New Jersey

MARCH 2004HIGH SCHOOL

PROFICIENCY ASSESSMENT

STUDENT PREPARATIONBOOKLET

Copyright 2004 by New Jersey Department of EducationAll rights reserved.

PTM 1503.93

ISD4083

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STUDENT PREPARATION BOOKLET

WHAT IS THE HIGH SCHOOL PROFICIENCY ASSESSMENT?

In March 2004, all students who entered the eleventh grade for the first time ON or AFTERSeptember 1, 2001, will take the High School Proficiency Assessment (HSPA). The HSPA willmeasure your knowledge and skills in the Core Curriculum Content Standards, which aredesigned to make sure that you have the skills you will need to be a productive citizen and tosucceed on the job, in college, or in the military. You will have to pass the HSPA to graduatefrom high school. If you do not pass the HSPA in March of your junior year, you will have theopportunity to take the HSPA again in October and March of your senior year. In addition, youwill begin a Special Review Assessment for the HSPA in the fall of your senior year. The HSPASRA is an alternative assessment that will enable you to show whether or not you have masteredthe same knowledge and skills assessed by the HSPA.

The HSPA currently has two test sections, Language Arts Literacy and Mathematics. You willtake the test over a three-day period for approximately two hours each day. Mathematics will betested on Tuesday, March 2 and Language Arts Literacy will be tested on Wednesday andThursday, March 3 and 4.

HOW WILL MY SCORES BE REPORTED?

When you receive your HSPA scores, the report will show total scores in Language Arts Literacyand Mathematics. It will also show subtotal scores for the specific knowledge and skillsmeasured in each content area. The total scores will be reported in one of three proficiency levels– Advanced Proficient, Proficient, or Partially Proficient. If you have not met the appropriatelevel of proficiency, your school may give you additional help to develop the skills you will needto pass the HSPA in the fall or spring of the twelfth grade.

WHAT WILL THE TEST BE LIKE?

Like other tests you may have taken, the HSPA contains multiple-choice questions that requireyou to choose your response from among four answer choices (A, B, C, or D) and record it bydarkening the appropriate choice in your answer folder. The test also contains open-endedquestions that require you either to respond in your own words in written text, to draw a diagram,or to construct a numerical response.

Your responses to all multiple-choice and open-ended questions must be recorded in a separateanswer folder. Information recorded in your test booklet or on scratch paper does not counttoward your score.

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Language Arts Literacy

The Language Arts Literacy Section of the test includes reading and writing activities that willmeasure your achievements in interpreting, analyzing, and critiquing text. The reading materialswill require you to read passages selected from published books, newspapers, and magazines,and to respond to related multiple-choice and open-ended questions.

In addition, you will write two extended responses. One will be based on a picture prompt; andthe second will be based on a persuasive prompt.

Mathematics

The Mathematics Section of the test will measure your ability to solve problems by applyingmathematical concepts. The areas to be tested are: number sense, concepts, and applications;spatial sense and geometry; data analysis, probability, statistics, and discrete mathematics; andpatterns, functions, and algebra.

Most mathematics questions are multiple choice, which have a weight of one point each forcorrect answer choices. The open-ended questions, requiring you to construct and explain yourown written or graphic responses, receive a score from 0 to 3. For 3 points, a response mustshow complete understanding of a problem’s concepts and have a clear, effective explanation.For 2 points, there must be a nearly complete understanding of a problem’s concepts, but theresponse may have minor errors. A 1-point response shows limited understanding of amathematical concept and has an incomplete explanation of how the problem was solved. A 0-point response shows insufficient understanding of the concept and may contain major errors.

You will be provided with a calculator when you take the test, and will receive a MathematicsReference Sheet that contains formulas and other useful information you can use during the test.

HOW CAN I PREPARE MYSELF TO TAKE THE HSPA?

• Relax. You will think more clearly if you are relaxed when you take a test. Dresscomfortably on the day of the test so that you are at ease and not distracted. Put all your otheractivities on hold so that you can give all your attention and energy to taking the test anddoing well.

• Get a good night’s sleep the night before the test. Start your day off with a good breakfast sothat you have plenty of energy to take the test.

• Don’t cram. The skills measured by the HSPA are learned over a long period of time.

• Think positively. Believe that you will do your very best. Be confident of your ability.

• Read the directions carefully before beginning each part of the test. If you understand whatyou are supposed to do, it will save time and help you avoid careless mistakes.

