OGT Ohio Graduation Test, 3rd Edition (REA) - Ready, Set, Go!

Overview


OGT (Ohio Graduation Test) Mathematics – with Online Practice Tests

Fully aligned with the Ohio Academic Content Standards

REA helps Ohio students get ready for OGT Mathematics!

- Provides the instruction and practice students need to pass the test
- In-depth OGT math review covers all test topics
- Color ...

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OGT Ohio Graduation Test Mathematics 3rd Ed.

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Overview


OGT (Ohio Graduation Test) Mathematics – with Online Practice Tests

Fully aligned with the Ohio Academic Content Standards

REA helps Ohio students get ready for OGT Mathematics!

- Provides the instruction and practice students need to pass the test
- In-depth OGT math review covers all test topics
- Color icons for easy navigation of questions, tips, and key concepts
- Students at all levels will benefit from the chapter-by-chapter review questions and full-length practice tests
- 4 full-length OGT math practice tests: 2 tests in the book, and 2 practice tests online
- Detailed explanations of answers for all practice test questions

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Product Details

  • ISBN-13: 9780738609423
  • Publisher: Research & Education Association
  • Publication date: 11/28/2010
  • Edition description: Third
  • Edition number: 3
  • Pages: 320
  • Sales rank: 1,397,779
  • Product dimensions: 8.50 (w) x 10.90 (h) x 0.90 (d)

Read an Excerpt

Introduction
Passing the OGT Mathematics Test

 
About This Book
REA’s Ohio Graduation Test (OGT) Mathematics book is an accurate and comprehensive
guide aligned with the Academic Content Standards of the Ohio Department
of Education. Inside you will find chapters designed to equip you with the information
and strategies needed to prepare for and pass the test. The standards covered are listed
at the beginning of each chapter.

We provide you with a total of four full-length practice tests—two at the end of this
book and two online—each of which is based on the official OGT. The online tests can
be found on our website at www.rea.com/OGT.
 
The practice tests contain every type of question that you can expect to encounter
on the OGT. At the end of the book, you will find an answer key with detailed explanations designed to help you completely understand the content upon which your success on the test depends.

About the Test

Who Takes These Tests and What Are They Used For
?
The five parts of the Ohio Graduation Tests are aligned to Ohio’s academic content
standards in mathematics, writing, reading, science, and social studies, which were
adopted by the State Board of Education.

The graduating class of 2007 was the first class responsible for taking the OGT
and passing all five tests as a graduation requirement. Students must pass these tests
in order to earn an Ohio high-school diploma. Students in grades 3 through 8 take
Achievement Tests.

Is There a Registration Fee?
No.

When and Where Is the Test Given?
Students take the OGT for the first time in the spring of their sophomore year. If
they do not pass, students can continue to take the tests in the fall and spring of their
junior and senior years, and in the summer. The OGT is administered as follows:

• Spring of 10th grade
• Summer between 10th and 11th grade (optional)
• Fall and spring of 11th grade
• Summer between 11th and 12th grade (optional)
• Fall and spring of 12th grade

Tests are given in school. Students have up to two-and-a-half hours to take each of
the tests.

Test Accommodations and Special Situations
Federal law requires every student to take the OGT or an alternate assessment.
Every effort is made for students with disabilities seeking a standard high school
diploma to take the OGT. Students whose Individual Education Plan (IEP) excuses
them from having to pass the OGT to graduate may be awarded a diploma.

Students whose primary language is not English must achieve passing scores on
the OGT in order to be awarded a diploma. However, bilingual forms of the OGT are
available. English audio CD-ROMs, large-print formats, and oral translation scripts
are also available to those requiring such accommodations.

Additional Information and Support
Additional resources to help you prepare to take the OGT can be found on the Ohio
Department of Education Web site at http://www.ode.state.oh.us.

 
How to Use This Book

What Do I Study First?

Read over the review sections and the suggestions for test taking. Studying the
review sections thoroughly will reinforce the basic skills needed to do well on the test.
Be sure to take the practice tests to become familiar with the format and procedures
involved in taking the actual OGT.

