HSPA Review - Wikispaces · PDF fileMonroe Township High School HSPA Review * For adoption by...

Monroe Township High School

HSPA Review

* For adoption by all regular education programs Board Approved: June 23, 2004 as specified and for adoption or adaptation by all Special Education Programs in accordance with Board of Education Policy # 201.

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Table of Contents Monroe Township Schools Administration and Board of Education Page 3 Members Acknowledgments Page 4 District Mission Statement and Goals Page 5 Introduction/Philosophy/Educational Goals Page 6 National and State Standards Page 7 Teachers: How to Use the Review Packet Pages 8 - 9 Understanding the HSPA Mathematics Exam Pages 10 - 13 HSPA Packet 1 Pages 14 - 55 HSPA Packet 2 Pages 56 - 100 HSPA Packet 3 Pages 101 - 141 HSPA Packet 1 Solutions Pages 142 – 145 HSPA Packet 2 Solutions Pages 146 - 149 HSPA Packet 3 Solutions Pages 150 – 152 HSPA Fall 2001 Sample Test Form Test Booklet (PDF) Page 153 HSPA March 2004 Student Preparation Booklet Page 154

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MONROE TOWNSHIP BOARD OF EDUCATION

MONROE TOWNSHIP ADMINISTRATION

Dr. Ralph P. Ferrie, Superintendent

Dr. Gail D. Brooks, Assistant Superintendent

BOARD OF EDUCATION

Mr. Joseph Homoki, President Ms. Kathy Kolupanowich, Vice President

Mr. Marvin Braverman Ms. Carol Haring Mr. Lew Kaufman

Mr. John Leary Ms. Kathy Leonard Mr. Harold Pollack Ms. Amy Speizer

JAMESBURG REPRESENTATIVE

Ms. Patrice Faraone

Student Board Members

John Ronan

J. W. DeBaun

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Acknowledgments

The following individuals are acknowledged for their assistance in the preparation of this Curriculum Management System: Writers Names: Janet Bluefield

Susan Patikowski Supervisor Name: Robert O’Donnell,

Supervisor of Mathematics and Educational Technology Technology Staff: Al Pulsinelli Reggie Washington Bill Wetherill Secretarial Staff: Debbie Gialanella Geri Manfre Gail Nemeth

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Monroe Township Schools Mission and Goals

Mission

The mission of the Monroe Township School District, a unique multi-generational community, is to collaboratively develop and facilitate programs that pursue educational excellence and foster character, responsibility, and life-long learning in a safe, stimulating, and challenging environment to empower all individuals to become productive citizens of a dynamic, global society.

Goals

To have an environment that is conducive to learning for all individuals. To have learning opportunities that are challenging and comprehensive in order to stimulate the intellectual, physical, social and emotional development of the learner. To procure and manage a variety of resources to meet the needs of all learners. To have inviting up-to-date, multifunctional facilities that both accommodate the community and are utilized to maximum potential. To have a system of communication that will effectively connect all facets of the community with the Monroe Township School District. To have a staff that is highly qualified, motivated, and stable and that is held accountable to deliver a safe, outstanding, and superior education to all individuals.

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INTRODUCTION, PHILOSOPHY OF EDUCATION, AND EDUCATIONAL GOALS

Philosophy

Monroe Township Schools are committed to providing all students with a quality education

resulting in life-long learners who can succeed in a global society. The mathematics program, grades K - 12, is predicated on that belief and is guided by the following six principles as stated by the National Council of Teachers of Mathematics (NCTM) in the Principles and Standards for School Mathematics, 2000. First, a mathematics education requires equity. All students will be given worthwhile opportunities and strong support to meet high mathematical expectations. Second, a coherent mathematics curriculum will effectively organize, integrate, and articulate important mathematical ideas across the grades. Third, effective mathematics teaching requires the following: a) knowing and understanding mathematics, students as learners, and pedagogical strategies b) having a challenging and supportive classroom environment and c) continually reflecting on and refining instructional practice. Fourth, students must learn mathematics with understanding. A student's prior experiences and knowledge will actively build new knowledge. Fifth, assessment should support the learning of important mathematics and provide useful information to both teachers and students. Lastly, technology enhances mathematics learning, supports effective mathematics teaching, and influences what mathematics is taught.

As students begin their mathematics education in Monroe Township, classroom instruction will reflect the best thinking of the day. Children will engage in a wide variety of learning activities designed to develop their ability to reason and solve complex problems. Calculators, computers, manipulatives, technology, and the Internet will be used as tools to enhance learning and assist in problem solving. Group work, projects, literature, and interdisciplinary activities will make mathematics more meaningful and aid understanding. Classroom instruction will be designed to meet the learning needs of all children and will reflect a variety of learning styles.

In this changing world those who have a good understanding of mathematics will have many opportunities and doors open to them throughout their lives. Mathematics is not for the select few but rather is for everyone. Monroe Township Schools are committed to providing all students with the opportunity and the support nececssary to learn significant mathematics with depth and understanding. This curriculum guide is designed to be a resource for staff members and to provide guidance in the planning, delivery, and assessment of mathematics instruction.

Educational Goals

The goal of the HSPA Review packet is to prepare all students for the 11th grade HSPA in a planned, systematic way over a three-year period. It is hoped that by familiarizing students with the nature and types of problems they will likely encounter on the actual test they will gain the confidence and ability to achieve on the real test.

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New Jersey State Department of Education

Core Curriculum Content Standards A note about Mathematics Standards And Cumulative Progress Indicators. The New Jersey Core Curriculum Content Standards for Mathematics were revised in 2002. A complete copy of the new Core Curriculum Content Standards for Mathematics may be found in the Curriculum folder on the district servers and also at: http://www.nj.gov/njded/cccs/02/s4_math.htm.

http://www.nj.gov/njded/cccs/02/s4_math.htm

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Teachers: How to Use this Review Packet

This HSPA Review Project is divided into three packets. Packets 1 & 2 consist of 20 worksheets (#1-20) usually containing two multiple choice or short answer questions and one open-ended question. Packet 3 consists of 15 worksheets (#1-15) with two multiple choice or short answer questions and one open-ended question. These can be done as a warm-up in class and are meant to take students anywhere from 5 to 10 minutes to complete. The last seven review sheets in Packet 1 & 2 and the last eight review sheets in Packet 3 contain Performance Assessment Tasks (PATs) from the New Jersey Department of Education (August 2002). We suggest that these be assigned as homework. They will probably take closer to 20 minutes to review once the students have completed the task. Solutions and rubrics to the PATs are included. They may only be used as practice as stated by the New Jersey Department of Education. The packets should be administered according the following plan: Packet 1 Packet 2 Packet 3 Honors Algebra I Honors Geometry Honors Algebra II Algebra I Geometry Algebra II Dynamics of Algebra I Dynamics of Geometry Dynamics of Algebra II Algeom 1 Algeom 2 Algeom 3 For maximum effectiveness the worksheets should be spread out over the course of the year. Additionally, there are three practice tests to be given in all eleventh grade classes before the Spring HSPA is administered. Also included are some frequently asked questions and answers about the High School Proficiency Assessment that might be helpful. Good luck!

Janet Bluefield Susan Patikowski

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Many of the problems and explanations given are due to the following source: Glatzer, David J. and Glatzer, Joyce, Preparing for the New Jersey HSPA, Amsco School

Publications, Inc., New York, 2001

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Understanding the HSPA Mathematics Exam

1. What is the HSPA?

The High School Proficiency Assessment (HSPA) is a graduation test required of all New Jersey public school students. It includes mathematics from the four content clusters of the New Jersey Core Curriculum Content Standards. The HSPA has been developed to show whether or not a student has a satisfactory level of achievement in the specified areas. The HSPA in mathematics is not a minimum competency or basic skills test; it is a test of the student’s ability to do higher order thinking and to integrate topics in mathematics.

2. When do students take the HSPA?

Students first take the HSPA is in the spring of their junior year.

3. What mathematics topics are included in the HSPA?

There are four math clusters in the HSPA i. Number Sense, Concepts, and Applications ii. Spatial Sense and Geometry iii. Data Analysis, Probability, Statistics, and Discrete Mathematics iv. Patterns, Functions, and Algebra Please note: Problem-solving and measurement situations exist in each cluster; as a result, there is no separate problem-solving or measurement cluster. Isolated computation questions do not appear on the HSPA. Many of the mathematics questions involve a considerable amount of reading.

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4. What types of math questions appear on the HSPA? There are two types of mathematics questions. i. Multiple-choice items ii. Open-ended items

There are 40 multiple-choice questions that test a student’s higher-level cognitive processes. These questions will take an average between one and two minutes to answer and have a weight of 1 point for each correct response. Students are not penalized for guessing. There are 8 open-ended questions that require the student to construct and explain his own written or graphic responses, and receive a score from 0 to 3 based on the rubric below

3-Point Response

The response shows complete understanding of the problem’s essential mathematical concepts. The student executes procedures completely and gives relevant responses to all parts of the task. The response contains few minor errors, if any. The response contains a clear, effective explanation detailing how the problem was solved so that the reader does not need to infer how and why decisions were made.

2-Point Response The response shows nearly complete understanding of the problem’s essential mathematical concepts. The student executes nearly all procedures and gives relevant responses to most parts of the task. The response may have minor errors. The explanation detailing how the problem was solved may not be clear, causing the reader to make some inferences.

1-Point Response

The response shows limited understanding of the problem’s essential mathematical concepts. The response and procedures may be incomplete and / or may contain major errors. An incomplete explanation of how the problem was solved may contribute to questions as to how and why decisions were made.

0-Point Response

The response shows insufficient understanding of the problem’s essential mathematical concepts. The procedures, if any, contain major errors. There may be no explanation of the solution, or the reader may not be able to understand the explanation. The reader may not be able to understand how and why decisions were made.

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5. What are some general guidelines for answering open-ended questions? In answering open-ended questions, you will find the following suggestions helpful.

Write in complete sentences. Be concise, not wordy. Make sure to explore different cases. Make sure to answer each part of the questions. Make sure you answer the question that is being asked. Use a diagram to enhance an explanation. Label diagrams with dimensions. As appropriate, give a clearly worked-out example with some explanation. In problems involving estimation / approximation, make sure you do precomputational

rounding. Provide generalizations as requested. When using a grid, follow specific instructions for the location of the origin, axes, etc. Avoid assumptions that have no basis, such as assuming that a triangle is isosceles. Double-check any computation needed within the open-ended response. Be aware that the question may have more than one answer.

6. Do the student’s have to memorize formulas? No, A Mathematics Reference Sheet is distributed to each student along with the test. This reference sheet contains any formulas you may need on the mathematics questions. The reference sheet may also contain materials such as a ruler or figures to be cut out and used in the process of solving specific questions.

7. Are calculators allowed on the HSPA?

Yes, students are allowed to use a calculator when they take the mathematics section of the HSPA. Not all questions will require the use of a calculator. Determining which questions to answer with the calculator is an important skill for the students to develop.

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*****insert reference sheet *****

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HSPA

Packet – 1

Honors Algebra I Algebra I

Dynamics of Algebra I Algeom I

Worksheet 1 1. Arrange the following from LEAST to GREATEST.

13 , 2

5 , 0.6, 0.125

a) 0.125, 0.6, 13 , 25

b) 0.125, 13 , 2

5 ,0.6

c) 0.125, 13 , 0.6, 25

d) 13 , 2

5 , 0.125, 0.6

2. Following a series of eight football plays, a team had the following results:

+4 yards, +3 yards, +9 yards, -4 yards, -5 yards, + 10 yards, -5 yards, +8 yards

What is the average yardage for this series of plays? a) 20 b) 6 c) 2.5 d) -2.5

3. If you know that 18

= 0.125, how can you use that fact to find the value of 78

.

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Worksheet 2

1. A fraction is equal to 12

. If its numerator is increased by 1 and its denominator is increased

by 5, the value of the resulting fraction is 49

. Find the original value of the fraction.

a) 612

b) 713

c) 918

d) 1122

2. Which of the numbers below has all of the following characteristics?

It is a multiple of 12 It is the least common multiple of two one-digit even numbers. It is not a factor of 36.

a) 12 b) 24 c) 36 d) 48

3. If 2, 3, and 5 are factors of a number, list three other factors of the number. 4. Jack believes that the larger a number is, the more factors the number has. Write an

argument in support or contradiction of Jack’s belief.

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Worksheet 3

1. A basketball player makes 3 out of every 5 of her foul shots. At this rate, if she attempts 55 foul shots, how many will she miss?

a) 50 b) 40 c) 33 d) 22

2. Which proportion does NOT represent the given question? If 48 oz. cost $1.89, what will 72 oz. cost?

a) 48 721.89 x

= c) 1.8972 48

x=

b) 48 1.8972 x

= d) 1.8948 72

x=

3. Which of the following situations represents a better salary offer? Explain why.

A salary of $504.50 per week $12.50 per hour for 40 hours

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Worksheet 4

1. Which of the following is NOT a correct statement? a) 63% of 63 is less than 63. b) 115% of 63 is more than 63.

c) 13

% of 63 is the same as 13

of 63.

d) 100% of 63 is equal to 63.

2. The sale price of a chair is $510 after a 15% discount has been given. Find the original price.

a) $76.50 b) $433.50 c) $586.50 d) $600

3. Norma received a commission of 5% on her sales. In November, Norma’s gross sales were $12,500. How much more would she receive if her commission were raised to 7%?

