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- Math In Standardized Tests Like The GMAT, GRE, SAT & ACT
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Math In Standardized Tests Like The GMAT, GRE, SAT & ACT
INTRODUCTION
What is a standardized test?
Standardized tests (e.g. SAT, ACT, GRE, GMAT, etc.) are aptitude tests designed to assess students’ competence in a given field of study. Scores on standardized tests should predict individual success in the workplace or profession after completing the course. For example, research shows that the Graduate Management Admission Test (GMAT) is a valid predictor of student performance in an MBA program. Research also supports the proposition of post-MBA career success with GMAT test scores.
Most standardized tests consist of an assessment of two subjects (English and mathematics). The first part of English, often called the Verbal Ability Test, assesses the test takers’ ability to read and write grammatically correct English. Several years of reading textbooks, writing papers, speaking in front of the class in elementary and high school allows standardized test takers to get good results without much effort.
Mathematics in standardized tests
The math standardized test, on the other hand, is not as natural or easy as the English section. Often, students receive less than adequate training to develop their mathematical abilities, and the format of the questions doesn’t help either. For example, how often do you have to figure out how odd the probability is if a two-digit number is chosen at random. Or what is Jack’s total average speed if Jack traveled one way at 40 miles per hour and returned at 50 miles per hour?
A standardized exam may consist of a math question format. The Maths section, sometimes called Quantitative, may have the following types of questions: Problem Solving, Data Sufficiency, Comparing Data, Graphing Problems, and Grids. Despite the many forms of quantitative problems, they test a limited number of concepts. Concepts can be classified into three parts of mathematics: arithmetic, algebra and geometry.
- Arithmetic part
Most standardized tests place significant emphasis on arithmetic concepts such as percentage, ratio, mean, and numbers. The arithmetic portion often makes up 50% or more of the quantitative portion of the test. The number of arithmetic problems in GMAT or GRE math is about 55-60% of the total number of questions. For the SAT and ACT, the arithmetic portion of the math section is about 50%.
- Algebra section
Algebra is not that important in terms of the number of questions asked on the test. Areas tested in algebra are: solving simple equations, binomial theorem and quadratic equations, and developing algebra with inequalities. About 15-25% of the problems come from the Algebra section of Math. The percentage distribution may vary for different exams.
- Geometry section
Test takers prefer to ask questions in geometry in many different forms and flavors. Key concepts tested in this area come from: angles and triangles, squares and rectangles, circles, coordinates, and solid geometry. While preliminary questions require knowledge and practice with important concepts, easier problems are often intuitive and based on aptitude. Every standardized math test has about 20-40% of all questions from the geometry section. About 35% of the pf questions on the SAT exam are geometry. Only 20% of all questions on the GMAT exam have geometry problems.
Various problems
Standardized test takers especially like weird questions. These questions stem from concepts from more than one topic and often require common sense in addition to the basic concepts of the section. It is not uncommon to find a problem in a geometric figure that can be solved into an algebraic expression by some simple common sense method. In the world of the GMAT and GRE, the category of miscellaneous problems is called Word Problems. The keys to doing well in this section are twofold: (1) you know the basics of arithmetic, algebra, and geometry; (2) Use common sense to translate the given information and question into mathematical equations.
MATHEMATICS PROBLEM FORM
Mathematics problems in standardized tests are almost always in the form of objective multiple-choice questions. Grid-in questions on the SAT exam are an exception. A common format includes a description of the problem with one or more helpful pieces of information. The given information is followed by a question sentence. The task is then followed by 4 or 5 answer choices.
Students taking the test are obliged to use the given information when answering the question. The answer thus found is one of many options. There is no single strategy for solving a multiple-choice math problem. Experts usually recommend one or more of the following methods:
- Connecting numbers: helps to avoid complex algebraic calculations
- Resolving back: Using answer choices to eliminate wrong choices
- Prominent and approximate: Helpful in solving simple geometric problems
- A smart guess: Eliminating unlikely answers to reduce choices
The strategies described above work best when test-takers are equipped with basic concepts of arithmetic, algebra, and geometry and invest time and effort in practicing sample questions in the actual exam format.
Other math problem formats (such as Data Sufficiency on the GMAT, Grid-in on the SAT, Graphing on the GRE and SAT) make up a small percentage of all questions on the test. Students are encouraged to develop their own strategy for such questions. Once again, knowing the basics and practicing with such problems is the key to solving such problems.
Sample problems:
1. After the 20% discount, the price of the book is $40 due to the Christmas sale. What is Jim’s savings over the usual price if he buys two volumes of the book on sale?
A. 100
B. 50
C. 40
D. 20
E. 10
2. In 2000, Mary was twice as old as her sister Sally. In 2008, Mary is five years older than Sally. How old is Mary now (in 2007)?
A. 6
B. 10
C. 17
D. 18
E. 20
3. The numerical value of the ratio of the area of a circle to its circumference is 2. What is the diameter of a circle?
A. 4
B. 8
C. 16
D. 18
E. 32
Answers:
1. D
2. C
3. B
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