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• Read each question carefully. Try to answer the question before you look at the responses. Ifyou find your answer there, mark that response. If not, ask yourself whether your answer isreasonable. Reread the question, keeping the responses in mind. Make sure that youunderstand what the question is asking.

• Make sure that your answers are reasonable. Do you understand what the question is asking?Have you made use of all the relevant information provided to answer the question correctly?Does your response answer the question? Did you choose the best answer among thoselisted?

• If you aren’t sure of the answer to a question, try to eliminate some of the responses. Thinkabout the reasons why you were able to eliminate some of the choices. These reasons mayprovide you with the information you need to choose the correct answer. If you can eliminatesome of the choices, select the remaining answer choice that makes the most sense.

• Skip a question and go on to the next one if you have no idea of the answer. Spending toomuch time on one question might keep you from having enough time to answer others thatyou do know. You should not leave any question unanswered. If there is time, you shouldcome back to it later at the end of that part of the test.

• Pace yourself during the test. Budget your time so that you have a chance to answer all of thequestions. Your teacher will periodically let you know the time remaining in the part of thetest you are taking.

• Fill in your separate answer folder carefully. Make sure that you record all your responses inyour separate answer folder in the right spaces. You may know the answer to a question, butif you do not mark your answer in the right place, you will not receive credit for your answer.

• Check your answers as you take the test. Make sure that you have chosen the response thatbest answers the question. Checking your answers as you work through the test will savetime later in rethinking a question. Check your answer folder to make sure that you havedarkened the correct answer space.

• Some questions require more planning than others. This is especially true of open-endedquestions and writing tasks. First, outline the steps required to respond to the question. Then,identify related information and eliminate non-related information when you can.

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WHAT WILL THE HSPA LOOK LIKE?

The rest of this booklet will give you an idea of what the HSPA materials are like.

Language Arts Literacy

New Jersey’s Core Curriculum Content Standards identify five categories of Language ArtsLiteracy: speaking, listening, writing, reading, and viewing. These five activities are essentialaspects of our everyday lives and critical to what we think, learn, communicate, and create.

The HSPA provides a variety of writing and reading activities and texts that will allow you todemonstrate your skills and knowledge in using language arts literacy. The assessment presentstwo types of reading passages, narrative and persuasive texts, that are followed by a set of 10multiple-choice and two open-ended questions for each passage. You will be required to readtwo narrative passages and two persuasive passages. The HSPA also provides two different typesof writing prompts and a student text that you will revise and edit. For the two writing tasks, youwill be provided with blank pages for prewriting in either your test booklet (for the pictureprompt) or in a separate writing task folder (for the persuasive prompt). Use this space to planyour ideas. Then use the lined pages in your answer folder for your written draft. In addition, youwill receive a copy of the Writer’s Checklist/Revising-Editing Guide for each writing activity.This checklist and guide list important points for you to remember as you write, critically read,and revise your writing. As you complete these different sections of the HSPA, you will bedemonstrating your skills in using language for thinking, learning, and communicating.

The HSPA language arts literacy activities are sequenced to give you varying experiences inusing language for different kinds of tasks, just as you do in your everyday life. As preparationfor taking the HSPA language arts literacy assessment, read through the sample test materials inthis booklet to familiarize yourself with the sequence and content of each test section. Alsoacquaint yourself with the type of scoring procedure and criteria that will be used to assess yourdemonstrated skills. This preview will help you understand what each task involves and howyour work will be evaluated. Copies of the rubrics that will be used to score your writing areincluded on pages 14–16 of this booklet.

Following are sample materials illustrating the content of the HSPA language arts literacyassessment. The reading passages are only excerpts from stories and articles that were chosen toillustrate the HSPA texts. Complete versions of these texts are printed in the Directory of TestSpecifications and Sample Items for the Elementary School Proficiency Assessment (ESPA),Grade Eight Proficiency Assessment (GEPA), and High School Proficiency Assessment (HSPA)in Language Arts Literacy. That document is available in your school district.

This booklet includes an example of each writing activity and both types of questions for eachreading passage. As you read through the following pages, notice that the scoring procedure foreach open-ended item or activity is identified to help you understand how your work will beassessed.

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One writing task begins with a picture that serves as a prompt for a story. The setting andcharacters, when applicable, portrayed in the picture suggest an event or relationship that you areinvited to develop and describe through a story. In this activity you may speculate about whathas happened, what is happening, or what will happen at some other time. Use your imaginationto create a good story that is detailed and vivid. The answer folder will provide two lined pagesfor the first draft of your writing.

