MCAS GRADE 8 MATHEMATICS TEST

Transcription

1 PRENTICE HALL PRENTICE HALL BRIEF REVIEW SERIES Preparing for the Massachusetts Comprehensive Assessment System: MCAS GRADE 8 MATHEMATICS TEST Chapter 1: Problem Solving and Reasoning Chapter 2: Number Sense and Operations Chapter 3: Integers and Order of Operations Chapter 4: Number Theory and Rational Numbers Chapter 5: Proportions and Percents Chapter 6: Algebra Concepts Chapter 7: Plane Figures and Coordinate Geometry Chapter 8: Circles, 3D Figures and Measurement Geometry Preparing for the Massachusetts Comprehensive Assessment System MCAS GRADE 8 MATHEMATICS TEST Comprehensive coverage of all the tested standards Essential test taking tips and strategies Chapter 9: Statistics and Probability Preparing for the Massachusetts Comprehensive Assessment System: MCAS GRADE 8 MATHEMATICS TEST Exclusive! Online Video Tutor for virtual help anytime Comprehensive coverage of all of the tested standards PEARSON PRENTICE HALL Test taking strategies for success with important facts about the MCAS exam Chapter-by-chapter practice questions in MCAS format Actual Grade 8 Math MCAS exams

2 Acing the Massachusetts MCAS Test x Chapter 1 Problem Solving Strategies Massachusetts Cumulative Progress Indicators 1.1 Finding Information to Solve a Problem M.3 Determining measures 8.M.5 Modeling simple problems 8.N.12 Using appropriate operations 1.2 Making Complex Problems Simpler N.12 Using appropriate operations 8.M.4 Applying ratio/proportion 1.3 Interpreting Solutions P.1 Patterns in tables, graphs, and expressions 8.P.4 Creating and using symbolic expressions 8.P.7 Linear equations and inequalities 1.4 Working Backwards N.9 Inverse relationships 8.N.12 Using appropriate operations 1.5 Using Models M.4 Applying ratio/proportion 1.6 Using Different Strategies D.3 Measures of central tendency 8.P.7 Linear equations and inequalities Chapter 1 MCAS Test Prep iii

3 Chapter 2 Number Sense and Operations 2.1 Reviewing the Base 10 Number System Review of pre-grade 8 standards 2.2 Comparing and Ordering Numbers N.1 Comparing and translating numbers 2.3 Real Number Properties N.8 Properties of operations 2.4 Adding and Subtracting Numbers N.8 Properties of operations 8.N.10 Computing with rational 2.5 Multiplying and Dividing Numbers N.9 Inverse relationships 8.N.10 Computing with rational 2.6 Using the Laws of Exponents N.7 Powers and roots 2.7 Negative Exponents N.7 Powers and roots 2.8 Scientific Notation N.4 Scientifi c notation 2.9 Square Roots N.7 Powers and roots 8.N.2 Irrational numbers 2.10 Finding Cubes M.3 Determining measures Chapter 2 MCAS Test Prep Chapter 3 Integers and Order of Operations 3.1 Integers and Absolute Value N.6 Absolute value 3.2 Adding and Subtracting Integers N.10 Computing with rational iv

4 3.3 Multiplying and Dividing Integers N.8 Properties of operations 8.N.9 Inverse relationships 8.N.10 Computing with rational 3.4 Order of Operations N.7 Powers and roots Chapter 3 MCAS Test Prep Chapter 4 Number Theory and Rational Numbers 4.1 Factoring and the Greatest Common Factor (GCF) Review of pre-grade 8 standards 8.N.5 Number theory concepts 4.2 Multiples and the Least Common Multiple (LCM) Review of pre-grade 8 standards 4.3 Equivalent Fractions Review of pre-grade 8 standards 4.4 Operations with Fractions N.9 Inverse relationships 8.N.10 Computing with rational 4.5 Decimals and Repeating Decimals N.10 Computing with rational 4.6 Rational and Irrational Numbers N.2 Irrational numbers 8.N.10 Computing with rational Chapter 4 MCAS Test Prep v

5 Chapter 5 Ratios, Proportions, and Percents 5.1 Using Ratios and Proportions N.3 Ratio and proportion 8.M.4 Applying ratio/proportion 8.M.5 Modeling simple problems 5.2 Percents, Fractions, and Decimals N.1 Comparing and translating numbers 5.3 Percents Greater Than 100 and Less Than N.10 Computing with rational 5.4 Solving Percent Equations P.9 Proportional relationships 8.N.10 Computing with rational 5.5 Finding Interest N.10 Computing with rational 5.6 Estimating Percents N.10 Computing with rational 8.N.11 Applying estimations 5.7 Percent of Increase and Decrease N.10 Computing with rational 5.8 Solving Other Percent Problems N.10 Computing with rational Chapter 5 MCAS Test Prep Chapter 6 Patterns and Algebra 6.1 Identifying and Extending Patterns P.1 Patterns in tables, graphs, and expressions 6.2 Translating Expressions P.4 Creating and using symbolic expressions vi

6 6.3 Evaluating Algebraic Expressions P.2 Evaluating algebraic expressions 8.P.3 Understanding ( x)( y) = xy 6.4 Function Patterns in Tables P.1 Patterns in tables, graphs, and expressions 8.P.8 Effect of change in variable 6.5 Solving Equations P.7 Linear equations and inequalities 6.6 Writing and Solving Inequalities P.7 Linear equations and inequalities 6.7 Representing Patterns on Graphs P.1 Patterns in tables, graphs, and expressions 8.M.5 Modeling simple problems 6.8 Graphing Equations and Functions P.5 Slope of a line 6.9 Finding Slope and Intercepts P.5 Slope of a line 8.P.6 Variables within equations 6.10 Linear Growth P.1 Patterns in tables, graphs, and expressions 8.P.10 Linear growth patterns Chapter 6 MCAS Test Prep Chapter 7 Plane Figures and Geometry 7.1 Parallel Lines G.3 Intersecting lines and angles 7.2 Finding Reflections, Translations, and Rotations G.6 Transformations 7.3 Finding Dilations G.6 Transformations vii

