excel de resumo de estudo para teste de matemática do gre (2014)

Termo/notação

Factor RemainderPrime numberComposite numberOnes/Units digitTens digitHundreds digitThousands digitTenths digitHundredths digitThousandths digit4 3/8 is 35/8-10 1/2 is -21/20!=10^0 is not definedf(g(x))Similar trianglesCongruent trianglesHypotenuseLegs of a triangleOpposite sides of a lineRight anglex-interseptCurly bracketDisjoint setsMean Value

MedianValue

Mode value

RangeInterquartile rangeQuartilePercentile

Outcome

(Population) Standard Deviation

Sample Standard Deviation

Mean of a random variable

FulcrumRevenueProfitQuartBoxplotScatter PlotYield1 mile = 5280 feet

RadiusIrrational numbersRatio of A to BPrime factorizationLike termsQuadratic equation(xâ)(x^b)=x^(a+b)(xâ)( yâ)=(xy)â(xâ)^b=x^(ab)Fatorar expressões de segundo grau (ver métodos 1 e 2): http://pt.wikihow.com/Fatorar-Polin%C3%B4mios-de-Segundo-Grau-(Equa%C3%A7%C3%B5es-Quadr%C3%A1ticas)Simple interest rate

Compound interest rate


Simetria em relação ao y=x

The graph of h(x)+c is the graph of h(x) shifted upward by c units. The graph of h(x)−c is the graph of h(x) shifted downward by c units. The graph of h(x+c) is the graph of h(x) shifted to the left by c units. The graph of h(x−c) is the graph of h(x) shifted to the right by c units.Fatores notáveis


Mean and median of a continuous random variable

Vírgula é ponto e ponto é vírgula (português para inglês)

Dicas de convenções

Ratios (ver segundo exercicio)

Significado

Fator (número inteiro pelo qual um outro número inteiro é divisível)Resto de uma divisão. É sempre positivoNúmero primo (maior que um)Número maior que um que não é primoDígito da unidadeDígito da dezenaDígito da centenaDígito do milhar0.X0.0X0.00X4*(8/8) + 3/8-(10*(2/2)+1/2)Zero fatorial é igual a 1

Composition of f with gTwo triangles that have the same shape but not necessarily the same sizeTwo triangles that have the same shape and sizeHipotenusaCatetosDe um lado da linha e do outro lado da linhaÂngulo retoThe insersection of a graph at the x-axis in a coordinate system{}If A and B have no elements in common, they are called disjoint sets or mutually exclusive sets.

The median of an odd number of data is the middle number when the data arelisted in increasing order; the median of an even number of data is the arithmeticmean of the two middle numbers when the data are listed in increasing order.

Diferença entre o maior e menor número da listathird quartile minus the first quartile (o que está entre o primeiro e terceiro quartis?)3 números que dividem uma lista em 4 partes iguais (baseado em medianas)99 números que dividem uma lista em 100 partes iguais (baseado em medianas)

For a list of data, where the arithmetic mean is denoted by m, the standarddeviation of the data refers to the nonnegative square root of the mean of thesquared differences between m and each of the data. This statistic is also knownas the population standard deviation and is not to be confused with the samplestandard deviation.

The same of the population standard deviation, but, as opposed to dividing by (n), divide by (n-1)Result

Value that occurs more often (if there isn't repeated values, then there is no mode value. Also, there may be more than one mode)

The mean of the random variable X is the sum of the products XP(X) for all values of X. It's also called the expected valueor the mean of the probability distribution.

