Exponents and radicals (Understanding Exponents)

Exponents and radicals are a core skill when it comes to transitioning to algebra, and many students struggle with the way that the concepts are presented in texts. Some have a hard time differentiating between exponents and multiplication as well as radicals and division.

Understanding Exponents

Using visual aids such as marbles is a great way to wrap your head around the idea of exponents. If you have two marbles in a group and there are three groups, then there are six marbles all together. This is like saying 3 groups of 2 makes 6, a multiplication problem. If you think, ___ x___ , the numbers represent what goes in the blanks. Exponents are a special type of multiplication where the exponent represents how many blanks there are instead of what goes in them. The base is the big number and the exponent, or power, is the small number. If you have 2 to the fourth power, that means you have four blanks: ___ x ____ x ____ x ____. The base goes in every blank, so 2 to the fourth power is 2 x 2 x 2 x 2. To represent this with marbles, think two groups with two groups in each with two groups in each of those and with two marbles in each of the last groups. Draw circles for the groups: two big ones with two smaller ones in each, two tiny ones in each of those, and two marbles in each tiny circle. Notice that numbers get bigger much faster with exponents than with multiplication.

GRE - Math (Arithmetic)

Arithmetic operations

The basic arithmetic operations are addition, subtraction, multiplication and division, although this subject also includes more advanced operations, such as manipulations of percentages, square roots, exponentiation, and logarithmic functions.

Arithmetic is performed according to an order of operations. The standard order of operations, or precedence, is expressed in the following chart:

1. terms inside brackets
2. exponents and roots
3. multiplication and division
4. addition and subtraction

This means that if a number or other symbol, or an expression grouped by one or more symbols of grouping, is preceded by one operator and followed by another, the operator higher on the list should be applied first.

Any set of objects upon which all four arithmetic operations (except division by zero) can be performed, and where these four operations obey the usual laws, is called a field. In abstract algebra, a field is an algebraic structure with notions of addition, subtraction, multiplication, and division, satisfying certain axioms. The most commonly used fields are the field of real numbers, the field of complex numbers, and the field of rational numbers, but there are also finite fields, fields of functions, various algebraic number fields, p-adic fields, and so forth.

How can uCertify help you prepare for the GRE-Math?

uCertify’s GRE-Math Prepkit is designed to help you prepare for this section of the overall exam, from the simple, easy to use GUI to the practice questions that closely mimic those you will encounter on the actual GRE. With their Prepkits, you will get plenty of practice questions that will help you prepare thoroughly for the exam. Practice tests contain questions in random order from all the three sections (Multiple Choice,

Numeric Entry, Quantitative Comparison)

Explanations for both correct and incorrect answer options help you understand the concept being tested by the question

1. Interactive quizzes
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3. Flash cards to help reinforce key concepts
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Cracking the GRE, uCertify way

uCertify's Prepkits contain enough material for you to practice on the topics that are being questioned in the real exam. They cover all the topics and subjects on which the questions come in the real exam. Their kits contain various kinds of simulation questions, study notes, and practice tests that will help you gain good marks in the test.

GRE Questions ( Analytical Reasoning)

Directions:All GRE sample analytical reasoning questions are based on a passage or set of conditions. While answering a few of the GRE sample analytical reasoning questions, you would find it useful to draw a rough diagram. To answer any question choose the answer you think is most appropriate among the given options.

Questions 

Three men (Tom, Peter and Jack) and three women (Eliza, Anne and Karen) are spending a few months at a hillside. They are to stay in a row of nine cottages, each one living in his or her own cottage. There are no others staying in the same row of houses.

1.        Anne, Tom and Jack do not want to stay in any cottage, which is at the end of the row.

2.        Eliza and Anne are unwilling to stay besides any occupied cottage..

3.        Karen is next to Peter and Jack.

4.        Between Anne and Jack’s cottage there is just one vacant house.

5.        None of the girls occupy adjacent cottages.

6.        The house occupied by Tom is next to an end cottage.

1.        Which of the above statements can be said to have been derived from two other statements ?

A.        Statement 1

B.        Statement 2

C.        Statement 3

D.        Statement 5

E.        Statement 6

Ans : D

2.        How many of them occupy cottages next to a vacant cottage ?

A.        2

B.        3

C.        4

D.        5

E.        6

Ans : C

3.        Which among these statement(s) are true ?

                                 I.            Anne is between Eliza and Jack.

                                II.            At the most four persons can have occupied cottages on either side of them. .

                              III.            Tom stays besides Peter.

A.        I only

B.        II only

C.        I and III only

D.        II and III only

E.        I, II and III

Ans : C

GRE ( Sentence Completion)

The __ tones of the flute succeeded in __ his tense nerves.

1. rhapsodic - minimising

2. blatant - enhancing

3. hovendous - calming

4. vibrant - portraying

5. mellifluous - soothing

Ans :E

Without the psychiatrist's promise of confidentiality, trust is __ and the patient's communication limited; even though confidentiality can thus be seen to be precious in thercopy, moral responsibility sometimes requires a willingness to __ it.