Robert Lewis/Robert Lewis Photography/New York, N.Y.

Writing Task AAn ancient proverb says, “A picture is worth a thousand words.” Regardless of the artist’s original intent,what we see in the picture can be very different from what others see. What story does this picture tellyou? Use your imagination and experience to speculate about what is happening. Then write your story.

SCORING PROCEDURE: Registered Holistic Scoring Rubric - Page 14

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A second writing activity will introduce a controversial issue that you will address in apersuasive letter or essay. This writing prompt is contained in a separate Persuasive Writing TaskFolder rather than in the test booklet. Following is an example of a writing prompt that focuseson a controversial issue.

WRITING SITUATION

In recent years, business representatives have expressed concern about the skills ofstudents entering the workforce. Responding to these concerns, state legislators have enacteda law that establishes high educational standards for all students. Now the state legislature isconsidering enacting a law that would prohibit students from participating in any after-schoolactivity after 6 pm. They believe this law would ensure that students have adequate time tostudy and complete daily homework assignments. However, many people believe this law wouldbe unfair, and the proposed legislation has become a controversial issue in communities acrossthe state.

Your social studies teacher has asked students to write an essay explaining theiropinions of this controversial issue. What is your point of view? How would this legislation affectyou and other students in your school?

DIRECTIONS for WRITING TASK

Write an essay either supporting or opposing the proposed legislation to prohibitstudents from participating in any after-school activity after 6 pm. Use facts, examples, andother evidence to support your point of view.

The answer folder will provide four lined pages for this writing task. In addition, you will haveblank pages in the Persuasive Writing Task Folder to use for planning your writing. The planningspace is for your benefit because it gives you a place to brainstorm and organize your ideasbefore you begin writing. Readers who score your writing will consider the organization andelaboration of key ideas and details as well as grammar and sentence structure. Only your writingin your answer folder will be scored.

SCORING PROCEDURE: Registered Holistic Scoring Rubric - Page 14

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The third writing activity focuses on a student’s essay that needs revising and editing. The essaywill present a variety of problems in organization, elaboration of details, sentence structure,usage, word choice, punctuation, and spelling. In this activity, you will decide what to change toimprove the essay. Since there is not one right way to complete this task, your revisions may bequite different from the revisions your classmates make. To begin, read through the essay first toacquaint yourself with the writer’s ideas.

The student’s essay will be printed in your answer folder to allow you to make changes directlyon the text. The test materials will include a Revising/Editing Guide to help you focus on thekinds of writing problems you may encounter. The guide also illustrates four editing marks,which are simple ways to show your revisions. If you have learned other editing marks, such aswhich means “start a new paragraph,” you may use them too.

The answer folder also provides two lined pages for you to use if you want to reorganize theentire essay or if you decide to add new text. Those pages are there to make it easy for you tocomplete the task, but you are not required to copy the essay onto those pages.

This task provides you with an opportunity to show what you know about revising and editing.What is most important is that your revisions develop the student’s ideas and improve the clarityof the text. It is also important that your changes are clear and neat to help readers understandwhat revisions you are making.

SCORING PROCEDURE: Revising/Editing Scoring Guide - Page 15

NOTE: REVISE/EDIT WILL NOT BE PART OF THE OPERATIONAL HSPA IN MARCH2004. HOWEVER, IT WILL BE FIELD TESTED.

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Some school boards have mandated community service as a high school graduation requirement. In districtsconsidering such a requirement, the discussion of required community service is a controversial issue.

One student has written an essay for her school newspaper expressing her views on the board of education’sproposal to mandate community service in her school district. Read her first draft and think about how toimprove the meaning and the clarity of the text. Then make your revisions.

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The HSPA also presents a narrative reading passage, followed by 10 multiple-choice and twoopen-ended questions that relate to the text. The answer folder will provide a lined page forresponses to each open-ended question.

1. The purpose of memories in this story isto

A. describe true love.B. reveal missed opportunities.C. tell an engaging story.D. find a telescope.

2. The experience with the telescope has aprofound effect on the boy and Old ManCorey.

• What does each character see, and whatis his response to what he sees in thetelescope?

• How will the experience with thetelescope change each of them?

Use information from the story tosupport your response.

SCORING PROCEDURE: Open-Ended Scoring Rubric - Page 16

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You will also read a persuasive passage and then answer 10 multiple-choice and two open-endedquestions that relate to and extend your understanding of the text. The answer folder will providea lined page for each open-ended question.

