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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

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Origins of the word balloon

The word balloon was originally derived from the French word ballon, meaning large ball. This was in turn probably derived from the latin ballone, or possibly from the old German word balla, meaning ball. Other related words include the Middle English bal, which was probably from the Old English beall, both meaning ball.

History of balloons

Early balloons were made out of animal bladders and intestines (yuk!) and often used by jesters who would manipulate them into amusing shapes for entertainment. Galileo also inflated a pig’s bladder in an experiment to measure the weight of air.
Modern balloons can be made from materials such as rubber, latex or plastic some use metallic coatings for added shine.

Rubber balloons

The first rubber balloons called “caoutchoucs” were invented by Michael Faraday in 1824 and used in his experiments with hydrogen. He made his balloons simply by cutting out two sheets of rubber, placing them on top of each other and pressing the edges together. The sticky rubber welded automatically and he rubbed the inside of the balloon with flour to prevent the opposing surfaces joining together.

Latex balloons

Today’s more familiar latex balloons, made from a highly flexible substance extracted from plants, were first manufactured in London in 1847, by J.G. Ingram, but it is only the 1930s that we started to mass produce latex balloon.

Foil balloons

Beginning in the late 1970s, some more expensive (and longer-lasting) foil balloons have been made of thin, un-stretchable, less permeable aluminised plastic films which keep the helium gas from escaping for several days.

Foil balloons are also light weight which increases buoyancy.

Foil balloons are not elastic like rubber balloons, so when detailed and colourful pictures printed on their surfaces, they are not distorted when the balloon is inflated.

Important: metallic or foil balloons could cause short circuits when caught in overhead power lines and should never be released in the environment.

bigfatballoons.co.uk Helium balloons

Initially hydrogen was used to make balloons float. However, it easily explodes and is highly flammable so understandably it was used mainly for scientific experiments.

Hydrogen was eventually replaced by helium. Helium is a non-toxic, non flammable, inert gas that occurs naturally in the air we breathe and is also found underground it has 92.64% of the lifting power hydrogen.
Although considered a safe gas, it should never be inhaled intentionally as it can cause suffocation.

Increased safety due to the use of helium meant it was possible to use balloons in new ways.

When latex balloons are filled with helium they typically retain their buoyancy for only a day or so. The helium gas escapes through small pores in the latex which are larger than the helium atoms. You can treat latex balloons with a hi-float gel that makes them less porous and helps keep the helium in the balloon.

Latex balloons filled with air usually hold their size and shape much longer.

Foil and plastic balloons are less permeable and can float anything from 5 days to 5 weeks depending on size and material used for manufacture.

Balloons are not just for fun

Balloons’ properties, including their low density and relatively low cost, have led to a wide range of applications. While some balloons are purely decorative, others are used for specific purposes such as meteorology, medical treatment, military defence, or transportation.

For instance, on the 18th of September 2006 three Cambridge University Engineering students made the headlines after they successfully sent a camera to the edge of space for less than £1,000 using a helium balloon.

They simply attached the tiny camera to a helium balloon, which flew to nearly four times the height of Everest. Throughout the flight it took more than 800 images showing the curvature of the earth.
As the large helium balloon rose it expanded and exactly two hours after lift-off, at an altitude of 32.2km (20m) above sea level, it burst, releasing the camera which was brought back to earth by parachute.

Don’t try this at home…

In 1982, a man with no experience in ballooning or aviation, attached 40 helium-filled balloons to a garden chair hoping to ascend a few hundred feet. Instead, he rose to 16,000 feet over Long Beach in California. Remarkably, despite contacting power lines at landing, Larry Walters survived his flight, although he was fined several thousand dollars by the FAA!!

Closer to home in the UK Herefordshire man, Ian Ashpole made some ascents to 10,000 feet with several hundred large balloons as an advertising promotion for a champagne company in 1997. For safety reasons, Ashpole ascended with his cluster of balloons attached to a hot-air balloon and descended via parachute.

Sophie Baxter lives in the UK with her husband and two children. She runs bigfatballoons.co.uk bigfatballoons.co.uk and online shop that sells helium balloons, teddy bear gifts and chocolates.