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Worksheet 5 1. Clue 1: I am a Real Number whose value is less than 1 Clue 2: I do not end Clue 3: My digits do not repeat. What kind of number am I?

2. Suppose that x

means x + 3.

x

means x2

X

means x + 1

For example,

= 7^2 = 49= 74 + 3=4

What would be the value of ?

3+3

3. A computer simulated tossing 3 coins 400 times. The results are shown in the table below.

HHH 41 TTH 50 HHT 54 THT 53 HTH 48 HTT 45 THH 57 TTT 52

Calculate the experimental probability of tossing two heads and one tail as shown by this

simulation.

Determine the theoretical probability of tossing two heads and one tail.

Compare the two probabilities and explain any differences. Worksheet 6

1. Salman has 6 gold coins, each of which weighs 2.625 ounces. How much do the gold coins weigh in all?

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a) 3154

oz b) 3144

oz c) 5128

oz d) 588

oz

2. What value of a makes the equation in the box true?

a2 – 9 = 5a + 5 a) 3 b) 5 c) 7 d) 9 3. A ball is dropped from a height of 2 meters (H0). On its first bounce, the ball rebounds to

80% of its original height (H1). The ball continues to bounce back to a new height that is always 80% of the previous height.

Determine the height H1 and H2, after the first and second bounce. Show the work that

leads to your answers.

Approximately how many bounces will it take to only rebound to a height of 25 centimeters?

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Worksheet 7

1. Which pair of points determines a line parallel to a line with slope 23

?

a) (1, 4), (2, 5) b) (4, 5), (6, 8) c) (3, 2), (0, 0) d) (-3, 2), (0, 0)

2. A line segment extends from the point (6, 4) to point P on the line y = 8 such that the slope of the segment is ¼. What are the coordinates of point P?

3. The given table is generated from which of the following rules? X -2 -1 0 1 2 F(x) -2 -3 -4 -5 -6 a) f(x) = 2x + 2 b) f(x) = -4 – x c) f(x) = x + 4 d) f(x) = -3x

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Worksheet 8 1. A tree grows 1.4 cm each day. In 120 days, how many METERS will the tree have grown?

a) 0.168 m b) 1.68 m c) 16.8 m d) 168 m

2. Which of the conversions below would be done using the following procedure? 5,280 ft 12 in6 mi

1 mi 1 ftx x

a) Miles to feet b) Feet to miles c) Miles to inches d) Inches to miles.

3. Change 75 km/hr to m/min. Show your process.

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Worksheet 9

1. At 6:00 am, the temperature in Nome, Alaska was 15o below zero Fahrenheit. The average increase in temperature per hour was 3o. What was the temperature at noon?

a) -12oF b) -3oF c) 3oF d) 33oF

2. For which of the following objects would 180 cm be a good estimate of its length?

a) The length of a driveway b) The length of a dining room table c) The height of a kindergarten child d) The length of a city block

3. Temperature can be measured in either of two systems: Celsius (0o freezing point of water and 100o boiling point of water) and Fahrenheit (32o freezing point of water and 212o boiling point of water). The two systems are related by the formula:

9 325

oF C= +

20oC is considered an appropriate measure for room temperature. Express this measure in

degrees Fahrenheit. Show your process.

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Worksheet 10

1. Pauline walked 4 km due east and then 7 km due north. Which of trhe following is the most reasonable answer for the distance between Pauline’s start and endpoint?

a) 6.5 km b) 8.1 km c) 9 km d) 11 km

2. A right triangle has two sides of lengths 3 and 4. Which of the following could be the length of the third side?

I. 5 II. 7 III. 7 a) I only b) II only c) I and II d) I and III

3. A baseball diamond is a square with 90-foot sides. The pitcher’s mound is exactly 66’ 6” from home plate. How far is the pitcher’s mound from second base? Show your procedure in doing the problem.

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Worksheet 11

1. Which of the following is NOT correct?

a) 20 ft < 7 yd b) 100 in < 3 yd c) 198 cm < 2 m d) 2010 m < 2 km

2. In which list below are the units of measurement for area arranged in order from LEAST to GREATEST?

a) in2, cm2, km2 b) km2, m2, cm2 c) cm2, m2, km2 d) cm2, km2, in2

3. A college lecture hall has 15 rows of seats. If the first row has 18 seats and the last row has 46 seats. The numbers of seats in each row form an arithmetic sequence.

a) How many more seats are in row (n + 1) than row n? Explain your approach. b) How many total seats are in the lecture hall?

1. You flip a fair coin. The first eight flips come up heads. What is the probability that the ninth flip of the coin will be a tail?

a) 12

b) 89

c) 1 d) 19

2. A coin is tossed and a die with numbers 1-6 is rolled. What is P(heads and 3)?

a) 112

b) 14

c) 13

d) 23

3. A basketball player is given two free throws for a foul committed against him. During the season, he has made 36 out of 50 free throws attempted. Using this experimental probability, find the probability of each event as a percent.

a) Making both free throws b) Making neither free throw c) Making one free throw

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Worksheet 13

1. What is the range of the function y = x2 + 1 when the domain is {0, 2, 4}?

a) {1, 3, 5} b) {1, 5, 9} c) {1, 9, 25} d) {1, 5, 17}

2. Marcia, Doris, Roberta, and Carmen are running a race. If there are no ties, in how many different ways can they finish the race?

a) 6 b) 12 c) 24 d) 36

3. Suppose a state’s license plates have three digits, then a picture of the state bird, and then three more digits.

a) If any digit (including zero) can go in any position, how many license plates are

possible? b) If the state expects to use up all of the license plate numbers within the next year, it

needs to have a plan to develop more numbers. If it decides to replace the first three digits with letters of the alphabet, how many license plate numbers are now possible? Show your process.

c) A member of the state transportation board suggested that one additional digit for a

total of 7 digits would be better than 6 spaces with three letters and three digits. Is this suggestion accurate? Explain.

Worksheet 14

1. Assume that there is an equal probability that a baby will be born on a given day of the week and that there is also an equal probability that a baby will be either male or female. What is the probability that a baby will be a male born on a Sunday?

a) 149

b) 114

c) 17

d) 12

2. A sporting goods company surveyed 800 baseball players to see what type of bat they preferred. Aluminum bats were preferred over wood by 300 players. Which statement is true?

a) More than ½ of the players surveyed preferred aluminum b) More than 40% of the players surveyed preferred aluminum. c) More than 75% of the players surveyed do not prefer aluminum. d) More than 1/3 of the players surveyed prefer aluminum.

3. A television rating service found that 945 households out of a sample of 3,340 households

watched the Super Bowl. Estimate to the nearest million how many of the 94 million households with a television watched the Super Bowl.

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Worksheet 15 1. Which of the following is NOT an example of a direct variation?

a) The number of gallons of gasoline purchased and the total cost. b) If speed is constant, the distance traveled and the time traveled. c) The value of a used car and the age of the car. d) The circumference of a circle and the length of the diameter.

2. y is directly proportional to x. If y = 20 when x = 16, find the constant of variation.

a) 0.8 b) 1.25 c) 32 d) 320

3. If it takes 2.5 hours to make a trip traveling at 50 mph, how long would it take to make the same trip at a speed of 40 mph? Show your process.

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Worksheet 16

1. During a baseball season, the National League home-run champion had the following home-run statistics by month:

April May June July August September October 5 13 7 11 6 8 6 Which month contains the median for the player’s home-run statistics? a) June b) July c) August d) September

2. For the given scores, the mean is 40. Scores: 20, 30, 40, 50, 60

If the 20 is changed to a 17, which of the following would have to be done in order for the mean to remain at 40?

a) Change the 50 to a 47 b) Change the 60 to a 57 c) Change the 50 to a 53 d) Change the 30 to a 27

3. Mr. Abbott asked his math students to use the following data to find average test scores. Mr. Abbot’s Classes Period No. of Students Test Average 1 Algebra 20 80 2 Algebra 20 70 3 Geometry 30 84 5 Geometry 10 80 In computing the average test score for the combined algebra classes, Bill suggested that Mr.

Abbott take the average of 80 and 70 to get 75. For the two combined geometry classes, however, using the same approach gives a wrong result of 82. Explain why the first average (75) was correct but the second average (82) was NOT correct. Find the correct average for the two geometry classes. Explain your approach.

Worksheet 17

1. Given matrices A and B, where56 73 29 41

69 84 37 52

A B⎡ ⎤ ⎡= =

⎤⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦

, what is the value of 2A + B?

a) b) c) 85 114

106 136⎡ ⎤⎢ ⎥⎣ ⎦

114 155143 188⎡ ⎤⎢ ⎥⎣ ⎦

141 187175 220⎡ ⎤⎢ ⎥⎣ ⎦

d) 170 228212 272⎡ ⎤⎢ ⎥⎣ ⎦

2. Two 4 by 2 matrices have exactly the same values in the corresponding positions. Show what the matrix looks like representing the difference of the two matrices.

3. Matrix A represents the number of tickets sold for a performance of a musical play on Saturday. Matrix B represents the number of tickets sold for the performance of the same musical play on Wednesday. The columns represent matinees and evening performances. The rows represent orchestra, mezzanine, and balcony seats.

275 295 220 251A = 143 158 B = 133 140

65 87 52 45

⎡ ⎤ ⎡⎢ ⎥ ⎢⎢ ⎥ ⎢⎢ ⎥ ⎢⎣ ⎦ ⎣

⎤⎥⎥⎥⎦

If orchestra seats cost $50, mezzanine seats $45, and balcony seats $30, how much more did the theater make on the two evening performances compared to the two matinee performances.

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Worksheet 18

1. Find the starting number for the given flowchart.

Start ↓

Multiply by 2 ↓

Add 8 ↓

Divide by 2 ↓

Result = 13

2. A plumber charges $48 for each hour she works plus an additional service charge of $25. At this rate, how much would the plumber charge for a job that took 4.5 hours?

3. Problem: Find the sum of the first 50 odd numbers.

Martin decided to develop a pattern to help obtain the solution to the above problem. The first sum he looked at was 1 + 3 + 5 + 7 = 16. Write a suggestion for Martin so that he could formulate a helpful approach to the original problem. Solve the original problem.

Worksheet 19

1. Which of the following would yield a repeating decimal pattern?

a) 16

b) 14

c) 316

d) 125

2. What digit is in the 45th decimal place in the decimal value of 711

?

a) 1 b) 3 c) 6 d) 7

3. What is the units digits in 240?

a) 2 b) 4 c) 6 d) 9

4. Mary notices that on a 2 x 2 checkerboard there are 5 squares of various sizes.

This 2 x 2 board has four 1 x 1 squares and one 2 x 2 square. Mary thinks that a 4 x 4 checkerboard would have twice as many squares. Do you agree or disagree with Mary’s idea? Explain your reasoning.

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Worksheet 20

1. This table indicates a linear relationship between x and y. X 1 3 5 7 9 Y 1 7 13 ? 25 According to this pattern, which number is missing from the table? a) 15 b) 19 c) 21 d) 23

2. The cost of a long-distance telephone call can be computed based on the following formula:

T = C + nr, where T = total cost of the call in dollars. C = charge for the first three minutes in dollars. n = number of additional minutes the call lasts r = rate per minute for each additional minute in dollars.

What is the cost of a 15-minute-long distance call if a person is charged $1.75 for the first three minutes and $0.15 for each additional minute?

3. A local parking lot charges $1.75 for the first hour and $1.25 for each additional hour or part of an hour. Represent the relationship of parking charges to hours parked:

a) In a table of values of 1 go 6 hours. b) In an equation in which t represents time parked in hours and C the total cost of

parking. c) As a graph with hours parked on the horizontal and total cost on the vertical.

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HSPA Review Cluster: Data Analysis…

Math Test The following chart shows the score distribution on a recent mathematics test: Score Number of Students 41-52 5 53-64 11 65-76 7 77-88 32 89-100 40 A) If the lowest score for a passing grade is 65, then, to the nearest percent, what percent of

students failed the test? What percent passed the test (to the nearest percent)? B) In what interval would the median score lie? How do you know? C) Construct a graph to display the data shown in the table above. What general statement can

be made based on the graph? D) From the data above can you determine the mean score? The median score? The mode?

Explain your thinking.

HSPA Review Math Test Solutions A) 16/95 = 17% 79/95 = 83% B) 77-88 is the range of scores where the median is found because this is the middle point of all

of the scores. C) Students make an appropriate graph. According to their graph it seems that the test was very

fair. The majority of students passed the test with a 65% or better.

05

10152025303540

41-5253-6465-7677-8889-100

Number of Students D) You can’t determine the mean, median or the mode because the scores aren’t specific

enough. The information given is only a range of scores.

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HSPA Review Math Test Assessment Rubric Points

3 Accurately calculates percent of passing and failing grades. Clearly states the interval

containing the median and gives explanation for choice. Accurately constructs a graph, which summarizes the given data. Uses the information on the graph to justify the fairness of test. Clearly states that measures of central tendency cannot be determined because data is not individually listed. Support statements are evident. Any calculation errors are minor.

2 Accurately calculates percent of passing and failing grades. Accurately constructs a

graph which summarizes the given data. Clearly states the interval containing the median and gives an explanation for choice. Uses the information on the graph to justify fairness of test. Explanation that measures of central tendency cannot be determined is weak. Support statements are evident but weak.

