The Best Test Preparation For The GHSGT: Georgia High School Graduation Test Mathematics

Passing the GHSGT

Mathematics Test

About This Book

This book will provide you with an accurate and complete representation of the Georgia High School Graduation Test (GHSGT) in Mathematics. Inside you will find reviews that are designed to provide you with the information and strategies needed to do well on these tests. Two practice tests are provided, which are based on the official GHSGT. These practice tests contain every type of question that you can expect to encounter on the GHSGT. Following each test, you will find an answer key with detailed explanations designed to help you completely understand the test material.

About the Test

Who Takes These Tests and What Are They Used For?

The GHSGT is given to all students throughout Georgia who have entered the ninth grade since July 1, 1991. It is given to ensure that graduating students have mastered essential core academic content and skills. The test is given in four content areas:  Mathematics, English Language Arts (ELA), Science, and Social Studies.

The GHSGT measures achievement in the skills and competencies outlined in the Georgia Performance Standards (GPS). Students must pass the test in order to earn a high school diploma; however, students who do not pass the test the first time are given many retest opportunities to pass the test and graduate in the spring of their GHSGT Mathematics twelfth-grade year. Those who fail to pass the test at this point, but have met all the other requirements necessary for graduation, may be able to obtain a Certificate of Performance or a Special Education Diploma. Students who leave school with either of these documents may retest again as often as necessary to obtain a high school diploma.

Is There a Registration Fee?

No. Because all Georgia public high school students are required to take and pass the GHSGT and GHSWT in order to receive a high school diploma, no fee is required.

When and Where Is the Test Given?

The GHSGT is administered to Georgia high school students for the first time in their eleventh-grade year. The GHSGT is administered in the spring, with retest opportunities in the following fall. Students will have five opportunities to take the GHSGT in each content area before the end of their twelfth-grade year.

Test Accommodations and Special Situations

Every effort is made to provide a level playing field for students with disabilities taking the GHSGT and seeking a standard high school diploma. Waivers and variances are made for students who meet certain criteria.

A waiver is a decision by the State Board of Education (SBOE) not to apply all or part of the requirements of the GHSGT to a Georgia student who meets certain basic qualifications, such as:

* A disability, documented in a student’s Individual Education Program (IEP), that makes the student incapable of passing a section of the test, even with specified testing accommodations.

*A substantial hardship beyond the student’s control that has prohibited the student from having a reasonable opportunity to pass a section of the GHSGT.

An accommodation is an adjustment that is made to the testing situation based on a disability and identified in a student’s IEP. Accommodations may include adjustments in the test setting, the amount of time provided in which to take the test, the way in which the test is administered, or the need for assistive technology.

A variance is a decision by the State Board of Education (SBOE) to modify all or part of the literal requirements for the GHSGT for students who have

* attempted the relevant section(s) of the GHSGT four or more times without passing and the most recent attempt is within the last calendar year; and

* successfully completed a structured remedial class(es) after each required attempt to pass the relevant section(s) of the GHSGHT; and

* passed any three of the graduation tests (four content sections of the GHSGT); and

* met the attendance and course requirements for graduation defined by the SBOE for the student’s graduating class; and if the students has a 90 percent or better attendance record, excluding excused absences, while enrolled in grades 9–12; and

* at any time obtained a scaled score that falls within one standard error of measurement (SEM) for passing the relevant section of the GHSGT; and

* successfully passed each of the End-of-Course Tests (EOCT) related to the sections of the GHSGT in which the variance is being sought.

Federal law requires that students with disabilities must participate in statewide assessments such as the GHSGT. Students seeking a waiver or variance must request consideration for a waiver through their local superintendent. More information on variances and waivers may be obtained at the Georgia Department of Education website at www.doe.k12.ga.us. Additional resources to help you prepare to take the GHSGT may also be found on this website. Students may also ask questions of their school counselors.

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 you 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 GHSGT.

When Should I Start Studying?

It is never too early to start studying for the GHSGT—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.

Overview of the GHSGT

The sixty multiple-choice questions on the mathematics portion of the GHSGT

are based on four broad strands, which are broken down into smaller standards:

Strand 1 standards focus on Number and Computation.

Strand 2 standards focus on Data Analysis.

Strand 3 standards focus on Measurement and Geometry.

Strand 4 standards focus on Algebra.

ITEM TYPES

Number and Computation, Data Analysis, Measurement and Geometry, Algebra

Item Type: 1  

Stimulus Characteristics: Direct question requiring recall of facts and definition

Cognitive Level: Low                 

Correct Response Characteristics:Demonstrates knowledge of facts and basic ideas

Item Type: 2

Stimulus Characteristics:  Direct question requiring some interpretation or simple computation (one-step problem)

Cognitive Level:  Medium

Correct Response Characteristics:Demonstrates ability to substitute values in formulas  and equations; identifies appropriate operation, unit of measure, type of graph, or geometric figure; applies problem solving skills to real-word situations

Item Type: 3

Stimulus Characteristics:Direct questioning requiring application of mathematical theories, analysis, or more complicated problem situations (two- and three step problems), evaluating data and drawing conclusions

Cognitive Level: High

Correct Response Characteristics:  Demonstrates the ability to solve complex problems, analyze data, apply mathematical principles to real-world situations, differentiate between correct and incorrect responses

NOTE:

Cognitive levels are based on learning expectations, not item difficulty, although the higher-level items generally prove to be more difficult.

Low: Requires recognition only and typically deals with terminology, identification, or other low-level activities

Medium: Requires some degree of interpretation of a problem or situation in which a mathematical principle is applied

High:Requires a significant degree of interpretation, problem solving, and analysis (e.g., devising a solution to a problem by applying a mathematical principle)

Summary of Mathematics Test Content

The following are standards from the Quality Core Curriculum in mathematics.

