Use tree diagrams, tables, organized lists, and area models to compute probabilities for simple compound events About the Practice Tests Page 177 Practice Test 1 Practice Test 2 Page T1 Page T37

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7 Number Sense and Operations 1. If these fractions were marked on a number line, which of them would be CLOSEST to zero? A. 3/16 B. 3/7 C. 1/4 D. 1/6 4. Ten billion (10,000,000,000) is equal to A. one million million. B. ten thousand million. C. one hundred thousand million. D. ten million million. 2. How much would the value of 859,400 change if the 8 was replaced by a 3? A. +500,000 B. -50,000 C. -500,000 D Which of the following numbers is the SMALLEST? A B C D How is three hundred six million, thirty-eight thousand, four written as a numeral? A. 36,038,400 B. 306,038,004 C. 306,038,400 D. 306,380, Which of the following numbers is the LARGEST? A B C D Reproducing copyrighted material is against the law!

8 Number Sense and Operations 140. Using the rules for the order of operations, simplify the following: (8-3) 2 A. -13 B. 67 C. 28 D Which of the following equations is TRUE? A. (4 + 5) 2 = B. (4 + 5) 2 = C. (4 + 5) 2 = (4 + 5)(4 + 5) D. (4 + 5) 2 = Look at the following equation: = Which shows the proper placement of the parentheses and brackets in order to make this statement true? 143. Put parentheses and brackets in the proper places to make the following equation true. 9 x = 58 A. (2 4 5) + [(7-6) 4] B. [2 4 ( )] 4 C. [2 4 (5 + 7)] - (6 4) D. [(2 4 5) + (7-6)] 4 23 Reproducing copyrighted material is against the law!

9 Number Sense and Operations The chart below shows the area of some of the world s largest lakes in square kilometers. Lake Area 266. Texas has a land area of 261,797 square miles. Rhode Island s land area is 1,045 square miles. Write an expression to show how many states the size of Rhode Island can fit into a state the size of Texas. Caspian Sea 371,000 Lake Superior 84,500 Aral Sea 64,500 Lake Huron 63, Which of the following expressions shows the area of the Caspian Sea in square meters? A. 371,000 x 1,000 x 1,000 B. 371,000 x 100 x 100 C. 371,000 1,000 1,000 D. 371, Which of the following expressions shows how much larger Lake Superior is than Lake Huron, in terms of percent? A. 84,500-63,500 84,500 B. 84,500-63, C. (84,500-63,500) 63,500 D. 84,500 63, Carl put 112 feet of fencing around the perimeter of his rectangular garden. If the area of Carl s garden is 780 square feet, then which of the following expressions could be used to find the area of Carl s garden? A. 15 x 52 B. 30 x 26 C. 39 x 20 D. 12 x Reproducing copyrighted material is against the law!

10 Patterns, Relations, and Algebra 351. A delivery truck is transporting televisions and computer monitors to an electronics store. The weight limit for the truck is 3,500 pounds. One television weighs 65 pounds, and one computer monitor weighs 28 pounds. If t equals the number of televisions and m equals the number of computer monitors this truck can carry, which of the following would be an inequality for the above information? A. 28t + 65m < 3,500 B. 28m + 65t 3,500 C. 65m - 28t 3,500 D. 65t + 28m > 3, The distance d that an automobile travels varies directly as the time t that it travels. After four hours, an automobile has traveled 232 miles. Which of the following is an equation that relates d and t? A. d = t B. t = 232d C. t = d D. d = 58t 353. Connie drove 638 miles on the second day of a road trip. This distance was 23 miles more than six times as far as she drove on the first day. Which of the following equations could be used to determine x, how far Connie drove on the first day? A. 23x - 6 = 638 B. 6x = 23 C. 6x + 23 = 638 D. (23x 6) = The temperature at 6:00 a.m. was 7 C. At 3:00 p.m., the temperature rose to 11 C. To find r, the number of degrees the temperature rose, which of the following equations would you use? A = r B r = 11 C r = 11 D. r - (-7) = You are studying population growth patterns. You find that the population of a town is doubling every five years. The population is 15,000 now. In how many years will the population reach 480,000 if this pattern continues? 67 Reproducing copyrighted material is against the law!

11 Geometry ABC is similar to DEF. Use the above figure to solve the following problems Which of the following is the scale factor of ABC to DEF? A. three B. two C. one-half D. four 401. What is the length of segment DF? A. 28 B. 36 C. 32 D Reproducing copyrighted material is against the law!

12 Geometry 433. What three-dimensional shape would the above circle create if it were translated along the axis shown? 435. What three-dimensional shape would the above triangle create if it were translated along the axis shown? 434. What three-dimensional shape would the above square create if it were translated along the axis shown? 436. What three-dimensional shape would the above rectangle create if it were translated along the axis shown? Reproducing copyrighted material is against the law! 100

13 Measurement Farmington Middle School is repainting the floor of the basketball court in the gym. In the diagram shown below, the shaded portions of the floor need repainting. The special paint to be used costs $21.75 per gallon container and $6.50 per quart container. One gallon of this special paint can cover 85 square feet Excluding tax, approximately what is the MINIMUM amount of money the school must spend to repaint the shaded areas? A. $ B. $ C. $85.00 D. $ The school wants to paint the circle in the middle of the court with a special red paint that costs $28.00 per gallon. One gallon of this paint can cover 75 square feet. ABOUT how many gallons of this special paint will the school need? A. 8 gallons B. 1 gallon C. 3 gallons D. 6 gallons Reproducing copyrighted material is against the law! 114

14 Measurement 517. If a cube has a surface area of 486 square inches, which of the following would be the length of each edge of this cube? A. 16 inches B. 11 inches C. 9 inches D. 5 inches 518. A certain aquarium is 50 centimeters long, 30 centimeters wide, and 40 centimeters high. If the water level of this aquarium is three centimeters from the top, what percent of the aquarium s volume would be filled with water? A % B % C % D % 519. How many 400-milliliter bottles can 600 liters of water fill? A. 150 B. 1,500 C. 15,000 D. 150,000 Aurora Electronics uses shipping boxes like the one shown above for its products. The production department has decided to increase the height of this shipping box by 25% and to reduce the length in order to maintain the same volume. The width of this box will remain the same Which of the following will be the new height and new length of Aurora Electronics shipping boxes? A. new height: 15 inches, new length: 4 inches B. new height: 16 inches, new length: 3.75 inches C. new height: 7.5 inches, new length: 8 inches D. new height: 12 inches, new length: 5 inches Reproducing copyrighted material is against the law! 130