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Math In Standardized Tests Like The GMAT, GRE, SAT & ACT
What is a standardized test?
Standardized tests (e.g., SAT, ACT, GRE, GMAT, etc.) are aptitude tests to assess student proficiency for a given course of study. Scores on standardized tests are believed to predict individual success in employment or occupation after completing the course. For example, research shows that the Graduate Management Admission Test (GMAT) is a valid predictor of student performance in the MBA program. Studies also support the proposition of post-MBA career successes with GMAT test scores.
Most standardized tests consist of some form of assessment for two subjects: English and mathematics. The first part of English, often referred to as the Verbal Ability Test, assesses candidates’ ability to read and write grammatically correct English. Several years of reading textbooks, writing articles, speaking in front of the class in elementary and secondary schools allow candidates for standardized tests to obtain good results without much effort.
Mathematics in standardized tests
The standardized math test, on the other hand, is not as natural or easy as the English part. Students often receive less than satisfactory training in the development of their mathematical abilities and the question format does not help either. For example, how many times must one determine the probability that a number is odd when a two-digit number is chosen at random. Or what is Jack’s total average speed, when Jack drove one way at 40 mph and back at 50 mph?
The standardized exam may consist of its own format of math questions. The Mathematics section, sometimes referred to as the Quantitative section, may contain questions of the following types: Problem Solving, Data Sufficiency, Data Comparison, Graphing Problems, and Grid-Ins. Despite quantitative problems appearing in many forms, they test a limited number of concepts. The concepts can be classified into 3 major sections of mathematics: arithmetic, algebra and geometry.
- Arithmetic section
Most standardized tests place considerable emphasis on arithmetic concepts such as percent, ratio, average, and numbers. The arithmetic section often makes up 50% or more of a portion of the quantitative section of the test. The number of arithmetic problems in the GMAT or GRE Math is about 55% to 60% of the total number of questions. In the SAT and ACT exam, the arithmetic part of the Math section is around 50%.
- Algebra Section
In terms of the number of questions asked in the test, algebra is not as important. The areas tested in algebra are: solving simple equations, binomial theorem and quadratic equations, and advanced algebra with inequalities. About 15% to 25% of the problems come from the Algebra section of Math. The percentage breakdown may vary between exams.
- Geometry section
Testers prefer to formulate geometry questions in many different forms and flavors. The basic concepts tested in this area come from: Angles and triangles, Squares and rectangles, Circles, Coordinates and Solid geometry. Although the advanced questions require knowledge and practice with important concepts, the easier problems are often intuitive and skill-based. In any standardized math test, about 20% to 40% of all questions come from the Geometry section. On the SAT exam, about 35% of the questions come from geometry. In the GMAT exam, only 20% of all questions are geometry problems.
The creators of standardized tests have a particular taste for bizarre questions. These questions are derived from concepts from more than one topic and often require common sense in addition to the basic concepts in the section. It is not uncommon to find a problem in a geometric figure, which can be solved into an algebraic expression with a simple common sense method. In the world of GMAT and GRE, the category of miscellaneous problems is called Word Problems. The key to doing well in this section is twofold: (1) Knowing the basics of arithmetic, algebra, and geometry; (2) Apply common sense to translate given information and question into mathematical equations.
MATHEMATICS PROBLEM FORMAT
Math problems in standardized tests are almost always in the form of an objective multiple-choice question. An exception is the SAT exam Grid-in questions. The usual format includes a description of the problem with one or more useful information. An interrogative statement follows the given information. Then the problem is followed by 4 or 5 answer choices.
Students taking the test are required to use the information provided to answer the wording of 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,
- Branch numbers: Helps to avoid complex algebraic calculations
- Rear resolution: Take the help of answer choices to weed out bad options
- Eye-ball and approximation: Useful in simple geometric problems
- Smart riddles: Eliminate improbable answers to reduce options
The strategies outlined above work best when test takers are equipped with the basic concepts of arithmetic, algebra, and geometry, and invest time and effort in practicing sample questions in a similar format. to a real exam.
Other math problem formats (e.g. Data Sufficiency in GMAT, Grid-in in SAT, Graph in GRE & SAT) make up a small percentage of all questions on the test. Students are advised to develop their own strategy for these questions. Again, knowing the basics and practicing with such problems is the key to success in such problems.
Examples of problems:
1. After 20% off, due to Christmas sale, the price of one book is $40. What is the total saving over regular price for Jim when he buys two volumes of the book on sale?
2. In the year 2000, Mary was twice the age of her sister Sally. In 2008, Mary will be 5 years older than Sally. How old is Mary now (in 2007)?
3. The numerical value of the ratio of the area and the circumference of a circle is 2. What is the diameter of the circle?
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