1 Presents some understanding of the problem. 0 Presents no understanding of the problem.

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HSPA Review Cluster: Number Sense

Keeping Records at the Gas Station Juan has a part-time job at a gas station. Part of his responsibility is to keep records of all sales of stock items. During one week last July, the station sold the following: 160 quarts of oil at an average price of $1.45 per quart 25 gallons of antifreeze at $6.50 per gallon 24 tires at an average price of $49.75 per tire 4 batteries at a total price of $140 various auto supply accessories at a total price of $254.75

A) What was the total income from the sale of all these items? B) What percent of the sales did the accessories represent? C) If Juan received a 5% commission on total sales, and a salary of $100 a week, how much did

Juan earn that week? D) If Juan is offered another job for a salary of $150 a week without commission, should he quit

his current job? Why or why not? Support your answer.

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HSPA Review Cluster: Number Sense Keeping Records at the Gas Station Solutions A) Oil 160X$1.45= $232.00 Antifreeze 25X$6.50= $162.50 Tires 24X$49.75= $1,194.00 Batteries $140.00 Accessories $254.75 Total $1983.25 B) Accessories represent 12.8% or 13% if rounded C) He earned $99.17 in commission + $100.00 in salary=$199.17 D) No. The possibility of making more money exists because of the opportunity to earn a

commission. However, the commission is not guaranteed. Or yes, because the $150 is guaranteed.

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HSPA Review Keeping Record at the Gas Station Assessment Rubric Points

3 Correctly calculates the total from the sale of the items and figures the percent of sales from accessories. Calculates Juan’s earnings and gives a clear explanation for the answer to D.

2 Calculates the total from the sale of these items and figures the percent of sales from

accessories. Calculates Juan’s earnings and gives a clear explanation for answer to D. Any calculation errors are minor.

1 Only begins to demonstrate an understanding of the task by responding to Part A

correctly. 0 Demonstrates no understanding of the problem.

41


Competitive Salaries Yolanda and Lou take similar jobs in competing companies. Yolanda’s starting salary is $28,000 per year with an 8% raise at the end of each year. Lou’s starting salary is $30,000 per year with a 5% raise at the end of each year. A) What would the raises be for each at the end of the first year? What will their new salaries be

at the end of the first year? B) Generate a table to show their salaries for the first five-year period. C) Does Yolanda’s salary ever overtake Lou’s salary? Explain your answer.

HSPA Review Competitive Salaries Solutions A) Raises: $28,000(.08)=$2240 Yolanda’s raise $30,000(.05)=$1500 Lou’s raise At the end of the first year: $28,000+$2240=$30,240 Yolanda’s salary $30,000+1500=$31,500 Lou’s salary B) .

Start of year Yolanda Lou 1 $28,000.00 $30,000.00 2 $30,240.00 $31,500.00 3 $32,659.20 $33,075.00 4 $35,271.94 $34,728.75 5 $38,093.70 $36,465.19

C) Yes, by the fourth year Yolanda will overtake Lou’s salary by $543.19.

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43

HSPA Review Competitive Salaries Assessment Rubric Points

3 Correctly calculates the salaries and generates the table. Determines that by the fourth year her salary will overtake his.

2 Calculates the salaries and generates the table. Determines that by the fourth year her

salary will overtake his. May contain minor computational flaws. 1 Attempts to calculate the salaries and generate the table. May not determine that her

salary will overtake his or may contain major calculation errors. 0 Student demonstrates no understanding of the problem.

44

HSPA Review Cluster: Patterns, Functions, & Algebra

Jose’s Cellular Phone Jose, a traveling salesman, wants to buy a cellular phone to use while he is on the road. His employer allows him $50.00 a month for this expense. He researches different options. Company A’s rate is a minimum charge of $15.00 per month and $2.00 per minute of usage. Company B’s rate is $17.00 per month and $1.50 per minute of usage. A) Write two equations representing each company’s month rate in terms of minutes. B) For his $50.00 per month allowance, how many minutes of usage will he get from each

company? C) Which company permits more usage and by how many minutes? D) Jose contracts with Company B. In March, Jose uses his cellular phone for 19 minutes. What

was his monthly bill for March? Explain the process used to arrive at this answer.

45

HSPA Review Jose’s Cellular Phone Solutions A) Let x = minutes of usage Company A = $15.00 + 2X Company B = $17.00 + 1.5X B) Company A 50 = 15 + 2X 35 = 2X 17.5 = X 17 minutes 30 seconds Company B 50 = 17 + 1.50 X 33 = 1.50 X 22 = X 22 minutes C) Company B offers the better buy because Jose gets four and one-half more minutes of

usage per month than Company A. D) 17 + 1.50 (19) = 445.50 = Monthly fee plus the cost for the 19 minutes.

46

HSPA Review Jose’s Cellular Phone Assessment Rubric Points

3 Writes a logical equation to represent the given information for each rental company. Calculates the usage with each company and makes a comparative statement regarding the difference in the usage per month. Determines that Company B offers the better buy and accurately calculates his monthly bill; provides mathematical and written explanation for conclusion.

2 Writes a logical equation to represent the given information for each rental company.

Calculates (with minor flaws) the usage with each company. Comparative statement regarding the difference in the usage per month is present. Determines that Company B offers the better buy and calculates his monthly bill; mathematical and written explanation for conclusion is weak.

1 Calculates the usage for each company. Comparative statement regarding the

difference in the usage per month is weak or missing. Attempts to determine that Company B offers the better buy and calculates the monthly bill; mathematical and written explanation for conclusion are weak or missing or makes major calculation errors.

0 Presents no understanding of the problem.

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Credit Card Calculations Credit card companies charge interest. Sarah charges a $540 stereo. She must pay 18% annual interest compounded monthly on the unpaid balance. At the end of the first month, she makes a $150 payment. A) After her first payment is deducted, the interest is computed on the unpaid balance. How

much interest is Sarah charged at this time? B) If Sarah made monthly payments of only $50 instead of $150, how many months will it take

Sarah to pay off her credit card if she did not make any other purchases? C) Suppose Sarah deposited the $540 into her saving account and was paid an annual rate of

3.65%. What would be the balance in this account at the end of 4 months? D) Based on the above information, list the financial advantages and disadvantages of making

purchases on a credit card versus saving the money until there is enough to pay the total price for the stereo.

HSPA Review Credit Card Calculations Solutions A) $540 stereo - $150 payment = $390.00 balance after 1st payment X .18 interest ÷12 = $5.85

interest Sarah would pay $5.85 for interest fee B) 1st payment $540-50=$490+7.35 interest = $497.35 2nd payment $497.35-50=6.72=$454.06 3rd payment $454.06-50+6.07=$410.12 4th payment $410.12-50+5.40=$365.52 5th payment $365.52-50+4.74=$320.29 6th payment $320.29-50+4.06=$274.35 7th payment $274.35-50+3.37=$227.72 8th payment $227.72-50+2.67=$179.39 9th payment $179.39-50+1.95=$131.34 10th payment $131.34-50+1.23=$82.51 11th payment $82.51-50+.49=$33.00 12th payment $33.00+.50=33.50 & last payment It would take a year to pay off the balance. C) $540 deposit 3.65% annually 12=.3041666 per month ÷ 1st month $540+1.65=$541.65 2nd month $541.65+1.65=$543.30 3rd month $543.30+1.66=$544.96 4th month $544.96+1.66=$546.62 After four months Sarah’s balance would be $546.62 D) The advantages of using the credit card are that you have the stereo right away and can use it

while you pay for it. You are able to get it for a smaller initial payment. However, it will cost you more in the end. By saving the money and then purchasing the stereo, it will cost you less, however, you will have to wait until you have enough money in order to get it.

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49

HSPA Review Credit Card Calculations Assessment Rubric Points

3 Calculates the interest correctly for the first month, figures that it would take 12 months to pay off the credit card, calculates the total money in the savings account after four months and develops a reasonable description of the advantages and disadvantages of credit cards vs. saving for purchases.

2 Provides a satisfactory response to two parts (A, B, or C) and provides a reasonable

description of the advantages and disadvantages of credit cards vs. saving for purchases.

1 Student provides a satisfactory response to one part and provides a reasonable

description of the advantages and disadvantages of credit card vs. saving for purchases.

0 Student demonstrates no understanding of the problem.

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Board Game Bonus The new Wild Wallaby board game determines the bonus points by doubling your score and adding three to the total as illustrated in the table below. Note that negative and fractional scores are not possible.

Score 0 1 2 3 4 Bonus 3 A) Complete the table and represent the bonus points with an algebraic equation. B) On the graph paper provided, plot the data. C) If you earned 57 bonus points, what was your score? D) Is it possible to earn 8 bonus points?

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HSPA Review Board Game Bonus Solutions A)

Score 0 1 2 3 4 Bonus 3 5 7 9 11 If s = score: Bonus Points = 2s + 3 OR If x = score and y = Bonus Points: y = 2x + 3 B) x-axis = score, y axis = bonus points Plot ordered pairs from table above (x, y) C) 2s + 3 = 57 2s = 54 s = 27 D) 2s + 3 = 8 2s = 5 s = 2.5 It is not possible because the score is a fraction

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HSPA Review Board Game Bonus Assessment Rubric Points

3 Demonstrates a complete understanding of the problem and provides correct responses to all parts of the problem.

2 Correctly completes the table, writes an algebraic equation and correctly plots the

points. 1 Successfully completes the table and determines an algebraic equation to represent the

bonus points. 0 Demonstrates no understanding of the problem.

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XYZ Technologies The information below represents the year, gross income and profit for the XYZ Technologies Company. The data is presented as an ordered triple: (year, gross income, profit) – Gross Income and Profit are presented in millions of dollars. (1987,132,14), (1988,163,17), (1989,202,22), (1990,275,33), (1991,357,47), (1992,446,45), (1993,604,52), (1994,755,74), (1995,866,74), (1996,872,68) A) Use the above information to complete the chart below. Be sure to use a positive sign to

denote increase and negative sign to denote a decrease. Years Increase or Decrease

In Gross Income (millions)

Increase or DecreaseIn Profit (millions)

1987-1988 +31 +3 1988-1989 1989-1990 1990-1991 1991-1992 1992-1993 1993-1994 1994-1995 1995-1996 B) Between which two years was the greatest dollar increase in gross income recorded? In profit? C) Using the information in the chart A), what is the mean of the numbers recorded in the profit

column? What is the median? Maria asks, “When a company’s gross income increases, does it follow that its profit also increases? How would you answer her? Explain your reasoning.

54

HSPA Review XYZ Technologies Solutions A) Years Increase or Decrease

In Gross Income (millions)

Increase or DecreaseIn Profit (millions)

1987-1988 +31 +3 1988-1989 +39 +5 1989-1990 +73 +11 1990-1991 +82 +14 1991-1992 +89 -2 1992-1993 +158 +7 1993-1994 +151 +22 1994-1995 +111 0 1995-1996 +6 -6 B) Greatest gross income increase between 1992 and 1993 - $158 million Greatest profit increase between 1993 and 1994 - $22 million C) Mean = 6 Median = 5 No. As the data indicate in this example. Expenses may also increase, thereby lowering the

profit.

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HSPA Review XYZ Technologies Assessment Rubric Points

3 Demonstrates an understanding of data analysis by completing the given chart.

Correctly identifies the one-year period which saw the greatest increase in gross income (1992-1993) and the one-year period which saw the greatest increase in profit (1993-1994). Correctly provides the mean (6) and the median (5) of the yearly increases (decreases) in profit from 1987 through 1996. Provided a reasonable answer to Maria’s question, citing either the data presented or similar information to demonstrate that profit does not necessarily increase as gross income increases.

2 Demonstrates an understanding of data analysis by completing the given chart.

Correctly identifies the one year period which saw the greatest increase in gross income and the one year period which saw the greatest increase in profit. Correctly provided the mean and median of the yearly increases (decreases) in profit from 1987 through 1996. May have trouble providing a reasonable answer to Maria’s question or citing an example to justify the answer given.

1 Only begins to demonstrate an understanding of data analysis by completing the given

chart and attempting to identify the one year period which saw the greatest increase in gross income and the one year period which saw the greatest increase in profit and the mean and median of the yearly increases (decreases) in profit from 1987 through 1996. Cannot provide an example to justify a response to Maria's question.

0 Demonstrates no understanding of the problem.

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HSPA

Packet – 2

Honors Geometry Geometry

Dynamics of Geometry Algeom II

57

Worksheet 1

1. The distance on the number line between a number x and –5 is 7 units. Find all possible values for x.

a) -12, 2 b) 12, -2 c) -12 d) -2

2. What is the measure of the complement of the complement of an angle of 30o ?

a) 30o b) 60o c) 120o d) 250o

3. Draw and label the following figure. Planes P and Q intersect each other. They both intersect plane R.

Worksheet 2 1. In which of the following diagrams are a∠ and b∠ vertical angles?

b

ab

a

b

a

i i i .i i .i .

a) I only b) I and II c) I and III d) I, II, and III

2. A(1,4), B(2,1), C(6,1)

a) acute b) obtuse c) right d) isosceles

3. If BDuuur

is the angle bisection of ABC∠ and BEuuur

is the angle bisector of ABD∠ , what is if = 36m ABC∠ m DBE∠ o.