1. Which of the following would the authormost likely support?

A. expenditures for new texts ratherthan a driver’s education course

B. jobs for students as long as theydon’t require cars

C. financial rewards for earning goodgrades

D. fewer intra- and extracurricularactivities

2. A student in your high school has takena position that s/he is willing to work inorder to own a car. Based on the article,what arguments could be made to justifysuch a position?

• Clearly state your point of view.• Provide at least two supporting details

that would explain your opposition tothe author’s point of view.

Use information from the article tosupport your response.

SCORING PROCEDURE: Open-Ended Scoring Rubric - Page 16

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17

Mathematics

The Mathematics Section of the HSPA assessment is divided into four content clusters. Each ofthese clusters reflects knowledge and skills specified in New Jersey’s Core Curriculum ContentStandards.

High School Proficiency Assessment (HSPA) Mathematics Clusters

I. Number Sense, Concepts, and ApplicationsA. Understand types of numbers, our numeration system, and the ways they are used and

applied in real-world situations.B. Apply ratios, proportions, and percents in a variety of situations.

II. Spatial Sense and GeometryA. Recognize, visualize, analyze, and apply geometric properties, relationships, and

patterns in real-world and/or problem-solving contexts using models, manipulatives,or technology.

B. Use coordinate geometry in problem-solving situations and apply the principles ofcongruence, similarity, and transformations.

C. Apply the principles of measurement and geometry to solve problems involvingdirect and indirect measurement.

III. Data Analysis, Probability, Statistics, and Discrete MathematicsA. Determine, interpret, and use probabilities of simple and compound events.B. Understand and interpret statistical distributions and apply to real-world situations.C. Collect, organize, represent, analyze, and interpret data.D. Apply the concepts and methods of discrete mathematics to model and explore a

variety of practical situations.E. Use iterative and recursive patterns and processes to model a variety of practical

situations and solve problems.

IV. Patterns, Functions, and AlgebraA. Recognize, create, and extend a variety of patterns and use inductive reasoning to

understand and represent mathematical and other real-world phenomena.B. Use various types of functions to represent mathematical or real-world situations.C. Use algebraic concepts and processes to concisely express, analyze, and model real-

world situations.

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Types of Questions

The multiple-choice (MC) questions on the HSPA Mathematics test assess higher-level cognitiveprocesses than the questions in traditional multiple-choice tests. It will take you an average ofbetween one and two minutes to answer each MC question. The answers are computer scoredand have a weight of one point each.

Open-ended (OE) questions require you to construct your own written or graphical responses andexplain your responses. It will take approximately ten minutes to answer each OE question. Yourresponses are hand scored on a scale from 0 to 3.

The general scoring guide on page 20 was created to help readers score open-ended questionsconsistently within a single test and across different forms of the test. This scoring guide is usedby the trained readers who will score the Mathematics open-ended questions on the HSPA.

The following table shows you how many multiple-choice and open-ended questions to expect.

Number of QuestionsQuestion Type

11th Grade

MC 40

OE 8

You will be provided with a Mathematics Reference Sheet that contains a ruler, geometricshapes, formulas, and other information you may find useful as you take the test. You will alsobe provided with a calculator to help you solve problems.

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20

Scoring Guide for Mathematics Open-Ended (OE) Questions(Generic Rubric)

3-Point Response

The response shows complete understanding of the problem’s essentialmathematical concepts. The student executes procedures completely and gives relevantresponses to all parts of the task. The response contains few minor errors, if any. Theresponse contains a clear, effective explanation detailing how the problem was solved sothat 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 essentialmathematical concepts. The student executes nearly all procedures and gives relevantresponses to most parts of the task. The response may have minor errors. The explanationdetailing how the problem was solved may not be clear, causing the reader to make someinferences.

1-Point Response

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

0-Point Response

The response shows insufficient understanding of the problem’s essentialmathematical concepts. The procedures, if any, contain major errors. There may be noexplanation 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.

The generic rubric above is used as a guide to develop specific scoring guides or rubrics for eachof the open-ended (OE) questions that appear on the New Jersey fourth-grade (NJ ASK4),eighth-grade (GEPA), and eleventh-grade (HSPA) proficiency assessments in Mathematics. Thegeneric rubric helps ensure that students are scored in the same way for the same demonstrationof knowledge and skills regardless of the test question.

21

HSPA MATHEMATICS SAMPLE QUESTIONS

Cluster I, Macro A

• Find the length, width, and area of each ofthe 5 shaded rectangles.

• What is the total area represented by the 5rectangles?