The mean of a continuous random variable X is the point m on the x-axis at whichregion under the distribution curve would perfectly balance if a fulcrum wereplaced at x=m. The median of X is the point M on the x-axis at which the linex=M divides the region under the distribution curve into two regions of equalarea.Fulcro, eixoReceitaRevenue minus costMedida de volume: Aproximadamente 946,35mlDiagrama de Caixa (usa teoria da divisão por quartis)Gráfico de dispersãoResulta

Raio de um círculoNumber that do not terminate neither repeat.A/BFactors of a number that are only composed by prime numbersTerms in na equation that have the same variablesVariables are to a maximum power of two

Fatorar expressões de segundo grau (ver métodos 1 e 2): http://pt.wikihow.com/Fatorar-Polin%C3%B4mios-de-Segundo-Grau-(Equa%C3%A7%C3%B5es-Quadr%C3%A1ticas)

V=P(1+r/100)^t

Trocar o x por y e o y por x na equação. The graph of h(x)+c is the graph of h(x) shifted upward by c units. The graph of h(x)−c is the graph of h(x) shifted downward by c units. The graph of h(x+c) is the graph of h(x) shifted to the left by c units. The graph of h(x−c) is the graph of h(x) shifted to the right by c units.

(a+b)² = a² + 2ab + b²; (a-b)² = a² - 2ab + b²; a² - b² = (a+b)(a-b)


IMPORTANTE! VOCÊ JÁ CONFUNDIU ISSO E ERROU. ERA QUESTÃO DE ENTRADA NUMÉRICA, AÍ NÃO TEM NEM ITEM PRA CONFERIR A ORDEM DE GRANDEZA!

V=P(1+rt/100); sendo r o juros em percentagem

V=P(1+r/(100*n))^(n*t); sendo r o juros em um período e n o número de vezes neste período que o juros é contabilizado. As the compounding period decreases (when "n" is bigger), the final ammount of money is greater!

http://www.ets.org/s/gre/pdf/gre_math_conventions.pdf

Exemplo

the integer 4 has six factors: −4, −2, −1, 1, 2, and 4-17/4 resulta -3 com resto +42,3,5,7,11, etc2,4,6,7,9,10, etc

585=(3^2)*(5)*(13)In w3z+5z2−z2+6; the terms 5z2 and −z2 are like terms


Se é dado o juros anual "r", para saber o mensal, utilizamos n=12, ou seja, dividimos os juros por 12, e contabilizamos a cada mês (por isso multiplicada o expoente por 12).

y=x^2 e y=raiz(x) são simétricas em relação a x=y, assim y=raiz(x) é uma parábola na origem com a abertura para o lado direito.

O que pode ser assumido e o que não pode? Por exemplo, se não especificado, medidas de distâncias e ângulos não podem ser assumidos maiores ou menores que outros, mesmo que pareçam ser.

Termo/notação

Geometry

Regular polygon

Área trapézio

Área paralelogramo = b*h

Área triângulo equilátero

Área triângulo qualquerAltitude

Propriedade de triângulos


If a polygon has n sides, it can be divided into n−2 triangles

the sum of the measures of the interior angles of an n-sided polygon is (n−2)(180 )

A polygon is inscribed in a circle if all its vertices lie on the circle, or equivalently,the circle is circumscribed about the polygon

Propriedade de triângulos (cai bastante - figuras ficam fora de escala, tem que imaginar bem ou desenhar)

Circle Properties

Speacial Right triangles

Similar triangles

Rhombus

Área de losango (2 formas)

Convex polygonRegular polygonPythagorean triples

Diagonais de losangos formam ângulo reto

Geometry Strategies

Dicas de convenções

Significado

All the internal angles are equal

A=(1/2)*(b1+b2)*hParalelogramo: quadrilátero cujos lados opostos são paralelos.

A=(raiz(3)*L^2)/4

height of triangleRAÍZ(p*(p-a)*(p-b)*(p.c)) em que p=(a+b+c)/2

Losango

All interior angles less than 180ºequal sides and equal angles3-4-5; 5-12-13; 8-15-17; 7-24-25

http://www.ets.org/s/gre/pdf/gre_math_conventions.pdf

Exemplo

É também a área de qualquer paralelogramo, mas nesse caso as bases são diferentes;

O que pode ser assumido e o que não pode? Por exemplo, se não especificado, medidas de distâncias e ângulos não podem ser assumidos maiores ou menores que outros, mesmo que pareçam ser.