Strand 1: Number and Computation (17–19% of the test),

Chapters 1 and 2

1. Expresses numbers in equivalent and approximate forms and orders these forms, using appropriate tools such as calculators (includes fractions, decimals, percent; scientific notation; square and cube roots, and second and third powers of whole numbers; approximations of fractions, decimals, and percents).

2. Recognizes, describes, and applies certain patterns for addition and multiplication.

3. Selects and uses problem-solving strategies and computational tools (mental computation, calculator, estimation, paper and pencil) to solve simple problems involving career, consumer, and leisure applications, and evaluates reasonableness of results.

4. Determines amounts of money, including price, amounts of change, discounts, sales prices, sales tax, interest, and best buy.

5. Uses estimation strategies such as rounding, front-end estimation, clustering, grouping, adjusting, compensation, and reference point to predict computational results.

6. Uses estimation and approximation to check the reasonableness of computational results.

7. Recognizes appropriate practical situations in which to use and to expect results with exact and approximate numbers.

Strand 2: Data Analysis (19–21% of the test), Chapters 3 and 4

8. Uses probability correctly to predict outcomes of given events, determines the probability of an event through experiments, and differentiates odds from probability.

9. Collects (through surveys and experiments) and organizes data into tables, charts, graphs, and diagrams.

10. Organizes information by using tables, charts, and a variety of graph types with appropriate labels and scales, and interprets displays such as those found in public media.

11. Reads and interprets tables, charts, graphs, and diagrams.

12. Recognizes a wide variety of occupational situations in which information is gathered and displayed, using tables, charts, and graphs.

Passing the Georgia High School Graduation Test

13. Determines the mean, median, mode, and range of data, and uses

these measures to describe the set of data.

14. Applies simple statistical techniques to problem-solving situations.

Strand 3: Measurement and Geometry (32–34% of the test),

Chapters 5, 6, and 7

15. Estimates measures in both customary and metric systems.

16. Estimates and solves problems involving measurement, including selecting appropriate tools such as calculators or mental calculation.

17. Applies customary or metric units of measure to determine length, area, volume/capacity, weight/mass, time, and temperature (includes evaluating reasonableness and precision of results, and reading different scales).

18. Identifies items from real life that commonly are measured in metric, in customary, or in both systems of units, as well as recognizing the appropriate-sized units to use.

19. Identifies and differentiates between similar and congruent figures, and identifies figures that have been transformed by rotation, reflection, and translation.

20. Uses proportions to find missing lengths of sides of similar figures, and to enlarge or reduce figures.

21. Solves problems involving similar figures and scale drawings.

22. Graphs points in the coordinate plane, identifies the coordinates, and uses the concept of coordinates in problem situations, such as reading maps.

23. Finds the perimeter and area of plane figures (such as polygons, circles, composite figures) and surface area, and the volume of simple solids (such as rectangular prisms, pyramids, cylinders, cones, spheres).

24. Calculates perimeter and area of plane figures; finds appropriate measures of objects and their models prior to such calculations for basic polygons and circles.

25. Identifies lines, angles, circles, polygons, cylinders, cones, rectangular solids, and spheres in everyday objects.

26. Applies geometric properties—such as the sum of the angles of a polygon property, percent of area of a circle determined by the central angle measure in a pie chart, or parallel sides and angle relations for parallelograms—to practical drawings.

27. Draws and measures angles; determines the number of degrees in the interior angles of geometric figures, such as right and straight angles, circles, triangles, and quadrilaterals; and classifies angles (right, acute, obtuse, complementary, supplementary) and triangles (right, acute, obtuse, scalene, isosceles, and equilateral).

28. Uses the Pythagorean theorem to solve problems (includes selecting appropriate tools such as the calculator).

29. Applies ratios to similar geometric figures, as in scale drawings, as well as with mixtures and compound applications.

Strand 4: Algebra (28–30% of the test), Chapters 8 and 9

30. Simplifies expressions with and without grouping symbols.

31. Evaluates simple algebraic expressions.

32. Substitutes known values in formulas and solves problems with formulas.

33. Identifies and applies mathematics to practical problems requiring direct and inverse proportions.

34. Translates words into simple algebraic expressions and equations.

35. Solves simple equations, including addition, subtraction, multiplication, division, proportions, and two-step equations.

36. Identifies ratio and proportion as they appear in applied situations and solves proportions for missing numbers in applied problems.

37. Solves linear inequalities in one variable and graphs the solution set on the number line.

38. Graphs a linear equation in two variables.

39. Finds the slope and intercepts of a graphed line.

40. Solves problems that involve systems of two linear equations in two variables.

Test-Taking Strategies

What to Do Before the Test

* Pay attention in class.

* Carefully work through the review sections 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 GHSGT Mathematics. 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. They may be able to help you learn some useful strategies that will help you feel more relaxed, so that you can do your best on the test.

What to Do During the Test

* 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 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, since there will only be two choices left from which to make your guess. 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 on 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. 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.

* 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 an educated guess after eliminating choices that you know do not fit into the problem.

* If you cannot determine what the correct answer is, guess anyway. The GHSGT 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.

The Day of the Test

On the day of the test, you should wake up early (it is hoped after a decent night’s rest) and have a good breakfast. Make sure to dress comfortably, so that you are not distracted by being too hot or too cold while taking the test. Make sure to give yourself enough time to arrive at your school early. This will allow you to collect your thoughts and relax before the test, and will also spare you the anguish that comes with being late.