7 7.4 Using Similarity G.2 Congruence and similarity 8.M.4 Applying ratio/proportion 7.5 Properties of Polygons G.1 Interior/exterior angles of polygons 7.6 Pythagorean Theorem G.4 Pythagorean theorem Chapter 7 MCAS Test Prep Chapter 8 Circles, 3D Figures, and Measurement Geometry 8.1 Finding Area and Perimeter M.3 Determining measures 8.P.8 Effect of change in variable 8.2 Properties of Circles M.3 Determining measures 8.3 3D Shapes and Surface Area G.7 Identifying 3D fi gures 8.G.8 Drawing 2D representations 8.M.3 Determining measures 8.4 Finding Volume M.3 Determining measures 8.5 Properties of Spheres M.3 Determining measures 8.6 Metric and Customary Units M.1 Units of measurement 8.7 Solving Measurement Problems M.1 Units of measurement 8.M.2 Converting between systems Chapter 8 MCAS Test Prep viii

8 Chapter 9 Statistics and Probability 9.1 Mean, Median, Mode, and Range D.3 Measures of central tendency 9.2 Bar Graphs, Histograms, and Circle Graphs D.2 Tabular/graphical representations 9.3 Box-and-Whisker, Stem-and-Leaf Plots, 8.D.2 Tabular/graphical and Scatter Plots representations 8.D.3 Measures of central tendency 9.4 Polls, Surveys, and Sampling D.1 Data samples 9.5 Finding Probability D.4 Compute probabilities 9.6 Counting Principle and Venn Diagrams D.4 Compute probabilities Chapter 9 MCAS Test Prep Glossary Massachusetts MCAS 2005 Test Massachusetts MCAS 2005 Test Index Cut-Out Tools ix

9 Chapter 5 Ratios, Proportions, and Percents Boston was home to the fi rst subway system in America. When it opened in 1898, most people still traveled by horse and buggy. 87

10 Chapter 5 MCAS Test Prep DIRECTIONS FOR QUESTIONS 1 THROUGH 14: Each question is followed by four possible answers. Circle the letter of the best answer. 1 Which of the following is the ratio 272 to 8 written in simplest form? A. B C. D Aisha has 12 pages of math homework. If she takes 20 minutes to complete one page, how long will it take her to finish all 12 pages? A. 6 hours C. 2 hours, 30 min 6 5.2% is equivalent to what fraction? A. B C. D A restaurant adds an 18% service fee to a dinner bill of $ What is the amount of the service fee? A. $16.26 C. $24.03 B. $23.05 D. $28.46 B. 4 hours D. 1 hour, 20 min 3 Write 9 as a percent. 10 A. 0.9% C. 90% B. 9% D. 900% 8 Theo takes out a loan for $9,000 at a simple interest rate of 7% for 5 years. What is the total amount of interest he will pay by the end of the 5 years? A. $12,150 C. $3,150 B. $11,250 D. $2,700 4 What is 205% of 20? A C. 41 B. 25 D Jamil hit 1,560 pitches out of 5,000. Ariel hit 1,404 pitches out of 6,500. Trevor missed 3,885 pitches out of 5,250. Issay hit of 30% of 6,000 pitches. Who hit the greatest percentage of pitches? A. Jamil C. Trevor B. Ariel D. Issay 9 Liz put $650 in a savings account that pays 6% interest, compounded annually. After one year, her account balance is $689. What will her balance be after two years? A. $750 C. $ B. $ D. $ A new TV sells for $1,120. An older model costs $ What percent can you save by buying the older model? A. 48% C. 38% B. 42% D. 37% 118

11 11 Ben earns a 5% commission as a realestate agent. In August, he sells two houses for $245,000 each. How much commission does Ben earn in August? A. $12,250 C. $36,750 B. $24,500 D. $49, A university charges $33,690 per year in tuition, or $16,845 per semester. If the school is expecting a 5% tuition increase next year, what will be the new cost per semester? A. $11, C. $25, B. $17, D. $35, Estimate 39.2% of 178. A. 55 C. 72 B. 60 D Jackie wants to sell her guitar for $75 on a web site. The table below shows three different sites she is considering. Which site should Jackie choose to pay the least amount of commission? Web Site Site A Site B Site C Commission Fee 2.5% $4 listing fee $5 listing fee 4% A. Site C C. Sites A and B B. Site A D. Site B DIRECTIONS FOR QUESTION 15: Respond fully to the following short-answer question. Show and label all your work, and clearly explain your answer. 15 Reggie and her drama troupe went to a café. After sales tax, their total bill came to $ If the sales tax was 8%, what was the cost of their meal before tax? 119

12 DIRECTIONS FOR QUESTION 16: Respond fully to the following open-ended question. Show and label all your work, and clearly explain your answer. 16 Zane is going to be taking out a student loan for $4,800. The table below shows the loan repayment plans for several lenders. Lender Principal (p) Simple Interest Rate (r) Time (t) in years Monthly Payments Sallyforth $4,800 5% 10 CityCircle $4,800 0% 2 $80 (remaining amount) 8% 6 Accessible $2,400 $2,400 9% 4% 5 CityCircle doesn t charge interest for the first two years. However, Zane would still have to make monthly payments of $80 during this period. What would be the remaining balance on the CityCircle loan after the first two years? Find the monthly payment amount for each plan, and complete the table. Find the total amount Zane would pay under each plan. 120