Termo/notação

Writing Equations of Lines

x_intercepty_intercept

Significado

The x point when y=0The y point when x=0

slope=(y2-y1)/(x2-x1); b=y_intercept ; Find "b" inserting one point (pair x,y) into the general equation

Exemplo

Termo/notação

Mean, median and mode

Weighed Averages

Normal Distribution

Properties when mean=mediam

Range and

Standard Deviation

Percentiles

TIP

Boxplot (or Box-and-Whisker-Plot)

Significado

Mode is the number that occurs more frequently

On the GRE QC's, always warm up your imagination and have an eye out for ---"could I answer this without doing a full calculation?". So.... Pay attention to the things explained in the videos that may seem obvious, but you usually don't use to solve questions! (for example, the "example" part of the line about "weighed averages in this plan"

Excluding Q2 from the lesser and greater numbers is particularly important when the list has an odd number of terms.

Exemplo

http://magoosh.com/gre/2012/how-to-do-gre-math-faster/

B is not necessarily true, because the last term of the lesser number and the first term of the greater numbers can be equal to each other and the median. (remembering that the list has an even number of terms)

Termo/notaçãoReciprocal of number X

Word problems

Comparação de frações ao adicionar números no numerador e no denominador

Comparando frações. Maior ou menor?

Significado=1/X

"Of"=multiply; "is"=equals

Exemplo

Termo/notaçãox^n2^5

Units Digit Question

Equations with exponents

Working with formulas

Leaving the denominator with no roots

Extraneous roots

Significadox=base ; n=exponent"Two root Five"

When there would be a complex calculation, maybe it's simpler to plug in a value in the formula (useful in comparison questions), e.g. value "1"

Na potenciação de equações com raízes, deve-se verificar as respostas para ver se são válidas quando estiver elevando a potências pares (2,4,6,8, etc)

Exemplo

Termo/notação

Listing

Counting Strategy 1

Fundamental Counting Principle

Counting Strategy 2: Restrictions

Arrangement when there are alike objects

Combination

Counting Strategies II

Important property!

When to use combinations and when to use the fundamental counting principles or other methods?

Simplification of thecombinatorial formula

Significado

Listing the possible answer may be a good strategy when you have no insight about the problem.

Strategy 1: Directly adhere to the restrictions;Strategy 2: Use the restriction rule showed in the figure of the example.

Exemplo

If the problem allows repetition, that is like the example above (2*2*2=8). If there cannot be repetitions, it may be a permutation (e.g.: 3! = 3*2*1) (arrangement) (<-- Afirmação errada?)

Termo/notação

First rule

Mutually exclusive (disjoint)

Independent events

Generalized AND Rule

Binomial

Approximate rules (often, but not always)

Simple OR Rule andGeneralized OR Rule

With and without replacement

AND rule for independent events

Which technique to use?

The "At least scenario" (or "at most")

Guessing Strategy 1 - Instincts of real world life

Guessing Strategy 2 - Complement Rule = possible complement options

Guessing Strategy 3 - Knowing the possible range of responses.

Significado

When one event has no bearing or influence on the other events

For independent events:

Two events are mutually exclusive when they can't occur at the same time --> P(A and B)=0

where: P(A|B) = Probability of A, given condition B.

Exemplo

Rolls of a die; Successive flips of a coin;

Dice, cards, coins, etc.

Termo/notação

BE CAREFUL --> TRICK!!!

Strategies

Venn Diagrams

Scatter Plots

Significado

Check the answers first to see if you need to do calculations or extensive calculations, or you can just estimate na approximate answer

Exemplo

Termo/notação

Inequalities I

Inequalities II

Modules (absolute values)

Rational Expressions

Simplifying complex fractions

Testing Cases

Factoring Rational Expressions

Significado

In the example on the right: You can simplify the rational expressions of the second term, but you need to write a restriction: x is different of 4 (otherwise you would be permitting a division by zero --> indefinite)

Exemplo

Termo/notação

Motion QuestionsShrinking and Expanding Gaps

Rates and work problems(similar treatment of any velocity problem)

Significado

Exemplo

This one islike a shrinkingmotion problem

Termo/notação

Prime numbers facts

Factors of prime numbers

Testing prime numbers less than 100

Testing if any number is prime

Finding the number of factors of N

Odd and Even numbers

Odd and Even numbers

Divisibility Rules

Odd and Even numbers(see note 1)Another note: Zero is not positive neither negative

Pay attention to the question and DO NOT make deliberate assumptions!