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59

Worksheet 3

1. If three students share $180 in the ratio 1 : 2 : 3, how much is the largest share?

2. The measures of the angles of a triangle are in the ratio of 2 : 2 : 5. What type of triangle is it?

a) Isosceles triangle b) Acute triangle c) Right triangle d) Scalene triangle

3. Two sides of a triangle each measure 8 cm. a. Divide the following list of integers into two groups

1, 2, 3, 8, 10, 12, 18, 20, 30 Group 1: possible lengths for the third side of the triangle. Group 2: lengths that are not possible for the third side of the triangle. b. What is the smallest positive integer that cannot represent the length of the third side? c. For the triangles that are possible, with sides of integral lengths, draw and label the

lengths of the sides for one acute triangle and one obtuse triangle.

Worksheet 4

1. In parallelogram ABCD, what is the measure of C∠ ?

26

50

B

CD

A

a) 76o b) 86o c) 100o d) 104o

2. Which of the following statements is TRUE?

I. A rhombus with right angles is a square. II. A rectangle is a square. III. A parallelogram with right angles is a square.

a) I only b) II only c) III only d) I and III

3. There are 50 paper quadrilaterals in a box. If 18 are rectangles, 30 are rhombuses, and 7

are squares, how many of the quadrilaterals would be of a type other than rectangle, rhombus, or square?

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Worksheet 5

1. Three concentric circles are shown. The diameter of the largest circle is 16 units. The diameter of the middle circle is 12 units and the diameter of the smallest circle is 10 units. What is the distance between the smallest circle and the middle circle?

a) 1 b) 2 c) 4 d) 6

2. A circle with its center at P has a radius of 5 cm. Line segment PQ measures 6 cm and line segment PR measures 5.1 cm. Which of the following is a TRUE statement?

a) Points Q and R are inside the circle. b) Points Q and R are on the circle. c) Points Q and R are outside the circle. d) The distance from point R to point Q is 0.9 cm.

3. A circular swimming pool has a diameter of 20 feet. Two poles for a volleyball net are placed 15 feet from the center of the pool and as far apart as possible. What is the length of net needed to be strung tautly between the two poles? (Assume the net extends pole to pole.)

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Worksheet 6 1. Which vector represents a walk of 5 blocks north followed by a 6 blocks west?

a)

6

5

b)

65

c)

6

5

d)

6

5

2. Let vector OA be represented by the ordered pair (1, 4). If vector is represented by (6,

-1), what ordered pair represents vector

uuuvOBuuuv

ABuuuv

? a) (7, -3) b) (5, -5) c) (5, 3) d) (5, 5)

3. A boat starts at point A and travels 15 mph in a northern direction. A wind from the west is blowing the boat eastward at 8 mph. Find the speed of the boat and the direction the boat is moving.

a) Draw a diagram to illustrate the situation. b) Explain how you determine the speed and the direction of the boat.

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Worksheet 7 1. Which of the following would NOT represent three consecutive vertices of a rectangle?

a) (2, 0), (6, 0), (6, 3) b) (0, 0), (1, 4), (5, 3) c) (0, 0), (3, 3), (2, 4) d) (0, 0), (2, 1), (2, 3)

2. The perimeter of the rectangle ABCD is 40 units and its length is 15 units. Find the number

of units in the perimeter of the square. A B

D C a) 20 b) 25 c) 40 d) 60

3. Two vertices of a rectangle are A(0, 0) and B(0, 6). The other two vertices in the first quadrant are C(k, 6) and D(k, 0). The perimeter of ABCD is 28 units. Find the value of k. Show all your work.

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Worksheet 8 1. The coordinates of the image of P(2, -3) after a reflection about the x-axis are:

a) (2, -3) b) (-2, -3) c) (2, 3) d) (-2, 3)

2. Right triangle ABC, with the right angle at vertex C, is reflected about the x-axis. Which of the following properties of triangle ABC is changed as a result of the reflection?

a) The measure of angle A. b) The orientation of the triangle. c) The length of the hypotenuse. d) The area of the triangle.

3. ABCD is a parallelogram. Segments AE and CF are each perpendicular to diagonal BD. There are three pairs of congruent triangles present in the figure.

50

A

D

B

C

E

F

a) List the three pairs of congruent triangles. b) In order to make ∆AEB similar to ∆DEA, what type of quadrilateral would ABCD have

to be?

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Worksheet 9

1. Find cos A for the given triangle.

12

13

5

B

AC

a) 0.3846 b) 0.4167 c) 0.9231 d) 2.4

2. Which of the following would NOT be sufficient information to allow you to complete the task of finding the measures of the three sides and the three angles of a right triangle?

a) The lengths of the two legs. b) The measures of the two acute angles. c) The measure of one acute angle and the length of the hypotenuse. d) The measure of one acute angle and the length of one leg.

3. A painter positions the bottom of his 40 foot ladder 3 ½ feet from the base of a building.

How high up on the building will the ladder reach? (Round your answer to the nearest tenth of a foot.) Draw a sketch. Show all your work.

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Worksheet 10

1. If the circumference of a circle is increased from 30π inches to 50π inches, by how many inches is the length of the radius increased?

a) 10 b) 10π c) 20 d) 20π

2. A garden hose lies coiled in a circular pile about 2 feet across. If there are 6 coils, estimate the length of the hose

3. A circular piece of plywood is to be decorated to form a wall hanging. Elena wants to place

lace completely around the shaded sector( ABD ) of the circle. To the nearest inch, how much lace will she need if the diameter of the plywood piece is 18 inches and the measure of the central angle ( ) is 120ACD∠ o.

120

C

D

B

A

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Worksheet 11

1. The area of a rectangle is 200 sq cm and one dimension is 15 cm. Find the length of a diagonal of the rectangle.

a) 13.3 cm b) 20.1 cm c) 28.3 cm d) 48.1 cm

2. Find the area of the rectangle if the radius of each circle is 3 cm.

a) 48 cm2 b) 72 cm2 c) 144 cm2 d) 288 cm2

3. One rectangle has an area of 48 cm2. Another rectangle has an area of 80 cm2. The dimensions of each rectangle are whole numbers. If each rectangle is to have the same length, what is the greatest possible dimension, in centimeters, the length can be? Show all of your work, and explain how you arrived at your answer.

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Worksheet 12 1. If a radius of a circle is tripled, then the area is:

a) Increased by 3 b) Multiplied by 9 c) Tripled d) Cubed

2. Which of the following has a volume different from the other three volumes? a) A cylinder with a radius of 4 cm and a height of 9 cm. b) A cylinder with a radius of 5 cm and a height of 6 cm. c) A cylinder with a radius of 2 cm and a height of 36 cm. d) A cylinder with a radius of 6 cm and a height of 4 cm.

3. Sketch the figure that the net shown folds into.

4 cm

6 cm

a) What is the solid called? b) Find its volume. Show your process c) Find its surface area. Show your process. d) Suppose the “6 cm” and “4 cm” on the figure above were switched. What change

would result in the surface area?

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69

Worksheet 13 1. The volume of a cube is 27 cubic inches. Find the surface area.

2. The bottom of a box measures 18 cm by 20 cm. The box is 10 cm high and has no top. What is the surface area of the box?

3. A rectangular solid has a surface area of 42 square units. If the dimensions are each tripled, find the new surface area. Explain your procedure and generalize the relationship between the original surface area and the surface area after the dimensions are tripled.

70

Worksheet 14 1. Each side of a regular decagon (10-sided figure) has a length of 4.25 inches. Find the

perimeter.

a) 3 ft 6.5 in b) 3 ft 8 in c) 3 ft 11 in d) 4 ft

2. An open box is made from a square piece of cardboard by cutting out a 6-inch square from each corner and turning up the sides. If the volume of the box turns out to be 150 cubic inches, what was the length of a side of the original square piece of cardboard?

3. The length of a rectangle is increased by 20% and its width is decreased by 10%. Explain how to determine what happens to the area in terms of percent increase or percent decrease. Would the new area be the same if the original length were increased 10% and the original width were decreased by 20%? Explain.

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Worksheet 15

1. The dimensions of a rectangular park are 66 yards by 88 yards. Juanita needs to walk from the southeast corner of the park to the northwest corner. How many yards longer is it to walk along the edges than to walk along the diagonal?

a) 4 b) 44 c) 54 d) 110

2. A kite string 140 m long makes an angle of 40o with the ground. Determine the height of the kite.

3. A tree on the ground casts a shadow 32 feet long. The angle of elevation from the tip of the shadow to the top of the tree is 60o. Find the height of the tree. Show your process.

Worksheet 16

1. Rectangle ABCD is similar to rectangle WXYZ, with AB corresponding to WX . If AB = 24, BC = 30, and WX = 16, what is the area of rectangle WXYZ?

a) 20 b) 204.8 c) 320 d) 720

2. Two similar triangles have a ratio of similitude of 2.35 to 1. If the area of the smaller triangle is 8.4 square centimeters, what is the area of the larger triangle?

3. A pentagon has a perimeter of 50 cm. The shortest side of the pentagon has a length of 3 cm. Find the length of the shortest side of a similar pentagon if the perimeter of the second pentagon is 80 cm.

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Worksheet 17

1. A coin-toss game at a carnival has a square board as shown. To win, the coin must land in the shaded area. What is the probability of winning the game, expressed to the nearest percent?

42cm

42cm

27c m27cm

win

2. Four roads go from town A to town B. Three roads go from town B to town C. In addition,

there are two roads that go from A to C without going through B. In how many ways can you go from A to C?

3. Mary rolled a die 600 times. The results are:

Odd 252 Even 348

Calculate the experimental probability for rolling odd as shown by results given. Determine

the theoretical probability for rolling an odd number on a die. Compare the experimental and theoretical probabilities. What could Mary have done to see if the experimental results would come closer to the theoretical results?

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74

Worksheet 18

1. For each number shown below, the units digit is hidden. Which of the following could NOT be the mean of the set?

8∆ 8∆ 7∆ 9∆ 8∆ a) 85 b) 82 c) 80 d) 71

2. The list shows the prices for several different concerts: $40 $45 $50 $58 $60 $67 $80 $90 If an additional concert price of $16 is added to the list, which measure of central tendency

(mean, median, mode) is affected the most? 3. The South Side High School annual fundraiser involved the sale of tins of cookies. The

freshman class sold 2,586 tins of cookies; the sophomore class 3,014 tins; the junior class 3,274 tins; the senior class 3,326 tins. Construct a graph to show how the classes compared in amounts of cookies sold. Explain why you selected that type of graph to represent the data.

Worksheet 19

1. How many triangles (of any size) are in the diagram below?

2. A school committee consists of the Student Council president, 5 other students, the principal, and 3 other teachers. In how many ways can a subcommittee be selected if the subcommittee is to consist of the Student Council president, the principal, and 1 other teacher from the committee?

3. A restaurant offers a soup-and-sandwich lunch. There are 3 possible soups, 3 breads possible for the sandwich, and k types of meat available for the sandwich. If the tree diagram constructed yields a total of 45 different lunches possible, find the value of k.

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Worksheet 20

1. In working with iterations, arrow notation can be used to indicate the rule. For example, x → 2x meats “to get the new value, you multiply by 2.” Which of the following iterations will produce a sequence of zeros.

a) x → -x with an initial value of –2. b) x → x with an initial value of 1. c) x → 3x with an initial value of 0. d) x → x+5 with an initial value of –5.

2. Apply the following geometric iteration rule: Start with a unit square (side length of 1 unit). Split the square horizontally into two congruent rectangles. Remove the top rectangle, leaving behind the bottom rectangle.

a) Show the first four stages of this iteration. b) What are the dimensions of the remaining rectangle in each stage? c) If we carry out the iterations indefinitely do we generate a fractal? Explain your

response.

3) Start with a 45o – 45o – 90o triangle. The iteration rule is to draw the altitude to the hypotenuse, thereby forming two isosceles right triangles.

a) Draw the next three figures based on this iteration rule. b) How many small isosceles right triangles appear in the picture after your perform the

third iteration. c) Describe the appearance of the figure resulting from more and more iterations with the

rule stated.

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OPEN ENDED QUESTIONS

1. A wheel rolls along a straight path on the floor. If the diameter of the wheel is 30 centimeters, describe the path followed by the center of the wheel as the wheel rolls along the floor.

2. Triangle ABC is isosceles with a base of 10 cm and a perimeter of 36 cm. Show how you can use the Pythagorean Relation to find the height of the triangle. Give the steps used in your thinking.

B

A C

3. The scale on a map is ½ inch = 55 miles. How far apart are two cities that are shown as being 5 inches apart on the map?

4. If BDuuur

is the angle bisection of ABC∠ and BEuuur

is the angle bisector of ABD∠ , what is if = 36m ABC∠ m DBE∠ o.

77

78


Fencing the Field The width of a rectangular field is 8 feet shorter than its length. The length is represented by “L”. A) Write an expression in terms of “L” that represents the perimeter of the rectangle. B) Given that the length of the rectangular field is 32 ft., find the perimeter of the field. How many

4 ft. sections of fence are required to enclose the field? C) If the field perimeter is 80 ft., find the area enclosed by the fence. Support your answer.