When Should I Start Studying?
It is never too early to start studying for the OGT. 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 because 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.

Overview of the OGT in Mathematics
The 44 questions on the mathematics portion of the OGT are based on five broad
strands, or standards, as follows:

1. Number, Number Sense, and Operations (approximately 15%
of the test)
2. Measurement (approximately 15% of the test)
3. Geometry and Spatial Sense (approximately 20% of the test)
4. Patterns, Functions, and Algebra (approximately 25% of the test)
5. Data Analysis and Probability (approximately 25% of the test)

The test consists of 32 multiple-choice items, 5 short-answer items, and 1 extended response
item. In addition, there are six experimental questions. These are unscored.
You will not know which questions are unscored, so do your best on all of them.

Multiple-choice items require you to select the correct response from a list of four
options. Short-answer and extended-response items require you to generate a written
response. A short-answer item requires a brief response, usually a few sentences or a
numeric solution to a straightforward problem. An extended-response item requires
you to solve a more complex problem or task and to provide a more in-depth response.
The questions typically ask you to show your work or calculations, explain your reasoning,
and justify the procedures you used.

Short-answer items may each take up to five minutes to complete, and responses
receive a score of 0, 1, or 2 points. Extended-response items may each require 5 to 15
minutes to complete, and responses receive a score of 0, 1, 2, 3, or 4 points.

Brief descriptions of the levels of complexity used in item development include
the following:

• Low Complexity: Items rely heavily on recall and recognition of
facts, definitions and procedures. Items typically specify what
the students are to do and often involve carrying out a specified,
routing, procedure. (Approximately 25% of the items)

• Moderate Complexity: Items require more interpretation of
a problem or situation and choice among alternative solution
strategies than low complexity items. Students are expected
to make decisions about what to do, using informal reasoning
and problem-solving strategies. The solution process ordinarily
requires more than one step. (Approximately 50% of the items)

• High Complexity: Items require more sophisticated analysis,
planning, and reasoning in more complex or non-routine problem
situations. Students are often asked to think in an abstract
or sophisticated way and to justify their reasoning and solution
process. (Approximately 25% of the items)

Benchmarks by Standard

Numbers, Number Sense, and Operations
A. Use scientific notation to express large numbers and numbers
less than one.
B. Identify subsets of the real number system.
C. Apply properties of operations and the real number system, and
justify when they hold for a set of numbers.
D. Connect physical, verbal, and symbolic representations of
integers, rational numbers, and irrational numbers.
E. Compare, order and determine equivalent forms of real numbers.
F. Explain the effects of operations on the magnitude of quantities.
G. Estimate, compute, and solve problems involving real numbers,
including ratio, proportion, and percent, and explain solutions.
H. Find the square root of perfect squares, and approximate the
square root of non-perfect squares.
I. Estimate, compute, and solve problems involving scientific
notation, square roots, and numbers with integer exponents.

Data Analysis and Probability
A. Create, interpret, and use graphical displays and statistical
measures to describe data; e.g., box-and-whiskers plots,
histograms, scatterplots, measures of center and variability.
B. Evaluate different graphical representations of the same data to
determine which is the most appropriate representation for an
identified purpose.
C. Compare the characteristics of the mean, median, and mode for
a given set of data, and explain which measure of center best
represents the data.
D. Find, use, and interpret measures of center and spread, such as
mean and quartiles, and use those measures to compare and
draw conclusions about sets of data.
E. Evaluate the validity of claims and predictions that are based
on data by examining the appropriateness of the data collection
and analysis.
F. Construct convincing arguments based on analysis of data and
interpretation of graphs.
G. Describe sampling methods and analyze the effects of method
chosen on how well the resulting sample represents the
population.
H. Use counting techniques, such as permutations and
combinations, to determine the total number of options and
possible outcomes.
I. Design an experiment to test a theoretical probability, and
record and explain the results.
J. Compute probabilities of compound events, independent events,
and simple dependent events.
K. Make predictions based on theoretical probabilities and
experimental results.

