Read an Excerpt
A Message to Educators and Students
All New Jersey students are required to pass all sections of the HSPA before they can graduate high school. The state-administered Alternate Proficiency Assessment may be used to evaluate whether or not a student has attained proficiency in the necessary skills if he or she does not pass the HSPA.
The HSPA is not an easy test to pass. It was designed to be more challenging than the state’s previous high school exit exam, the HSPT. It is important, therefore, that students extensively review the subjects covered by the HSPA, and become well acquainted with the types of questions that can be expected to be on the test.
This book is arranged to help students pass the Mathematics section of the HSPA by providing:
1. An individual study plan and guidance to help students concentrate on subject areas that they need to work on most when preparing for the exam.
2. Four full-length practice exams based on the format of the most recent exams given. Two exams are printed in this book and two additional exams are available online at www.rea.com/HSPA.
3. Types of questions likely to be on the exam.
4. A full and detailed explanation of the answer to each exam question.
5. Comprehensive reviews of all subjects covered on the exam.
NOTE TO EDUCATORS:
A large number of class and homework assignments that may be assigned to students are included at the back of the book. Answers to the assigned questions are given in the Teacher’s Guide, which is available from REA.
PASSING the NEW JERSEY HSPA IN MATHEMATICS
About this book and bonus online tests
This book will provide you with an accurate and complete representation of the New Jersey High School Proficiency Assessment (HSPA) in Mathematics. Inside you will find subject reviews that are designed to provide you with the information and strategies needed to do well on this section of the HSPA. Four complete practice tests are provided: two printed in this book and two additional unique tests online at www.rea.com/HSPA.
All of the tests are based on the official HSPA. REA’s practice tests contain every type of question that you can expect to encounter on the HSPA. Following each model test, you will find an answer key with detailed explanations designed to help you completely understand the test material.
(Note to educators: Also included are over 200 class and homework problems that can be assigned to students. Answers to these questions can be found in the Teacher’s Guide, which is available from REA.)
About the Test
Who takes the test and what is it used for?
The HSPA is mandatory for New Jersey high school juniors. It gauges students’ knowledge and skills in the New Jersey Core Curriculum Content Standards for reading, writing, and mathematics.
All New Jersey high school students are required to pass the entire test in order to graduate. Students who do not pass a section are given an opportunity to retake the test in the fall or spring of the 12th grade.
Who administers the test?
The HSPA was developed and is administered by the New Jersey State Department of Education and involves the assistance of educators throughout the state. The test development process is designed and implemented to ensure that the content and difficulty level of the test are appropriate.
When and where is the test given?
The HSPA Math and English tests are administered in March and October. They are given at all public high schools. The testing lasts for three days, and may be taken on alternate days if a conflictsuch as a religious obligationexists.
To receive information on upcoming administrations of the HSPA, consult the Grade 11 High School Proficiency Assessment Parent Information Bulletin. The bulletin can be obtained from your guidance counselor or by contacting:
New Jersey State Department of Education
P.O. Box 500
Trenton, NJ 08625
Phone: (609) 292-4469
Is there a registration fee?
No. Because all New Jersey high school students are required to take this test, no fee is imposed.
How to Use this Book
What do I study first?
Read over the reviews and the suggestions for test taking. Studying the reviews thoroughly will reinforce the basic skills you will need to do well on the test. Be sure to take the practice tests to become familiar with the format and procedures involved with taking the actual HSPA in Mathematics.
To best utilize your study time, follow our HSPA Independent Study Schedule, located in the front of this book. Brushing up on the areas you did well on wouldn’t hurt, either.
When should I start studying?
It is never too early to start studying for the HSPA. The earlier you begin, the more time you will have to sharpen your skills. Do not procrastinate! Cramming is not an effective way to study, since it does not allow you the time needed to learn the test material. The sooner you learn the format of the exam, the more time you will have to familiarize yourself with the exam content.
Format of the HSPA in Mathematics
Each section of the HSPA in Mathematics contains 10 multiple-choice questions and 2 open-ended questions. For the multiple-choice questions, you are offered four answer options. The open-ended questions call for you to write a short answer, so you are not presented with answer choices. After each section of the test, you are given a brief break.
