Read an Excerpt
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 teststwo at the end of this
book and two onlineeach 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
Is There a Registration Fee?
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
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
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
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
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
H. Use counting techniques, such as permutations and
combinations, to determine the total number of options and
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
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
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
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
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
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
D. Use algebraic representations, such as tables, graphs,
expressions, functions, and inequalities, to model and solve
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,
H. Solve systems of linear equations involving two variables
graphically and symbolically.
I. Model and solve problem situations involving direct and inverse
J. Describe and interpret rates of change from graphical and
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 yo 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
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.