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HSPA Review Fencing the Field Solutions A) Let the length = L, and the width = L-8 Perimeter = 2L – 2(L-8) = 4L-16 B) L = 32 ft., W = 24 ft., (32-8) P = 2(32) + 2(24) = 64 + 48 = 112 ft. One needs 28 sections of 4 ft. to enclose the rectangular field (112/4 = 28) C) P = 4L – 16 Area of the Rectangle 80 = 4L – 16 A = L X W = 16 X 24 = 384 sq. ft. 96 = 4L 24 = L 16 = W

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HSPA Review Fencing the Field Assessment Rubric Points

3 Generates a practical expression to represent the given problem. Determines the number

of sections needed to enclose the field in the given situation. Clearly states and provides support statements for logical reasoning. Accurately determines the dimensions of the field with the given perimeter and states the correct area. Written and calculation support statements are evident.

2 Generates a practical expression to represent the given problem. Determines the number

of sections needed to enclose the field in the given situation, but support statements for logical reasoning are weak. Determines the dimensions of the field with the given perimeter and states an area. Written and calculation support statements are evident but weak. Any calculation errors are minor.

1 Generates a practical expression to represent the given problem. Attempts to determine

the number of sections needed to enclose the field in the given situation, but support statements for logical reasoning are weak or missing. Attempts to determine the dimensions of the field with the given perimeter. Written and calculations support statements are weak or missing or make major computational errors.


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HSPA Review Cluster: Spatial Sense & Geometry

Rearranging Rectangles On the attached page, rectangles A-D are drawn on grid paper where the side of each square on the grid has length equal to 1 unit. The measurement, in units, of the rectangles A, B, C, and D are given in the chart below. Rectangles E and F are drawn to the same scale. ( Note: You may cut out the six original rectangles to help in finding and drawing the solution.) A) Find the measurements of the rectangle E and F. Record these measurements in the

given chart. Then, write in the chart, the corresponding area and perimeter of each actual rectangle. (A-F).

Rectangle Dimensions in units Area in square units Perimeter in unitsA 3 X 17 B 7 X 9 C 5 X 13 D 4 X 12 E F B) Based on your findings, do you agree or disagree with each of the following statements?

Explain your answers by giving specific example(s) from your work in part A. i. If the area of one rectangle is greater than that of a second rectangle, then the perimeter of

the first rectangle is greater than the perimeter of the second ii. Two rectangles having the same perimeter could have different areas.

C) All six rectangles can be used to form one large rectangle having dimensions 24 units long and 16 units wide, with no overlapping pieces. Show in a drawing how the six small rectangles need to be arranged to form the large rectangle.

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HSPA Review Rearranging Rectangles B C A D E F

83

HSPA Review Rearranging Rectangles Solutions A) . Rectangle Dimensions in units Area in square units Perimeter in units

A 3 X 17 51 40 B 7 X 9 63 32 C 5 X 13 65 36 D 4 X 12 48 32 E 9 X 12 108 42 F 7 X 7 49 28

B) (1) Disagree: Area of rectangle B is 63, which is greater than the area of rectangle D that is

48, but their perimeters are equal. Or Area of rectangle D that is 49 is greater than the area of rectangle D that is 48, but the

perimeter of rectangle F that is 28 less than the perimeter of rectangle D that is 32. (2) Agree: Rectangle B and D have the same perimeter but have different areas. C) Dimensions of the large rectangle are 16 X 24. See diagram below. 9 X 7 9 X 1 2 5 X 1 3 4 X 1 2 7 X 7 3 X 1 3 HSPA Review Rearranging Rectangles Assessment Rubric Points

84

3 Student determines measurements of rectangles E & F and correctly calculates the area

and perimeter of all rectangles. Provides clear explanation and examples in support of areas and perimeter statements. Accurately creates a large rectangle from the six smaller ones. Any calculation errors are minor.

2 Student determines measurements of rectangle E & F and calculates the area and

perimeter of all rectangles. Provides some support when discussing area and perimeter statements. Attempts to create a large rectangle from the six smaller ones showing trials. Any calculations errors are minor.

1 Student determines measurements of rectangles E & F and calculates the area and

perimeter of all rectangles. Statements supporting area and perimeter explanation are incorrect. Attempts to create large rectangle are not present. Any calculation errors are minor.


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HSPA Review Cluster: Number Sense Pizza Party

The freshman class is planning a pizza party after the school play. The chairperson of the food committee decided to poll the class to find out how many large pizza combinations (with 8 slices in each large pie) should be ordered for the 240 freshmen. It is suggested that two slices be ordered for each class member. The following chart shows the types of pizza that are available.

Pizza With Pizzazz Type of Pizza Small

10” diameterMedium 12” diameter

Large 14” diameter

Plain Cheese $8.00 $9.00 $9.50 Bacon $8.60 $9.50 $10.00 Pepperoni $9.00 $9.75 $10.25 Sausage $9.25 $10.00 $10.75

*Add $.75 for each topping: Chili Pepper Green Pepper Mushrooms Onions Extra Cheese

Or

Buy 2 or moretoppings for $.50 each

Only 200 class members returned their survey forms. The results of the survey are:

• 50 plain • 80 sausage and onion • 30 bacon, onion, green pepper and extra cheese • 10 pepperoni and extra cheese • 30 no preference

A) Prepare a pizza order using the information obtained from the 200 class members who returned the survey. Explain any decisions you made along the way.

B) Members of the committee decided to include enough pizza for the 40 class members who did

not return the survey. What type and how much pizza would you order for these 40 class members? Why? Explain you reasoning.

C) Create an order for the freshman class pizza party that includes all the students.

D) What would be the total cost of the pizza for the party?

HSPA Review Pizza Party Possible Solutions A) Distribute the 30 students who had no preference to each pizza type. Answer will vary with the

distribution type selected. Pizza Order: # of people # of slices # of pies needed 60 plain X 2= 120 ÷8 = 15 pies 90 sausage X 2= 180 ÷8= 23 pies 35 bacon, etc X 2= 70 ÷8= 9 pies 15 pepperoni X 2= 30 ÷8= 4 pies 400 slices needed B) 40 students X2= 80 slices needed for the students who did not return the survey. Plain pizza

is the cheapest. Order 10 additional plain pizzas for a total of 25 plain. C) & D) Total cost: to feed 24 students, 60 pies are needed. 25 plain @$9.50= $237.50 23 sausage, etc. @$11.50= $264.50 9 bacon, etc. @$11.50= $103.50 4 pepperoni @$11.00= $ 44.00 61 pies $649.50 Other solutions are possible depending on the distribution of types of pizza selected.

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87

HSPA Review Pizza Party Assessment Rubric Points

3 Student demonstrates a clear understanding of the problem, uses appropriate processes, and provides a satisfactory response to all parts. Any flaws are minor.

4 Student answers parts A and B with minor flaws and begins to answer part C but incorrectly

calculates the price of the pizzas and based on the error completes the task. 1 Student only begins to demonstrate an understanding of the task. 0 Presents no understanding of the problem.

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Uninhibited Unicycle Floppsy, a local clown, has decided to add a unicycle act as part of her new show. There are however, two types of unicycles available for her to use: a regular unicycle and a circus unicycle. Floppsy found that the radius of a regular unicycle wheel is 18 inches whereas the circus unicycle has a diameter of 18 inches. She pedals each unicycle at a rate of 30 revolutions (spins of the wheel) per minute. Using this information, help Floppsy chooses a unicycle by answering the following questions. A) If Floppsy was to use a regular unicycle for the full length of her show, how far will she pedal in

one and a half hours? (Express your answer to the nearest tenth of a mile.) B) If Floppsy uses a circus unicycle for the full length of her show, how far will she pedal in one

and a half hours? (Express your answer to the nearest tenth of a mile.) C) How does the distance per revolution of the circus unicycle compare with that of the regular

unicycle tire? D) Describe the relationship between doubling the radius and the amount of distance traveled?

HSPA Review Uninhibited Unicycle Solutions A) Regular Unicycle r = 8 d = 16 C = 3.14(36) 113.04dπ = = inches for one revolution. 30 rev X 90 min X 113.04 in. = 305208 inches per show 305208 in. X 12 in. per foot X 5280 feet per mile = 4.817 miles per show B) Circus Unicycle d = 18 C = dπ inches for one revolution. 3.14(18) 56.52= = 30 rev X 90 min X 56.52 in. = 152604 inches per show 152604 in X 12 IN. per foot x 5280 feet per mile = 2.4 miles per show

C) circus unicycle 2.4 1= =regular unicycle 4.8 2

The circus unicycle travels half as far as the regular cycle.

D) When you double the radius, you double the circumference.

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90

HSPA Review Uninhibited Unicycle Assessment Rubric Points

3 Correctly determines the circumference of the regular and circus unicycles. Calculates the distance traveled in the given number of revolutions. Accurately discusses the relationship between radius and circumference.

2 Correctly determines the circumference of the regular and circus unicycles. Calculates

the distance traveled in the given number of revolutions. Discusses the relationship between the radius and circumference but support is weak. Any calculation errors are minor.

1 Determines the circumference of the regular and the circus unicycles. Partially calculates

the distance traveled in the given number of revolutions. Any calculation errors are minor.


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Topsoil Diego is in the landscaping business and is planning to put new topsoil on a customer’s property. The diagram on the next page gives the dimensions of the lot, the house, the front walk, and the semicircular driveway. The shaded areas represent the house, the walk, and the driveway that will not receive topsoil. The owner wants enough topsoil to cover the lot to a depth of at least 3 inches. A) Determine the area of the semi-circular driveway, the house, and the front walk between

the house and driveway. B) Determine the area of the lot to receive topsoil. C) If 27 cu. ft. = 1 cu. yd., find the number of truckloads of topsoil you need to have delivered if

one truckload contains 5 cu. yd. Of topsoil. Show how you arrived at your answer.

HSPA Review Diagram for Topsoil

80’

92

25’ 50’ 100’ 30’ 10’ 15’ 5’ 15’

10’ X 5’ 20’ 40’

HSPA Review Topsoil Solutions

A) Driveway: 2 2(20 ) (10) 471 . .

2 2sq ftπ π

− =

Walk: 5 X 10 = 50 sq. ft. House: 5 X 10 + 40 X 30 + 20 X 25 = 1750 sq. ft. B) Lot: 8000 – 471 – 50 – 1750 = 5729 sq. ft. C) Volume of topsoil = 2412 X ¼ = 1432 cu. ft. If 27 cu. ft = 1 cu. yd. You need 53.0 cu. yd. Of topsoil or 11 truckloads.

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94

HSPA Review Topsoil Assessment Rubric Points

3 Correctly finds all areas and volume of topsoil and correct number of truckloads with appropriate steps shown.

2 Correctly finds area of house, walk, lot, and driveway, subtracts appropriate areas and

multiplies result by ¼ to obtain correct volume of topsoil. OR Finds all correct areas. Student finds incorrect volume of topsoil, but determines a correct number of truckloads based on the flawed calculations.

1 Finds area of house and walkway, and lot, attempts to find the area of the driveway, but has

major flaws in computation, but appropriately subtracts areas to determine area to receive topsoil.



Sand & Salt Storage This year the State Department of Transportation is predicting a severe winter. This means that there is a need to increase the number of sand & salt storage bins across the state. Each storage bin is shaped like an inverted cone with a base diameter of 96 feet and a height of 20 feet. A) Draw a sketch to represent this problem. Label the radius and the height of the cone. B) What is the slant height (the distance from the peak to the outer edge of the base) of the

storage bin? C) How many cubic feet of the sand & salt mixture can each storage bin hold? (Use π =3.14

for calculation) D) Suppose the department of Transportation wants to save ground space by doubling the

height and cutting the diameter in half. What effect would this have on the number of cubic feet of sand & salt mixture that each storage bin can hold?

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HSPA Review Sand & Salt Storage Solutions A) D = 96, r =48 Note: Figure not drawn to scale 20’ 48’ B) 2 2 220 48 s+ = 400+2304 = 2s 22704 s= 52 = s The slant height is 52 feet

C) 213

V rπ= h

V= 21 (3.14)(48 )(20)3

V= 48,230.4 cu. ft.

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D) 213

V rπ= h 40’

V= 21 (3.14)(24 )(40)3

V= 24,115.2 cu. ft.

24,115.2 148, 230.4 2

= 24’

By doubling the height and taking half of the diameter, we cut the volume in half. OR The volume is decreased. OR The volume is decreased by approximately 24,000 cu. ft.

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HSPA Review Sand & Salt Storage Assessment Rubric Points

3 Accurately draws and labels sketch to represent this problem. Determines the slant height

of the storage bin. Determines and discusses the volume of the cones and describes the effect of doubling the height and cutting the diameter in half. Support for statement is evident. Any calculation errors are minor.

2 Draws and labels sketch to represent this problem. Attempts but incorrectly determines the

slant height of the storage bin. Determines and discusses the volume of the cones but the support is weak. Or Draws and labels a sketch to represent the problem. Correctly determines the slant height of the storage bins. Attempts, but incorrectly determines and/or discusses volume of cones.

1 Draws and labels sketch to represent this problem. Attempts but incorrectly determines the

slant height of the storage bin and volume of the cones. No discussion or volume changes.


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Compost Bin On the average, a household generates about 1650 pounds of garbage in a year. Of this, about 18% is yard waste and 8% is food waste. As a way to protect the environment, many people make compost bins in their back yards so that the food and yard garbage could be collected in a place where they can be broken down to other material to be used as fertilizer. One cubic foot of waste weighs about 2 pounds. Based on this information: A) How many cubic feet of garbage produced a year is yard waste? How many cubic feet is food

waste? B) Suppose you have a square section of your back yard measuring 8 feet on a side, which you

can use to make a compost bin. (You could use all of this space or only part of it.) The bin will be formed using 5 foot high mesh wire fencing for the sides. Is it possible to make a bin with a square base, which would fit in this space in your yard that would be large enough to hold the yard and food waste produced by your household in one year? Is it possible to do the same with a bin with a circular base? Draw diagrams and show calculations to support your answer.