Mathematics Content Clusters
In the mathematics sections, you will encounter questions on the following “clusters” of knowledge:
Number Sense, Concepts, and ApplicationsThese questions deal with the following topics: our numeration system (and its application in real-world situations); and ratios, percents, and proportions.
Spatial Sense and GeometryThese questions deal with the following topics: identifying geometric properties, relationships, and patterns in real-world and/or problem-solving situations; using coordinate geometry and principles of congruence, similarity, and transformations; and direct and indirect measurement.
Data Analysis, Probability, Statistics, and Discrete MathematicsThese questions deal with the following topics: probabilities of simple and compound events; statistical distributions; organization and representation of data; discrete mathematics; and iterative and recursive processes.
Patterns, Functions, and AlgebraThese questions test the student’s capability in the following topics: patterns and inductive reasoning; various types of functions; and algebraic concepts and processes.
Calculators will be permitted and, in fact, will be provided during the test. You may use a programmable or non-programmable four-function, scientific, or graphing calculator. No pocket organizers, hand-held minicomputers, paper tape, or noisy calculators may be used. In addition, calculators requiring an external power source will not be permitted. You will not be allowed to share a calculator.
About the Review Section
The reviews in this book are designed to help you sharpen the basic skills needed to approach the HSPA, as well as to provide strategies for attacking each type of question. You will also find exercises to reinforce what you have learned. By using the reviews in conjunction with the practice tests, you will put yourself in a position to master the HSPA.
The Mathematics Section Review covers the basics of what you need to know to pass the Mathematics Section of the HSPA. You will find strategies for the Mathematics Section, a review of each cluster and its individual “macros,” and exercises to strengthen your abilities in these areas.
Although you may not be familiar with standardized tests such as the HSPA, there are many ways to acquaint yourself with this type of examination and help alleviate your test-taking anxieties. Listed below are ways to help you become accustomed to the HSPA, some of which may be applied to other standardized tests as well.
Become comfortable with the format of the HSPA. When you are practicing, simulate the conditions under which you will be taking the actual test. Stay calm and pace yourself. After simulating the test only a couple of times, you will boost your chances of doing well, and you will be able to sit for the actual HSPA with much more confidence.
Read all of the possible answers. Just because you think you have found the correct response, do not automatically assume that it is the best answer. Read through each choice to be sure that you are not making a mistake by jumping to conclusions.
Use the process of elimination. Go through each answer to a question and eliminate as many of the answer choices as possible. By eliminating two answer choices, you can vastly improve your chances of getting the item correct, since there will only be two or three choices left from which to make your guess. Guess only if you can eliminate at least two answers, as wrong answers will be penalized.
Work quickly and steadily. You will have only minutes to work on each section, so work quickly and steadily to avoid focusing on any one problem for too long. Taking the practice tests in this book will help you learn to budget your precious time.
Learn the directions and format for each section of the test. Familiarizing yourself with the directions and format of the different test sections will not only save time, but will also help you avoid anxiety (and the mistakes caused by getting anxious).
Work on the easier questions first. If you find yourself working too long on one question, make a mark next to it on your test booklet and continue. After you have answered all of the questions that you can, go back to the ones you have skipped.
Be sure that the answer oval you are marking corresponds to the number of the question in the test booklet. Since the multiple-choice sections are graded by machine, marking one wrong answer can throw off your answer key and your score. Be extremely careful.
Eliminate obvious wrong answers. Sometimes an HSPA question will have one or two answer choices that are a little odd. These answers will be obviously wrong for one of three reasons: (1) they may be impossible given the conditions of the problem, (2) they may violate mathematical rules or principles, or (3) they may be illogical. Being able to spot obvious wrong answers before you finish a problem gives you an advantage because you will be able to make a more educated guess from the remaining choices even if you are unable to fully solve the problem.
Work from answer choices. One of the ways you can use a multiple-choice format to your advantage is to work backwards from the answer choices to solve a problem. This is not a strategy you can use all of the time, but it can be helpful if you can just plug the choices into a given statement or equation. The answer choices can often narrow the scope of responses. You may be able to make an educated guess based on eliminating choices that you know do not fit into the problem.