1. lost - forget

2. implicit - extend

3. impaired - sacrifise

4. ambiguous - apply

5. assumed - examine

Ans :C

Parts of seventeenth-century Chinese pleasure gardens were not necessarily intended to look __ they were designed expressly to evoke the agreeable melancholy resulting from a sense of the __ of natural beauty and human glory.

1. great - immutability

2. joyful - mortality

3. conventional - wildness

4. cheerful - transitoriness

5. colorful - abstractness

Ans :D

Despite the __ of many of their colleagues, some scholars have begun to emphasize ''pop culture'' as a key for __ the myths, hopes, and fears of contemporary society.

1. pedantry - reinstating

2. enthusiasm - symbolizing

3. skepticism - deciphering

4. antipathy - involving

5. discernment - evaluating

Ans :C

Clearly refuting sceptics, researches have __ not only that gravitational radiation exists but that it also does exactly what the theory __ it should do.

1. supposed - asserted

2. voubted -warranted

3. assumed - deduced

4. demonstrated - predicted

5. estimated - accepted

Ans :D

The Neolatonists' conception of a deity, in which perfection was measured by abundant fecundity, was contradicted by that of the Aristotelians, in which perfection was displayed in the __ of creation.

1. variety

2. economy

3. profusion

4. clarity

5. precision

Ans :B

It is a great __ to be able to transfer useful genes with as little extra gene material as possible, because the donor's genome may contain, in addition to desirable genes, many genes with __ effects.

1. Disappointment - superfluous

2. Convenience - exquisite

3. Advantage - deleterious

4. Accomplishment - profound

5. Misfortune - unpredictable

Ans :C

While admitting that the risks incurred by use of the insecticide were not - the manufacturer's spokesperson argued that effective __ were simply not available.

1. indeterminable - safeguards

2. unusual - alternatives

3. inconsequential - substitutes

4. proven - antidotes

5. increasing - procedures

Ans :C

Human reaction to the realm of though is often as strong as that to sensible presences; our higher moral life is based on the fact that __ sensations actually present may have a weaker influence on our action than do ideas of __ facts.

1. emotional - impersonal

2. familiar : symbolic

3. disturbing - ordinary

4. material - remote

5. defenitive - controvoisial

Ans :D

GRE ( Sentence Completion)

Sentence Completions

That the Third Battalion's fifty percent casually rate transformed its assault on Hill 306 from a brilliant stratagem into a debacle does not ___ eyewitness reports of its commander's extra-ordinary ___ in deploying his forces.

1. invalidate - brutality

2. gainsay - cleverness

3. underscore - ineptitude

4. justify - rapidity

5. corroborate -determination

Ans : B

No longer __ by the belief that the world around us was expressly designed for humanity, many people try to find intellectual __ for that lost certainty in astrology and in mysticism.

1. satisfied - reasons

2. reassured - justifications

3. restricted - parallels

4. sustained - substitutes

5. hampered - equivalents

Ans : D

In eighth-century Japan, people who __ wasteland were rewarded with official ranks as part of an effort to overcome the shortage of __ fields.

1. cultivated - domestic

2. located - desirable

3. conserved - forested

4. reclaimed - arable

5. irrigated - accessible

Ans :D

Clearly refuting sceptics, researchers have __ not only that gravitational radiation exists but that it also does exactly what the theory __ it should do.

1. assumed - deducted

2. estimated - accepted

3. supposed - asserted

4. doubted - warranted

5. demonstrated - predicted

Ans :E

Melodramas, which presented stark oppositions between innocence and criminality, virtue and corruption, good and evil, were popular precisely because they offered the audience a world __ of __.

1. deprived - polarity

2. full - circumstantiality

3. bereft - theatricality

4. devoid - neutrality

5. composed - adversity

Ans :D

Sponsors of the bill were __ because there was no opposition to it within the legislative, until after the measure had been signed into law.

1. well-intentioned

2. persistent

3. detained

4. unreliable

5. relieved

Ans :B

Ecology, like economics, concerns itself with the movement of valuable __ through a complex network of producers and consumers.

1. nutrients

2. dividends

3. communications

4. artifacts

5. commodities

Ans :C

Having fully embraced the belief that government by persuasion is preferable to government by __ the leaders of the movement have recently __ most of their previous statements supporting totalitarianism.

1. proclamation - codified

2. coercion - repudiated

3. participation - moderated

4. intimidation - issued

5. demonstration - deliberated.

Ans :B

It would be difficult for one so __ to be led to believe that all men are equal and that we must disregard race, color and creed.

1. tolerant

2. democratic

3. broadminded

4. emotional

5. intolerant

Ans :E

Many philosophers agree that the verbal aggression of profanity in certain redical newspapers is not - or childish, but an assault on - essential to the revolutionary's purpose.

insolent - sociability

trivial - decorum

belligerent - fallibility

serious - propriety

deliberate - affectation.

Ans :B