C) Would the bin with the square base or the bin with the circular base hold more garbage?

Which would require more of the fencing to make the bin? Show your work to support your answers.

HSPA Review Cluster: Spatial Sense & Geometry Compost Bin Solutions A) Yard Waste: 18% of 1650 lbs. .18(1650) = 297 lbs. 297 lbs./2 lbs. per cu. ft = 148.5 cu. Ft

Food Waste: 8% of 1650 lbs. .08(1650) = 132 lbs. 132 lbs./2 lbs. per cu. ft = 66 cu. ft B) Square Bin Maximum Round Bin Maximum V = lwh V = 2r hπ V = 8 X 8 X 5 V = 3.14 X X 5 24 V = 320 cu. ft. 251.2 cu. ft. The total waste (food plus yard) equals 214.5 cubic feet of space. Therefore, both the square and round-based bins would be large enough to hold the yard and food waste produced by a household in one year. C) The square bin would hold more yard and food waste (see Section B) Square Bin Fencing Round Bin Fencing P = 4s P = dπ P = 4 X 8 P = 3.14 X 8 P = 32 feet P = 25.12 feet Thus, the square bin requires more fencing.

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100

HSPA Review Compost Bin Assessment Rubric Points

3 Determines the number of cubic feet of yard waste and the number of cubic feet of food waste generated per household per year. Sketches, labels, and determines the volume of the square and the circular based bins. Calculates the perimeter of the square and the circular bins. Provides support for determining which bin will hold more compost and which bin requires more fencing. Any calculation errors are minor.

2 Determines the number of cubic feet of yard waste and the number of cubic feet of food

waste generated per household per year. Sketches, labels, and attempts to determine the volume of the square and circular based bins. Provides some support for determining which bin will hold more compost and which bin requires more fencing. Any calculation errors are minor.

3 Attempts to determine the number of cubic feet of yard waste and the number of cubic feet of

food waste generated per household per year. Sketches but does not attempt to determine the volume of the square and/or circular based bins. Provides little or no support for determining which bin holds more compost and which bin requires more fencing. Any calculation errors are minor.


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HSPA

Packet – 3

Honors Algebra II Algebra II

Dynamics of Algebra II Algeom III

Worksheet 1

1. Which of the following cannot be the answer to a probability question?

a) 0 b) 30% c) 1110

d) 1011

2. Two events, A and B, are considered complementary if P(B) = 1 – P(A). For example in

tossing a coin, P(heads) = ½ and P(tails) = ½ , which is equal to 1 – P(heads). Which of the following would NOT represent complementary events?

8

7

6

5 4

3

21

a) Spinning an odd number on the spinner shown. Spinning an even number on the

spinner shown. b) Picking a number divisible by 3 from the set of whole numbers between 1 and 30.

Picking a number not divisible by 3 from the set of whole numbers between 1 and 30.

c) Obtaining a sum less than 7 when tossing two dice. Obtaining a sum greater than 7 when tossing two dice.

d) Picking a red card from a regular deck of cards. Picking a black card from a regular deck of cards.

3. A dice game is played by two students using a pair of dice. Player 1 gets a point if the product of the numbers rolled on the dice is even. Player 2 gets a point if the product of the numbers rolled on the dice is odd. The player with more points after 20 rounds wins. Is this game, as outlined, fair or not, Explain.

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Worksheet 2

1. Two cards are selected from a deck of cards numbered 1 through 10. Once a card is selected it is not replaced. What is P(two even numbers)?

a) 14

b) 29

c) 12

d) 1

2. Maria rolls a pair of dice. What is the probability that she obtains a sum that is either a multiple of 3 OR a multiple of 4?

a) 13

b) 29

c) 38

d) 16

3. Suppose E and F are independent events. The probability that event E will occur is .7 and

the probability that event F will occur is .6.

a) Find the probability of E and F both occurring b) Explain why the answer should be less than each of the individual probabilities. c) Suppose E and F are independent events with the probability of E being p and the

probability of F being q. If P(E and F) = .36 and P(E) ≠ P(F), find a pair of possible values for p and q.

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Worksheet 3

1. In rolling two dice, the probability of obtaining a sum of 12 (the largest possible sum) is 136

.

What is the probability of obtaining the largest possible sum when you roll five dice?

a) 536

b) 11,296

c) 1216

d) 17,776

2. A box contains 15 marbles: 6 green, 4 red, and 5 blue. Name a compound event that

would have a probability of 4 3 215 14 13

x x .

3. In a family of three children there are 8 possibilities for the boy-girl combinations, such as BBG, GBG, etc.

a) The probability of all boys equals the probability of all girls. What would each of these

be?

b) The probability of 2 boys and 1 girl is equal to 38

. Explain why it is 38

and not 18

.

c) For this family of three children, what other situation would have a probability of 38

?

d) If the family had four children how would your answer to part a change?

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Worksheet 4

1. For which table do the data NOT represent direct variation? A. X Y B. X Y C. X Y D. X Y -2 -4 0 0 0 2 0 0 -1 -2 1 10 1 3 2 .5 0 0 3 30 3 5 4 1 3 6 6 60 10 12 8 2 10 100 20 5

2. In an inverse relationship, y = kx

or xy = k. x varies inversely with y. If x = 70 when y = 8,

find x when y = 28.

3. The depth of water in a tub varies directly as the length of time the taps are on. If the taps are left on for four minutes, the depth of the water is 24 cm.

a) Find the depth of the water if the taps are left on for 5 minutes. b) Find the length of time the taps were left on if the depth of the water is 42 cm. c) Write an equation relating depth to time. d) Graph the relation between depth and time.

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Worksheet 5

1. A quality tester finds two broken bulbs in every lot of 100. Suppose the margin of error is 3%. Estimate the interval that contains the number of broken bulbs in a lot of 5,000.

2. Biologists captured 400 deer, tagged them and released them back into the same region. Later that season, the deer population was sampled to estimate the size of the population that lived in the region. If a sample of 150 deer contained 45 tagged deer, what would be a good estimate for the deer population?

3. Edgardo had the following test scores in his science class:

90 73 86 89 97 What score must he get on the sixth test in order for his average to turn out to be 89?

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Worksheet 6

1. For which of the following situations would it NOT be appropriate to use a line graph to represent the data?

a) Show the population of the U.S. from 1900 to 1990 b) Show the sale of CD’s during a five-year period c) Show survey results of how students spend one hour of their time. d) Show the heating time for water at various altitudes.

2. The line plot displays scores on an 80-point mathematics test. X X X X X X X X X X X X X X X X X X X X X X X 60 62 64 66 68 70 72 74 76 78 80 82

a) Which measure of central tendency (mean, median, or mode) is most easily observed from this line plot? Explain why.

b) What is the median test score? Explain how you find it from this line plot. c) Suppose the teacher finds six scores that need to be added to the line plot: 72,

76, 76, 78, 80, 80. (i) Does the median change? If so, what is the new median? (ii) Does the mode change? If so, what is the new mode? (iii) In a general way, how does the mean change and why? (Do not actually

calculate the mean)

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Worksheet 7

1. The numbers 1 and 10 are the first two numbers of the tenth row of Pascal’s Triangle. What is the third number in this row?

2. The traveling squad for a college basketball team consists of two centers, five forwards, and four guards. The coach is interested in determining the number of ways she can select a starting team of one center, two forwards, and two guards.

a) Find the number of ways to select one center b) In finding the number of ways to select two forwards, are permutations or

combinations used? Explain. c) Find the number of ways to select the two starting forwards. d) Find the number of ways to select the two starting guards. e) In using answers to questions a, c, and d, is the answer to the number of

possible starting teams a + c + d or a x c x d? Explain.

Worksheet 8

1. For the network below, how many of the vertices are considered to be odd?

D C

B

F

A

E

a) 0 b) 2 c) 3 d) 4

2. Which of the following networks would NOT be traversable?

a) b)

c) d)

3. Draw a sketch of a network of five towns that would not be traversable.

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Worksheet 9

1. The first three stages of a fractal are shown:

How many of the smallest circles will appear in the fourth stage? a) 4 b) 8 c) 12 d) 15

2. An iterative process is used in which each term, after the first term, is found by adding 10 to 10 times the previous term. If the first term has a value of 5, what are the next three values obtained through the iteration?

3. Use the iteration rule x → x2 (to get a new value, square the current value) to investigate what happens for two different initial values: 2 and 0.5.

a) Show the first five terms based on each initial value b) What can you conclude about the limiting values that each sequence approaches.

110

Worksheet 10

1. How many arrangements are possible of all the letters in ALGEBRA if each arrangement must begin and end with A?

a) 5! b) 6! c) 7!2

d) 7! – 2

2. Write the rule that is defined by the operation * if 4 * 2 = 12 3 * 1 = 8 10 * 9 = 19 a * b = ______

3. Suppose you were talking to a friend on the telephone. Write a list of instructions you would give your friend to duplicate the given diagram without being able to see it. Note any tools or materials you would ask your friend to use.

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112

Worksheet 11

1. Terrence decides he is going to start saving pennies in a large plastic jar he has found. On Monday, he puts 1 cent into the jar. On Tuesday, he doubles the amount to 2 cents. On each succeeding day, he doubles the number of pennies he put in the day before. How many days will it take Terrence to save at least $20?

a) 11 b) 12 c) 15 d) 26

2. Analyze the pattern: PENCILPENCILPENCIL If the pattern is continued, what letter will be in the 83rd position? a) P b) E c) I d) L

3. Jared painted a 4 x 4 x 4 cube green on all 6 faces. When the paint dried, Jared cut the cube into 64 smaller cubes (1 x 1 x 1). If Jared looked at each small cube, how many would have green paint on exactly 2 faces? In completing this problem, discuss cases involving a smaller original cube in order to show a pattern to use to answer the question.

113

Worksheet 12

1. A special sequence is formed by taking twice the sum of the two previous terms to find the third term and all the succeeding terms. If the first four terms are 1, 2, 6, 16, find the 8th term.

2. A small business has sales of $50,000 during its first year of operation. If the sales increase 6,000 per year, what is its total sales in its eleventh year? Show your process.

3. A machine’s value depreciates annually at a rate of 30% the value it had at the beginning of that year. If its initial value is $10,000, find its value at the end of the eighth year. Show your process.

Worksheet 13

1. If f(x) = 2x, what is the value of f(10) – f(6)? a) 4 b) 64 c) 512 d) 960

2. If f(x) = 4x − , find the value of f(8) – f(-8). a) –8 b) –4 c) 0 d) 4

3. Consider the exponential functions y = 4x and y = 5x.

a) The graphs of these functions intersect at exactly one point. What are the coordinates of that point?

b) In the first quadrant, which graph is closer to the y-axis? Explain or show an illustration.

c) Explain what happens to the graphs as they cross the axis and enter the second quadrant.

d) Explain why these graphs do not dross into quadrant III or IV.

114

Worksheet 14

1. If y varies inversely with x (y = kx

or xy = k), what is the missing value in the table?

X Y 1 36 a) 16 2 18 b) 15.5 2.5 ? c)15 3 12 d) 14.4 4 9 2. A number cube has the following faces: 2, 3, 3, 4, 4, 4. Complete the table to show the

discrete probabilities for the outcomes of rolling the number cube. Outcome 2 3 4 Probabilities

3. An office supply store surveyed a group of 200 students to determine their preference for backpack colors. Backpacks come in green, black, blue, and red. Based on the survey results the store will determine the color distribution for it’s order of 1,000 backpacks. If 75 chose black, 25 chose red, 40 chose green, and the rest chose blue, how many green backpacks will they order.

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Worksheet 15

1. Find the equation of the line containing the points (-1, -3) and (0, 5).

a) y = 8x b) y = -8x + 5 c) y = 8x + 5 d) y = 18

+ 5

2. Which of the following diagrams suggests the existence of a function?

i ii

3 9 6 10 4 16 7 10 5 25 8 10 iii 8 3 0 -8 a) i only b) i and ii c) iii only d) i and iii 3. The table below shows the number of degrees in the sum of the measures of the interior

angles of a convex polygon with n sides. N 3 4 5 6 S 180 360 540 720

a. Write the formula to summarize the relationship shown. b. Explain why this is a function. c. Explain why this is a linear function as opposed to some other type of function such as

quadratic or exponential.

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Prom Expenses Hasson is making plans to attend his high school senior prom. He promised his parents that he would pay all the expenses. As part of his planning, he made a list of all the prom expenses. He has a part-time job at a supermarket where he works 20 hours a week for $5.20 an hour. Taxes and deductions (social security, federal and state taxes) are 12% of his salary. Since the prom is scheduled for the first week in June, he decided to save 60% of his weekly take home pay in order to insure that he has enough money to cover the expenses. The following table lists the expenses. Corsage $8 - $25 Tuxedo $80 - $125 Barber Shop $7 - $20 Boutonniere $3 - $8 Prom Bid $100 per couple Limousine $350 - $500 Pictures $35 - $45 Miscellaneous $50 A) Using the expense amounts listed, what is the least amount Hasson should plan on spending?