• How do you think the area of the 5rectangles compares to the area of theregion under the curve? Explain yourreasoning.

Rationale:Since each of the shaded rectangles has the same width of 2 units, you only need to read

the height of each from the graph and then multiply the width and height to obtain the area. Theheight of the first rectangle is 100 units, so its area is 100 units * 2 units or 200 sq. units.

The total area of the 5 rectangles is(100 * 2) + (90 * 2) + (75 * 2) + (50 * 2) + (20 * 2) = 670 sq. units.

The answer for the third bullet may vary, but you must explain your reasoning.

22

Cluster I, Macro B

2. The original ticket price of a shirt is $25.99.During a clearance sale, this shirt is reduced by40% of the ticket price; then 25% of the reducedprice is taken off at the cash register.

• Rounded to the nearest penny, what is theprice paid by the customer?

(Answer to first bullet: $11.69 or $11.70)

• What price would the customer have paid ifthis shirt were sold at a one-time reductionof 65% from the original price?

• Why didn’t the store simply sell this shirt at65% off the original sticker price?

Rationale:

Amount of 40% discount: $25.99 * 0.40 = $10.396 ≈ $10.40

Price after 40% discount: $25.99 – $10.40 = $15.59

Amount of 25% discount: $15.59 * 0.25 = $3.897 ≈ $3.90

Price after 25% discount: $15.59 – $3.90 = $11.69

($11.70 is acceptable if you round at the end instead of after each step.)

By breaking up the 65% discount into 40% and 25% discounts, the store was able to sellthe shirt at a higher price than it would have if the store sold the shirt at 65% off the originalprice.

23

Cluster II, Macro A

3. For a sewing project, Tanya cut isosceles

triangles from a striped piece of material

where the stripes are parallel. The vertex

angle of the isosceles triangle was 50° and

BC is parallel to the base.

Find the measure of ∠BCE as shown in the

diagram.

A. 50º

B. 65º

C. 115º

D. 130º

Rationale:Since the triangle is isosceles and the vertex angle is given to be 50°, the two remaining

angles must be 65°. 180° = 50° + x + x; x = 65°

The measure of ∠AGE is 180° since that is the measure of a straight line. Therefore,m∠ACB + m∠BCE = 180.

Since BC and FG are parallel and AG intersects both BC and FG , m∠ACB =m∠AGF = 65.To solve for m∠BCE, use the following:180 – m∠ACB = 180 – 65 = 115.

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24

Cluster II, Macro B

4. A boat starts at Point A, travels 6 miles dueeast to Point B, and then turns and travels8 miles due south to Point C on the shore.

• On the grid provided in your answerfolder, construct a scale drawing usingvectors to show the boat’s movement,starting from point A.

• Draw a vector that would show thedirect path from point A to point B.

• What would be the approximate numberof miles the boat could have traveledalong this path?

• Approximately how many degrees fromNorth would this path be? Explain howyou arrived at your answer.

Rationale:

If the boat travels 6 miles due east from Point A to Point B and then turns and travels

8 miles due south from Point B to Point C, the boat’s path forms a right angle. If you use straight

lines to connect Point A to Point B, Point B to Point C, and Point C to Point A, the result is a

right triangle. To find the length of AC , you apply the Pythagorean Theorem, 62 + 82 = c2.

Solving for c yields c = 10. The measure of ∠C is approximately 37° since tan 37° ≈ 36.869 ≈ 68

.

25

Cluster II, Macro C

5.

Describe in detail how you could use acalculator with trigonometric functions tohelp find the height of your school buildingif you knew the distance from the base ofthe building to the point where you werestanding and the angle from the ground atyour feet to the top of the building.

Rationale:

If you know the distance d from the base of the building to Point A where you are

standing and you know angle θ, which the ground makes with the hypothetical line from Point A

to the top of the building, you can apply the formula tan θ = hd

, where h is the height of the

building. Solving for h results in h = d (tan θ).

26

Cluster III, Macro A

6. Weatherpersons predict tomorrow’s weather

based on what has happened in the past on

the days following days just like today. During

the past 50 years, there have been 380 days

that have been just like today, and of those,

200 have been followed by a clear day. Which

of the following is the approximate probability

of a clear day tomorrow that would be given by

a weatherperson using the prediction rule

described in this problem?

A. 13%

B. 34%

C. 53%

D. 66%

Rationale:

Since there have been 200 days out of 380 days which were followed by a clear day, the

experimental probability of tomorrow being a clear day is 200380

≈ 0.5263 ≈ 53%.