Measurement
A. Solve increasingly complex non-routine measurement problems
and check for reasonableness of results.
B. Use formulas to find surface area and volume for specified three dimensional
objects accurate to a specified level of precision.
C. Apply indirect measurement techniques, tools, and formulas,
as appropriate, to find perimeter, circumference and area of
circles, triangles, quadrilaterals, and composite shapes, and to
find volumes of prisms, cylinders, and pyramids.
D. Use proportional reasoning and apply indirect measurement
techniques, including right triangle trigonometry and properties
of similar triangles, to solve problems involving measurements
and rates.
E. Estimate and compute various attributes, including length,
angle measure, area, surface area, and volume, to a specified
level or precision.
F. Write and solve real-word, multi-step problems involving
money, elapsed time and temperature, and verify reasonableness
of solutions.

Geometry and Spatial Sense
A. Formally define geometric figures.
B. Describe and apply the properties of similar and congruent
figures; and justify conjectures involving similarity and
congruence.
C. Recognize and apply angle relationships in situations involving
intersecting lines, perpendicular lines, and parallel lines.
D. Use coordinate geometry to represent and examine the properties
of geometric figures.
E. Draw and construct representations of two- and three-dimensional
geometric objects using a variety of tools, such as a straightedge, compass, and technology.
F. Represent and model transformations in a coordinate plane and
describe the results.
G. Prove or disprove conjectures and solve problems involving two and
three-dimensional objects represented within a coordinate system.
H. Establish the validity of conjectures about geometric objects,
their properties and relationships by counter-example, inductive
and deductive reasoning, and critiquing arguments made by
others.
I. Use right triangle trigonometric relationships to determine
lengths and angle measures.
 

Patterns, Functions, and Algebra
A. Generalize and explain patterns and sequences in order to find
the next term and the nth term.
B. Identify and classify functions as linear or nonlinear, and
contrast their properties using tables, graphs, or equations.
C. Translate information from one representation (words, table,
graph, or equation) to another representation of a relation or
function.
D. Use algebraic representations, such as tables, graphs,
expressions, functions, and inequalities, to model and solve
problem situations.
E. Analyze and compare functions and their graphs using attributes,
such as rates of change, intercepts, and zeros.
F. Solve and graph linear equations and inequalities.
G. Solve quadratic equations with real roots by graphing, formula,
and factoring.
H. Solve systems of linear equations involving two variables
graphically and symbolically.
I. Model and solve problem situations involving direct and inverse
variation.
J. Describe and interpret rates of change from graphical and
numerical data.
 

Test-Taking Strategies
What to Do before the Test

• Pay attention in class.

• Carefully work through the chapters of this book. Mark any
topics that you find difficult, so that you can focus on them
while studying and get extra help if necessary.

• Take the practice tests and become familiar with the format
of the OGT. 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 feel more confident, and this will boost your chances
of doing well.

• Students who have difficulty concentrating or taking tests
in general may have severe test anxiety. Tell your parents, a
teacher, a counselor, the school nurse, or a school psychologist
well in advance of the test if this applies to you. They may be
able to give you some useful strategies that will help you feel
more relaxed and then be able to do your best on the test.

What to Do During the Test
• Read all of the possible answers. Even if you think you have
found the correct response, do not automatically assume that it
is the best answer. Read through each answer 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 have given yourself
a better chance of getting the item correct, because there will
only be two choices left from which to make your selection.

Sometimes a question will have one or two answer choices that
are a little odd. These answers will be obviously wrong for one
of several reasons: they may be impossible given the conditions
of the problem, they may violate mathematical rules or principles,
or they may be illogical.

• Work on the easier questions first. If you find yourself working
too long on one question, make a mark next to it in your test
booklet and continue. After you have answered all of the questions
that you know, 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. The multiple-
choice sections are graded by machine, so marking one
wrong answer can throw off your answer key and your score. Be
extremely careful.