What is the greatest amount Hasson should plan on spending? Show your calculations. B) How many weeks salary should Hasson save to cover his expenses? Show your calculations. C) When would be a reasonable time for Hasson to begin his savings plan? Justify your answer.

HSPA Review Cluster: Number Sense Prom Expenses Solutions A) Least Amount Greatest Amount $8 $25 $80 $125 $7 $20 $3 $8 $100 $100 $350 $500 $35 $45 $50 $50 $633 $873 B) 20 hours X $5.20 = $104 (weekly salary)

$104 X .12 = $12.48 (deductions) $104 – 12.48 = $91.52 (take home pay) $91.52 X .60 = $54.91 (amount of weekly savings toward prom) $633 ÷ $54.91 11.5 = 12 weeks ≈ $873 ÷ $54.91 15.9 = 16 weeks ≈

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119

HSPA Review Prom Expenses Assessment Rubrics Points

3 Demonstrates a clear understanding of the problem, uses appropriate processes, and

provides a satisfactory response to all parts. 2 Demonstrates an understanding of how to estimate expenses and find the number of

week’s salary needed to cover his expenses. Uses appropriate processes with minor flaws. Indicates a reasonable time for Hasson to begin saving, with no explanation.

1 Only begins to demonstrate how to estimate expenses. Uses processes that are unclear or

have minor flaws. 0 Presents no understanding of the problem.

120


Logo Letters The Lancaster Hotel is designing a new logo for a billboard. It will include large sized letters “L” and “H”. The graphic artist used the rectangular coordinate system to make a scale drawing of the letters. He then made a list of the coordinates to draw the letter “L” – (0,0); (8,0); (8,2); (2,2); (2,14); and (0,4). He also gave some of the coordinates for the letter “H” – (12,8); (12,14); (10,14)); (10,0); (12,0); (12,6); and (16,6) but he did not write all of them because he knew the letter “H” had both horizontal and vertical lines of symmetry, and the remaining coordinates could easily be found. A) On the graph paper provided, make a set of coordinate axes and plot the points to form the

scale drawings of both letters. B) Label the remaining coordinates of the vertices of the letter “H”. C) If each block on the graph paper represents one square foot on the billboard, how many

feet high and how many feet wide will the actual letters be? D) What will be the area of each letter on the billboard?

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HSPA Review Logo Letters Solutions A) and B) C) “L” = 14 ft. high and 8 ft. wide “H” = 14 ft. high and 8 ft. wide D) The area for “L” is: 12 X 2 = 24 and 2 X8 =16, 28 + 12 = 40 sq. ft.

or (14X2)+(6X2) = 28 + 12 = 40 sq. ft. or I counted the blocks =40

The area for “H” is 14 X 2 = 28 14 X 2= 28 4 X 2 = 8 64 sq. ft.

122

HSPA Review Logo Letters Assessment Rubric Points

3 Accurately plots the coordinates to form both letters on the graph. Clearly and accurately labels the remaining coordinates of letter H. Determines actual length, width of each letter. Accurately calculates the area of each letter and provides support to justify statements.

3 Accurately plots the coordinates to form both letters on the graph. Labels the remaining

coordinates of letter H. Determines actual length, and width of each letter. Calculates the area of each letter, but the support to justify answer is weak.

1 Plots the coordinates to form both letters on the graph. Labels the remaining coordinates

of letter H; minor flaws may be present. Attempts to determine length, and width of each letter; calculation flaws are minor. Attempts to calculate the area of each letter, but support is weak or missing.



Triangular Numbers Consecutive integers can be arranged in a triangular pattern as shown: Row 1 1 Row 2 2 3 Row 3 4 5 6 Row 4 7 8 9 10 Row 5 11 12 13 14 15 The rows can be extended down indefinitely. A) Complete the next two horizontal rows. How many numbers are entered across Row 1?

Across Row 2? Row 3? How many numbers will be in Row 250? Explain how you know. B) Describe the pattern of the diagonal numbers down the extreme left (1,2,4,7…). Write the

pattern of the diagonal numbers down the extreme right, and describe it. Provide the two numbers that would be next in each pattern and clearly label which pattern they belong to. Explain how the two patterns are alike and how they are different. Circle another pattern in the triangular arrangement given above. Describe the pattern in detail.

C) If n represents the number of a row, which of the following expressions could be used to find

the numbers beginning at the left of each row.

2n - 1 2

3n n+ 2 2n n− +1

2 22

n n− + 2 12

n +

D) Show that the expression you chose does in fact give you the correct beginning number for

Row 3 when you substitute. Show it for Row 4. Show it for Row 5.

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HSPA Review Triangular Numbers Solutions A) Row 6 16 17 18 19 20 21

Row 7 22 23 24 25 26 27 28

Row 1 contains 1 number, Row 2 has 2 numbers, Row 3 has 3 numbers. Row 250 will have 250 numbers, because the pattern is that the row number equals how many numbers are in that row.

B) Accept any reasonable explanation. For the pattern at the left: 1,2,4,7,…Each number is

obtained by adding 1 more than the previous number added. So we add a 1 to get 2, then we add a 2 to get the 4, then a 3 to get a 5, and so on.

Diagonal at left: 11,16,… Diagonal at right: 21,28,…

Accept any reasonable explanation. The two patterns are alike because of what is added each time: 1 more than what is added to the previous term. They are different because each starts with a different number; the diagonal at the left has a beginning term of 1 less than the diagonal at the right.

Accept any circled pattern and reasonable explanation.

C) The correct answer is the one in the fourth position 2 2

2n n− +

D) Row 3 n = 3 23 3 2 4

2− +

=

Row 4 n = 4 24 4 2 7

2− +

=

Row 5 n = 5 25 5 2 11

2− +

=

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HSPA Review Triangular Numbers Assessment Rubric Points

3 Accurately completes Rows 6 & 7 of the pattern chart. Uses generated data when explaining how to determine future rows of the pattern chart. Accurately determines future table values by applying patterns to making predictions. Comparison of triangular arrangement patterns is clear and support for logical explanations is evident. Chooses a formula to represent data. Any calculation errors are minor.

2 Accurately completes Rows 6 & 7 of the pattern chart. Attempts to compare and discuss

triangular arrangement patterns but support for logical explanations is weak. Chooses a formula to represent data. Accurately determines future pattern chart values based on patterns. Any calculation errors are minor.

1 Accurately completes Rows 6 & 7 of the pattern chart. Uses method(s) other than

patterning to determine future stages of the pattern chart. Attempts to chose a formula to represent data. Support for logical explanations is missing. Any calculation errors are minor.


126


Saving for a New Stereo System Sita and Lodanna each plan to buy a new technology laser model stereo on December 31, 2002. At that time, the new model stereo will cost $1200. On December 31, 1998 each of them opened a $500 savings account, which pays 10% simple interest per year. They also have separate accounts at their bank worth $500 each at maturity on December 30, 2002. Because of all their other income from part-time and summer jobs would be for college and living expenses, the savings account would be used for the new technology laser stereo. They would like you to help them decide if they will each be able to buy a new stereo at that time.

A) How much money will each have in their savings account by December 31, 2002 if no other deposits are made?

B) Will Sita and Lodanna each be able to purchase their own new stereo by the end of the year

2002? Explain your answer and show your calculations.

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HSPA Review Saving for a New Stereo System Solutions A) Savings account in the year 2000

1999 - $500 + 500 X 10% = $550 2000 - $550 + 550 X 10% = $605 2001 - $605 + 605 X 10% = $665.50 2002 - $665.50 + 665.50 X 10% = $732.05

B) Yes, since the savings account ($732.05) plus the certificate of deposit ($500) equals $1232.05 and the new stereo cost $1200. They would have $32.50 left.

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HSPA Review Saving for a New Stereo Assessment Rubric Points

3 Correctly calculates the amount of money they will each have in their savings account and

concludes that they will have enough money to purchase the stereo. Explanations are clear.

2 Calculates the amount of money they will each have in their savings account and

concludes that they will have enough money to purchase the stereo. Explanations are somewhat clear. Any calculation errors are minor.

1 Calculates the amount of money they will each have in their savings account using

incorrect procedures. Explanations may be missing or unclear. Calculations contain some errors.


129


Cake Cutting The Kitchen Capers cooking school teaches its students a technique for packaging, cutting, and serving a two tiered circular layer cake. The two tiers of the cake have heights of 4 in. each, and diameters of 10 in. and 16 in. respectively. A) Allowing one inch of extra space around the top and the sides of the cake, what would be

the dimensions of the smallest rectangular box that could be used in order to package the cake?

B) In order to cut and serve the cake, the top layer and circle directly under it are each cut into

8 equal pieces, and the exterior ring of the 16 in. bottom layer, is cut into 12 equal pieces. Which piece of cake would be bigger: a piece of the top layer or a piece of the bottom outside section? Explain your answer.

HSPA Review Cluster: Spatial Sense & Geometry Cake Cutting Sample Solutions A. Box Dimensions: 9 in. high, 18in. long, 18 in. wide B. Volume of the top layer: 2 (25)(4) 100r hπ π= = π or 314 cu. in

Volume of one piece= 100 12.58π π= or 39.25 cu. in.

Volume of the bottom layer= (64)(4) 256π π= or 803.84 cu. in. Volume of the bottom ring= 256 100 156π π π− = or 489.84 cu. in. One piece of the bottom ring= 156 12 13π π÷ = or 40.82 cu. in. The bottom piece is bigger

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131

HSPA Review Cake Cutting Assessment Rubric: Points

4 Correctly determines the dimensions of the cake box. Calculates the volume of the top and bottom layers and pieces. States the bottom piece is bigger. Any calculation errors are minor.

2 Correctly determines the dimensions of the cake box. Calculates the volume of the top and

bottom layers. Attempts to calculate the volume of top and or bottom pieces. States that the bottom is bigger. Any calculation errors are minor.

1 Correctly determines the dimensions of the cake box. Attempts to calculate the volume or

the top and bottom layers and pieces. Does not state which piece is bigger. Provides little or no support for solution. Any calculation errors are minor.

2 Present no understanding of the problem.


Crazy Crystals Pictured below are the stages of a geometric fractal. They were generated by a computer to simulate the growth of a particular crystal which starts as a single strand at Stage 1. During Stage 2, which lasts one second, it grows two new branches at each end with each of these two new branches being half the length of the original strand. During the next second, every branch again grows two new branches half the length of the previous new branches as shown in Stage 3. ___________ ___________ __________ Stage 1 Stage 2 Stage 3

A) Draw the crystal as it would appear at the end of the fourth second (Stage 4) and the fifth second (Stage 5).

B) Complete the table that shows each stage starting with Stage 1, then 2, 3, 4, and 5 and

pairs it with the number of new tips for each stage.

Stage Number

1 2 3 4 5

New Tip Number

1 4

Study this pattern, calculate and explain how you could determine how many new tips there are for Stage 6? Stage 10? C) If the original crystal was 4 inches long, what is the length of each new tip of the crystal at the

end of Stage 2, Stage 3, Stage 4, Stage 5, and Stage 6? Organize your information in a chart or table.

D) If the length of the original crystal is 4 inches, what is the total length of the new tips grown on

each crystal at each stage?

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HSPA Review Crazy Crystals Solutions A) Drawings may vary. Stage 4 Stage 5 B)

133

Stage Number

1 2 3 4 5

New Tip Number

1 4 8 16 32

Answers may vary. Some students might realize that the answers are powers of 2 or . Others may use their calculators to multiply by two the correct number of times. Stage 6 has or 64 new tips. Stage 10 has or 1024 new tips.

2n

62102

C) Stage Number

2 3 4 5 6

New Tip Number

2 1 1/2 1/4 1/8

Each new tip length is half of the one before it. D) The total length of only the new tips at every stage is 8. This is true because while the length is cut in half every time, there are always twice as many new tips, and so their total never changes.

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135

HSPA Review Crazy Crystals Assessment Rubric Points

3 Accurately draws Stage 4 and 5 of crystal growth. Completes tables and applies patterns

to making predictions. Uses base two and/or generated data when explaining how to determine future stages of crystal growth. Support for summary explanation is evident. Any errors are minor.

2 Accurately draws Stage 4 and 5 of crystal growth. Completes tables and attempts to apply

patterns to making predictions. Provides some explanation for how to determine future stages of crystal growth. Summary explanation is attempted but support is weak.


136


Counting Numbers The counting numbers can be arranged in a table like the one given below. Column

A Column

B Column

C Column

D Column

E Row1 1 2 3 4 5 Row 2 6 7 8 9 10 Row 3 11 12 13 14 15 Row 4 Row 5

A) Complete the 4th and 5th rows in the table. Use the numbers in the right hand Column marked

E, and compare each of the number of the row where they are located. Write a formula to describe the relationship between the row number, and the number written in Column E. Let n represent the number of the row.

B) What number will be in Column E in the 10th row? Use this result to write all the numbers in

Row 10. What numbers are in Row 100? C) In which Row will the number 1001 be found? D) In which Column will the number 1001 be found? Explain your reasoning. In which Column

will the number 7,468 be found?

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HSPA Review Counting Numbers Solutions A) Row 4 16 17 18 19 20 Row 5 21 22 23 24 25 The formula would E = 5n B) The number in Column E in the 10th row would be 50, since E=5 X 10=50. Row 10 46 47 48 49 50 Row 100 496 497 498 499 500 C) The number 1001 will be found in Row 201. This is because 1000 would be in Column E in

the 200th Row (since it is a multiple of 5 and since 1000/5 =200) and 1001 is the very next number in the next row, 201.