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27

Cluster III, Macro B

7. The data provided show test scores for twelve students and the number of hours they studied for thetest during the three days prior to taking it.

• On the grid provided in your answer folder, construct a scatter plot of this data.

• Does there appear to be a relationship between a student’s test score and the time spentstudying? Use the scatter plot to support your answer.

• Do any of the points appear to be outliers? Explain.

Rationale:

Student must draw a correct scatter plot of the data.

For the most part, it looks as though a student’s test score improves with more time spentstudying. Answers as to which points are outliers may vary, as long as your response shows aclear understanding of the definition of outliers and you support your answers.

28

Cluster III, Macro D

8. The chart below shows the numbers of students

in a homeroom that voted for each student

council candidate.

If this data were drawn in a circle graph,

approximately how many degrees in the central

angle of the sector of that circle would represent

Tiko’s votes?

A. 22

B. 68

C. 79

D. 90

Rationale:Tiko received 7 votes out of the total 32

students who voted. 732

≈ 0.218 ≈ 0.22 = 22%.

Since there are 360° in a circle, 22% of360° would be 79.2° or 79°.

Cluster III, Macro C

9.

The diagram above represents a network of

direct air routes between cities. Which of the

following matrices can represent the network

above? A zero indicates no direct air route. A one

represents that a direct air route exists.

Rationale:Since there are line segments connecting A to

B and B to C, there are 1’s in Row A for ColumnB and C corresponding to AB & BC . The restof the matrix follows accordingly.

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29

Cluster III, Macro E

10. A sequence of shaded squares is displayedbelow. One vertex of each shaded square,after the first, is at the center of thepreceding shaded square.

The ratio of the area of the 10th shadedsquare to the area of the 12th shadedsquare is

A. 14

B. 41

C. 116

D. 161

Rationale:

The ratio of the area of any selectedshaded square to the area of the next shaded

square is 41

, that is, the area of the selected

shaded square is 4 times the area of the nextshaded square.

Therefore, the ratio of the area of the10th shaded square to the area of the 11th

shaded square is 41

. The ratio of the 11th to

the 12th is 161

. Thus, the ratio of the 10th to

the 12th is since 41

× 41

= 161

.

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30

Cluster IV, Macro A

11. Imagine that the table below continues, rowafter row, following the same pattern forever.

• Complete the 6th and 7th rows in youranswer folder.

• What numbers are in the 100th row?• Write expressions for the numbers in the

n th row.• In which row will the number 32 be

found?• In which column will the number 32 be

found? Explain your answer.• In which column will the number 1783 be

found? Explain your answer.

Rationale:

Column C is always 3 times the row number(that is, 3n)Column B is always 3 times the row numberless 1 (that is, 3n – 1)Column A is always 3 times the row numberless 2 (that is, 3n – 2)

Therefore, Row 6: 16, 17, 18Row 7: 19, 20, 21Row 100 298, 299, 300

Since the number in Column C is alwaysdivisible by 3 and 32 is 1 less than 33(which is divisible by 3), the number 32appears in Column B. To find the rownumber, substitute the number 32 into theequation for Column B.3n – 1 = 323n = 32 + 13n = 33 and n = 11 (the 11th row)

To find the column for 1783, divide by 3.Note that the answer is 594 with a remainderof 1. The remainder indicates that thenumber occurs in the first column (ColumnA) of the next row, which is Row 595. Youcan confirm your answer by using theformula for Column A:

3n - 2 = 17833n = 1783 + 23n = 1785and n = 595

31

Cluster IV, Macro B

12. The graph of a function, f(x), is given below.

Which graph would represent f(x) – 2?

Rationale:

The graph of the function, f(x), is shown.So, f(x) – 2 is just the graph of f(x) translated2 units in the negative y direction.

32

Cluster IV, Macro C

13. The players on a basketball team scored

75 points in the final game of the season.

During that game, they made twice as many

field goals as they did free throws. (Each

field goal is worth two points, and each free

throw is worth one point.) How many points

did the players on that team make on free

throws during the game?

Which of the following equations cannot be

used to solve the problem given above?

A. 2x + x = 75

B. 2(2x) + x = 75

C. 4x + x = 75

D. 5x = 75

Rationale:

75 = 2x + x only accounts for the factthat the team made twice as many field goalsas they did free throws. It doesn’t containthe additional stipulation that each field goalis worth two points while each free throw isworth only one point. All three of the otherdistractors simplify to 5x = 75, which is thecorrect equation.

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