• Work from answer choices. You can use a multiple-choice format
to your advantage by working backward from the answer
choices to solve a problem. This strategy can be helpful if you
can just plug the answers into a given formula or equation. You
may be able to make a better choice on a difficult problem if
you eliminate choices that you know do not fit into the problem.

• If you cannot determine what the correct answer is, answer
the question anyway. The OGT does not subtract points for
wrong answers, so be sure to fill in an answer for every question.
It works to your advantage because you could guess correctly
and increase your score.
 

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Table of Contents

Introduction
About This Book
About the Test
How to Use This Book
Overview of the OGT in Mathematics
Standards
Test-Taking Strategies
 

Chapter 1: Numbers, Number Sense, and Operations, Part 1
Types of Numbers
Rational and Irrational Numbers
Absolute Value
Equivalent Numbers
Let’s Review 1: Equivalent Numbers
Powers
Scientific Notation
Square Roots and Radicals
Let’s Review 2: Equivalent Numbers
Chapter 1 Practice Problems
Chapter 1 Answer Explanations

Chapter 2: Numbers, Number Sense, and Operations, Part 2
Estimation
Let’s Review 3: Estimation
Ratios
Proportions
Powers
Let’s Review 4: Ratios, Proportions, and Powers
Computing Money Problems
Let’s Review 5: Computing Money Problems
Chapter 2 Practice Problems
Chapter 2 Answer Explanations

Chapter 3: Data Analysis and Probability, Part 1
Probability
Let’s Review 6: Probability
Combinations
Let’s Review 7: Combinations
Mean, Median, Mode, and Range
Let’s Review 8: Mean, Median, Mode, and Range
Chapter 3 Practice Problems
Chapter 3 Answer Explanations

Chapter 4: Data Analysis and Probability, Part 2
Line Graphs
Bar Graphs
Circle Graphs
Venn Diagrams
Let’s Review 9: Graphs
Scatter Plots
Box-and-Whisker Plots
Stem-and-Leaf Plots
Bias
Let’s Review 10: Plots
Chapter 4 Practice Problems
Chapter 4 Answer Explanations

Chapter 5: Geometry and Spatial Sense, Part 1
Congruent Figures
Plane Figures
Three-Dimensional Figures
Let’s Review 11: Figures
Lines and Angles
Line and Angle Relationships
Let’s Review 12: Lines and Angles
Triangles
Pythagorean Theorem
Let’s Review 13: Triangles
Chapter 5 Practice Problems
Chapter 5 Answer Explanations

Chapter 6: Geometry and Spatial Sense, Part 2
The Coordinate Plane
Let’s Review 14: The Coordinate Plane
Transformations
Let’s Review 15: Figure Transformations
Nets
Slope
Let’s Review 16: Nets and Slope
Chapter 6 Practice Problems
Chapter 6 Answer Explanations
 
Chapter 7: Measurement
Similar Figures
Let’s Review 17: Similar Figures
Perimeter
Circumference
Central Angles
Let’s Review 18: Perimeter and Central Angles
Area
Volume
Surface Area
Multi-step Problems
Let’s Review 19: Area and Volume
Chapter 7 Practice Problems
Chapter 7 Answer Explanations
 
Chapter 8: Patterns, Functions, and Algebra
Expressions.  
Equations
Inequalities
Let’s Review 20: Equations and Expressions
Patterns
Linear Equations
Functional Relationships
Let’s Review 21: Linear Equations and Functional Relationships
Inverse Relationships
Rate of Change
Let’s Review 22: Rate of Change
Quadratic Functions
Quadratic Equations
Let’s Review 23: Quadratic Equations
Chapter 8 Practice Problems
Chapter 8 Answer Explanations

Practice Test 1
Practice Test 1 Answer Explanations
 
Practice Test 2
Practice Test 2 Answer Explanations
 
Answer Document: Practice Test 1


Answer Document: Practice Test 2

Index
 

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