INTRODUCTION
What is a standardized test?
Standardized tests (e.g., SAT, ACT, GRE, GMAT etc.) are aptitude tests to assess the proficiency of students for a given course of study. The scores obtained in standardized tests are supposed to predict individual success in job or profession after completing the course. For example, research shows that the Graduate Management Admission Test (GMAT) is a valid predictor of students’ 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 evaluation for two subjects: English and Math. The first part of English, often called verbal ability test, assesses test-takers ability to read and write grammatically correct English. Several years of reading text-books, writing papers, speaking in front of the class at elementary and high schools allows standardized test takers to score well without much effort.
Math in Standardized Tests
The standardized test on Math, on the other hand, is not as natural or easy as the English part. Students often receive less than satisfactory training in developing their mathematical abilities and the format of the questions does not help either. For example, how often does one have to figure out the probability of a number to be odd when a two-digit number is chosen at random. Or what is average speed of Jack in total, when Jack drove one way at rate of 40 mph, and returned at rate of 50 mph?
The standardized exam may be composed of its own format of math questions. The Math section, sometimes called Quantitative section, can have questions of the following types: Problem Solving, Data Sufficiency, Data Comparison, Graphical Problems, and Grid-Ins. Despite quantitative problems appearing in numerous forms, they test a limited number of concepts. The concepts can be categorized in 3 broad sections of Math: Arithmetic, Algebra, and Geometry.
- Arithmetic section
Most standardized tests give considerable importance to the arithmetic concepts such as Percent, Ratio, Average, and Numbers. The arithmetic section often makes for 50% or over part 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 portion of the Math section is about 50%.
- Algebra section
In terms of the number of questions asked in the test, Algebra is not as important. The areas tested in the Algebra are: Solving Simple Equations, Binomial Theorem & Quadratic Equations, and Advance Algebra with Inequalities. About 15% to 25% of problems are from Algebra section of Math. The percentage distribution may vary for different exams.
- Geometry section
Test-makers prefer to make questions in Geometry in many different forms and flavors. The basic concepts tested in this area come from: Angles & Triangles, Squares & Rectangles, Circles, Co-ordinate, and Solid Geometry. Even though advance questions require knowledge and practice with important concepts, the easier problems are often intuitive and aptitude based. In any given standardized Math test, about 20% to 40% of all questions are from the Geometry section. In SAT exam, about 35% pf questions are from the Geometry. In the GMAT exam only 20% of all questions are Geometry problems.
Miscellaneous Problems
Makers of standardized tests have a special liking for oddball questions. These questions are derived from concepts of more than one topic and often require common sense besides basic section concepts. It is not uncommon to find a problem on a geometrical figure, which can be resolved into an algebraic expression with some simple common sense method. In the world of GMAT and GRE, the category of miscellaneous problems is called Word Problems. The key to do well in this section is two-fold: (1) Know the basics of Arithmetic, Algebra, and Geometry; (2) Apply common sense to translate the given information and the question in the form of mathematical equations.
FORMAT OF MATH PROBLEMS
Math problems in standardized tests are almost always in the objective multiple choice question form. The Grid-in questions in the SAT exam are an exception. The usual format includes a description of problem with one or more useful piece of information. A question statement follows the given information. Then the problem is followed by 4 or 5 answer choices.
Students taking the test are required to utilize the given information in answering the question statement. The answer thus found is one among many options. There is no single strategy to solve a multiple-choice math problem. Experts usually recommend one or more of the following methods,
- Plugging numbers: Helps avoid complex algebraic calculations
- Back solving: Taking the help of answer choices to eliminate wrong options
- Eye-balling & approximating: Helpful in simple geometrical problems
- Intelligent guessing: Eliminating unlikely answers to decrease options
The strategies described above work best when test-takers are equipped with basic concepts of Arithmetic, Algebra, & Geometry, and invest time & effort in practicing sample questions in actual exam like format.
Other formats of Math problems (e.g., Data sufficiency in GMAT, Grid-in in SAT, Graph in GRE & SAT) form a small percentage of all questions in the test. Students are advised to develop their own strategy for such questions. Once again, knowing the basics and practicing with such problems is the key for doing well in such problems.
Sample Example Problems:
1. After 20% discount, due to Christmas sale, the price of a book is $40. What is the total saving than usual price, for Jim, when he purchases two volumes of the book in discount sale?
A. 100
B. 50
C. 40
D. 20
E. 10
2. In the year 2000, Mary was twice as old as her sister Sally. In the year 2008, Mary will be 5 yeas older than Sally. What is the age of Mary now (in year 2007)?
A. 6
B. 10
C. 17
D. 18
E. 20
3. The numerical value of the ratio of area and circumference of a circle is 2. What is the diameter of the circle?
A. 4
B. 8
C. 16
D. 18
E. 32
Answers:
1. D
2. C
3. B