D) The number 1001 will be in Column A since it is the first number after 1000 and therefore will

begin the next row after 200.

The number 7,468 will be found in Column C since it is 3 more than the multiple of 5 (7,465) which is in E.

138

HSPA Review Counting Numbers Assessment Rubric Points

3 Accurately completes Rows 4 & 5 of the table. Writes a formula to represent data. Applies patterns to making predictions. Uses generated data when explaining how to determine future stages of the table and accurately determines future table values. Support for logical explanations is evident.

2 Accurately completes Rows 4 & 5 of the table. Attempts to write a formula to represent the

data. Applies patterns to make predictions. Accurately determines future table values based on patterns. Support for logical explanations is evident but weak. Any calculation errors are minor.


139


Letter Frequency Use the given paragraph of the attached story “The Ring” and the two paragraphs of the short story “Chocolate” to answer the following questions.

The Ring (335 letters) On a summer morning a hundred and fifty years ago a young Danish squire and his wife went out for a walk on their land. They had been married a week. It had not been easy for them to get married, for the wife’s family was higher in rank and wealthier than the husband’s. But the two young people, now twenty-four and nineteen years old, had been set on their purpose for ten years; in the end her haughty parents had to give in to them.

Chocolate (200 letters) Chocolate is one of the world’s favorite foods. Very few people detest it. About 70 percent of today’s candy bars are chocolate covered. Many candies and candy bars are all chocolate. Chocolate comes from cocoa beans, which come from the cocoa tree. At the chocolate factory, the beans are cleaned and roasted. The roasting brings out the flavor and special smell of chocolate. A) Record the frequency for each of the letters e, c, and I in the first paragraph of the story

“The Ring” in the frequency column of Chart A provided. (Note: e’s frequency is given in the chart.

B) The first paragraph of “The Ring” has a total of 335 letters. Determine the experimental probabilities of each letter occurring e, c, and I and record your answer also in Chart A.

C) The short story “Chocolate” has a total of 200 letters. Assume the probabilities of each letter occurring in this story are the same as those in “The Ring”. Find the number of e’s, c’s and i’s that you would expect to occur in “Chocolate”.

D) Create a chart or table to compare the expected or predicted number of the letters e, c and I in “Chocolate” found in part C, with the actual frequency found by counting them in the story. Compare your findings and explain possible reasons for the results obtained.

Chart A Letter Frequency Experimental Probability e 45 c i

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HSPA Review Letter Frequency Solutions A) & B) Note: A student miscount of the frequencies should be considered minor without any loss of

points in scoring.

Chart A Letter Frequency Experimental Probability e 45 45/335=9/67=.1345 c 0 0/335=0 i 20 20/335=4/67=.0597

C) & D)

Chart A Letter Predicted Frequency Actual Frequency e 27 34 c 0 25 i 12 9

C) e: 45/335 X 200 = 27; i: 20/335 X 200 = 9; c: 0/335 X 200 = 0 D) The experimental probabilities are not very accurate because the sample size is small only 335

letters were used to determine the probability. Accept other reasonable explanations for the lack of accuracy.

141

HSPA Review Letter Frequency Assessment Rubric Points

4 Accurately completes frequency and experimental probability in chart. Accurately predicts frequency and calculates actual frequency for new paragraph. Gives clear explanation of reason for similarities and/or discrepancies in experimental and actual frequency results. Written and calculation support statements are evident. Any calculation/counting errors are minor.

2 Accurately completes frequency and experimental probability in chart. Accurately predicts

frequency and calculates actual frequency for new paragraph. Attempts to give explanation of reason for similarities and/or discrepancies in experimental and actual frequency results. Written and calculation support statements are weak. Any calculation/counting errors are minor.


HSPA –Packet 1 Solutions

Worksheet 1

1. B 2. C 3. Either 7 17( ) 7(.125) .8758 8= = =

OR

1- 1 78 8= , 1-.125=. 875

Worksheet 2

1. D 2. B 3. 6,10,15 4. Contradict Jack’s answer. Arguments may vary. Ex: factors of 48 are 1,2,3,4,6,8,12,16,24,48 factors of 49 are 1,7,49

Worksheet 3 1. D 2. C 3. A salary of $504.50 per week is the answer based on a 40- hour week. Students may state valid reasons to the contrary mentioning possible overtime for example. Worksheet 4 1. C 2. D 3. Either $12,500 X .05 = $625, 12,500 x .07 = $875, $875-$625=$250. OR 7%-5%=2%, 12,500 X .02=$250 Worksheet 5 1. Irrational number 2. 16 + 7 = 23

3. a. 159 .3975400

=

b. 3 .3758=

c. Answers will vary Worksheet 6 1. A 2. C 3. 1 2(.80) 1.6,H = = 2 1.6(.80) 1.28H = = 3. after 10 bounces

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Worksheet 7 1. C 2. (22,8) 3. B Worksheet 8

1. B 2. C 3. 75 1 1,000 75000 12501 60min 1 60min min

km Hour m m mHour km

• • = =

Worksheet 9

1. C 2. B 3. 09 (20) 32 685

F = + =

Worksheet 10 1. B 2. C 3. 90’ Let y=distance from y pitcher’s mound x to second base

66’6’’

Let x=distance from home plate to

second base 902 2 290 x+ = 8100 + 8100 = 2x 16200= 2x y+66.6=127.27 16200 127.27x= ≈ y=60.77 feet Worksheet 11 1. D 2. C 3. a. 46-18=28/14=2 2 more seats are in row n+1 than row n.

b. (18 46)15 4802

seats+=

Worksheet 12

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1. A 2. A 3. a. 36 37 52%50 51

• ≈ b. 14 15 8%50 51

• ≈ c. 36 14 20%50 51

• ≈

Worksheet 13 1. D 2. C 3. a. b. 610 1,000,000= 3 326 10 17,576,000= c. 710 10,000,000= No, there are more possibilities using a combination of letters and digits. Worksheet 14

1. B 2. D 3. 9453340 94,000,000

x= x 27million≈

Worksheet 15

1. C 2. B 3. 50(2.5) 3.125 3 7.5min40

hours hours utes= =

Worksheet 16 1. A 2. C 3. Since there is the same number of students in both Algebra classes the average of the combined classes is the same as the average of the averages. In geometry, since there are a different number of students in each class you will get the wrong answer. The correct answer is 83. Worksheet 17 1. C 2. 0 0 3. Matinee: 50(495) + 45(276) + 30(117) = 40680

0 0 0 0 Evenings: 50(546) + 45(298) + 30(132) = 44670 0 0 The theater made $3990 more during the 2 evening performances.

Worksheet 18 1. 9 2. $241 3. Let n=number of odd numbers the sum of the first n odd numbers nS =

144

1

2

3

42

250

14916

50 2500n

SSSS

S n

S

====

=

= = Worksheet 19 1. A 2. C 3. C 4. Disagree, a 4X4 checkerboard has 16-2X1 squares, 9-2X2 squares, 4-3X3 squares and 1-4X4 squares. Total of 30 Worksheet 20 1. B 2. Total cost = $1.75 + 12(.15) = $3.55 3. a. t 1 2 3 4 5 6 C 1.75 3 4.25 5.50 6.75 8 b. C = 1.75 +1.25(t-1) = 1.25t +.5

c. check student’s graph

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HSPA – Packet 2 Solutions WORKSHEET 1:

1. a 2. a 3. answers will vary

WORKSHEET 2:

1. A

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°2. C 3. 144m ABC∠ =

WORKSHEET 3:

1. largest share = $90 2. a 3. a) Possible Lengths: 1, 2, 3, 8, 10, 12

Not-possible Lengths: 18, 20, 30 b) 16 cm

c) answers will vary, the only obtuse triangle will have side lengths of 8, 8, and 12. WORKSHEET 4:

1. d 2. a 3. 2 are other quadrilaterals.

WORKSHEET 5:

1. A 2. C 3. 30 feet of net

WORKSHEET 6:

1. A 2. B 3. a) answers will vary

b) By the Pythagorean Theorem, the boat is traveling 17 mph in the direction of 28.07o from North. Use inverse trigonometry to find the direction.

WORKSHEET 7: 1. D 2. A 3. k = 8

WORKSHEET 8:

1. C 2. B

3. a) ADB CBDAED CFBAEB CFD

≅≅≅

b) Rectangle. WORKSHEET 9:

1. C 2. B 3. 39.8 feet

WORKSHEET 10:

1. A 2. C = 38 feet 3. 38 inches

WORKSHEET 11:

1. B 2. D 3. 16, we want the largest factor that goes into both 80 and 48, multiples of 48 are 1 x 48,

2 x 24, 3 x 16, etc. 48 and 24 are not factors of 80. But 16 is a factor of 80. WORKSHEET 12:

1. B 2. B 3. a) cylinder

b) 301.6 cm3

c) 251.3 cm2

d) 377.0 cm 2 WORKSHEET 13:

1. 54 in2 2. 1120 cm2 3. 378 units2. if the dimensions of the box are l, w, and h, then surface area = 2lw + 2wh +

2lh, if each of the l, w, and h are tripled, then the surface area becomes 2(3l)(3w) +

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2(3w)(3h) + 2(3l)(3h) or 9(2lw) + 9(2wh) + 9(2lh), or 9(2lw + 2wh + 2lh). Since the surface area formula is multiplied by 9, we must multiply the original surface area of 42 by 9 to get 378.

WORKSHEET 14:

1. A 2. 17 in 3. If length increased 20%, the new length would be 1.2l, and width decreased by 10%,

the new width would by .9w. Area = 1.08lw. If the length increased by 10% (1.1l) and the width decreased by 20% (.8w), making the area .88lw.

WORKSHEET 15:

1. B 2. 89.99 m 3. 55.42 ft

WORKSHEET 16:

1. C 2. 46,389 cm2 3. 4.8 cm

WORKSHEET 17:

1. 41% 2. 14 3. Exponential Probability = .42, Theoretical Probability = .5 Mary needs to roll die more

times to get experimental probability be closer to the theoretical probability. WORKSHEET 18:

1. D 2. mean 3. explanations will vary

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WORKSHEET 19: 1. 9 Triangles 2. 3 ways 3. k = 5

WORKSHEET 20:

1. C 2. a) check students drawings

b) 1x1, ½ x1, ¼ x1, 1/8 x 1 c) No, we never have similar figures because the width is staying the same.

OPEN-ENDED QUESTIONS:

1. The center follows the path of a line, 15 cm above the floor 2. h = 12 cm 3. 550 miles 4. 40o

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HSPA – Packet 3 Solutions WORKSHEET 1:

1. C 2. C 3. No, even x even = even, even x odd = even, odd x odd = odd

WORKSHEET 2:

1. B 2. A 3. a) .42

b) Multiplying a number by less than 1 reduces the number. c) Answers will vary, P(E and F) = pq = .36, p = .4 and q = .9

WORKSHEET 3:

1. D 2. A marble is removed and not replaced. P(red, red, red) 3. a) 1/8

b) It depends on when the girl was born, BBG, BGB, OR GBB. c) 2 girls and 1 boy d) The fourth child could be either a boy or a girl, so there are two times as many

possibilities as before. 16 possibilities. WORKSHEET 4:

1. C 2. x = 20 3. a) 30 cm

b) 7 min c) 6t d) check students graph

WORKSHEET 5:

1. 0 – 250 broken bulbs 2. 1,333 deer 3. 99

WORKSHEET 6: 1. C 2. a) mode – most x’s, highest

b) median is 70 – see student’s explanation d) i) yes, 72 ii) no

iii) mean increases since more high scores were added WORKSHEET 7:

1. 45 2. a) 2 ways

b) Combination, order does not matter. c) 20 d) 12 e) a x c x d, counting principle

WORKSHEET 8:

1. B 2. A 3. answers will vary

WORKSHEET 9:

1. B 2. 5, 60, 610, 6110 3. a) 2: 2, 4, 16, 256, 65536

.5: 1 1 1 1 1, , , ,2 4 16 256 65536

b) 2: approaches infinity .5: approaches 0, never turns negative.

WORKSHEET 10:

1. A 2. a2 – b2 3. answers will vary

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WORKSHEET 11: 1. A 2. C 3. 24, in a 3x3 box the middle piece on each edge is green on only 2 sides. Since there

are 12 edges, there are 12 cubes that are green on only 2 sides. In a 4x4 box there are 2 pieces on each edge.

WORKSHEET 12:

1. 896 2. 110,000 3. 576.48

WORKSHEET 13:

1. D 2. A 3. a) (0, 1)

b) y = 5x, the larger the a, a the narrower the graph. c) graphs approach x-axis d) y-values never become negative

WORKSHEET 14:

1. D 2. 1/6, 1/3, ½ 3. 200 green

WORKSHEET 15:

1. C 2. B 3. a) S = 180(n-2)

b) Each n has one and only on S. c) Linear because the variable is to the first power.

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HSPA Fall 2001 Sample Test Form Test Booklet This document is available on the district server. This is a PDF file. Open using Adobe Acrobat Reader.

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See also HSPA March 2004 Student Preparation Booklet which can be found on the district server or at: http://www.nj.gov/njded/stass/assessment/hspa_prep.pdf

http://www.nj.gov/njded/stass/assessment/hspa_prep.pdf

HSPA Review - Wikispaces · PDF fileMonroe Township High School HSPA Review * For adoption by...

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