Great Common FactororGreat Common Divisor

Least Common Multiple=Least Common Denominator (for simplifying equations)

Significado

A regra acima na verdade é a seguinte:1° passo: Tirar a raiz do número em questão √241 = 15,524...

2° passo: Aproxime o resultado para cima 15,524... => 16

3° passo: Ache todos os números primos menores que o resultado dado. Os primos menores que 16 são 2, 3, 5, 7, 11 e 13

4° passo: Veja se algum desses primos dividem o número inicial. Nenhum dos primos obtidos(2, 3, 5, 7, 11 e 13) dividem 241. Portanto, 241 é primo!

1) Put the numbers in prime factors2) Find the common factors and multiply them.

1) Find the Great Common Factor2) Multiply the two numbers and then divide by the Great Common Factor

By 2: Even numbersBy 3: Sum of all digits must be divisible by 3By 4: The last two digits must be divisible by 4By 5: Units digit must be "0" or "5"By 6: Must be divisible by 2 and 3By 9: Sum of all digits must be divisible by 9

Exemplo

In the example at the left, we do not know if Q or R are integers. They may be fractions. Then, one of then could be even too, or both could be fractions.

A=24; B=32

1) A=2^3 * 3 B=2^52) GCF=2^3 = 8

A=24; B=32

1) GCF= 82) LCM=24*32/8 = 96

Termo/notação

Factor 134Remainder 134Prime number 134Composite number 134Ones/Units digitTens digitHundreds digitThousands digitTenths digitHundredths digitThousandths digit4 3/8 is 35/8-10 1/2 is -21/20!=10^0 is not definedf(g(x))Similar trianglesCongruent trianglesHypotenuseLegs of a triangleOpposite sides of a line 137Right anglex-intersept 138Curly bracket

Disjoint sets138

Mean Value 139

MedianValue

139

Mode value

Range

Interquartile range

QuartilePercentile

Página do ETS guide


Outcome

140

FulcrumRevenue 142Profit 142QuartBoxplot 107Scatter Plot 107Yield1 mile = 5280 feet

RadiusIrrational numbers 214Ratio of A to B 215Prime factorization 210Like terms 222Quadratic equation 223(xâ)(x^b)=x^(a+b)(xâ)( yâ)=(xy)â(xâ)^b=x^(ab)Fatorar expressões de segundo grau (ver métodos 1 e 2): http://pt.wikihow.com/Fatorar-Polin%C3%B4mios-de-Segundo-Grau-(Equa%C3%A7%C3%B5es-Quadr%C3%A1ticas)Simple interest rate




Sample Standard Deviation


Mean and median of a continuous random variable

Vírgula é ponto e ponto é vírgula (português para inglês)

Simetria em relação ao y=x

The graph of h(x)+c is the graph of h(x) shifted upward by c units. The graph of h(x)−c is the graph of h(x) shifted downward by c units. The graph of h(x+c) is the graph of h(x) shifted to the left by c units. The graph of h(x−c) is the graph of h(x) shifted to the right by c units.Fatores notáveis

GeometryIf a polygon has n sides, it can be divided into n−2 trianglesthe sum of the measures of the interior angles of an n-sided polygon is (n−2)(180 )Regular polygon

Área trapézio = (1/2)*(b1+b2)*hÁrea paralelogramo = b*h

Área triângulo equiláteroÁrea triângulo qualquerAltitude



A polygon is inscribed in a circle if all its vertices lie on the circle, or equivalently,the circle is circumscribed about the polygon

Propriedade de triângulos (cai bastante - figuras ficam fora de escala, tem que imaginar bem ou desenhar)

Circle Properties

Significado

Fator (número inteiro pelo qual um outro número inteiro é divisível)Resto de uma divisão. É sempre positivoNúmero primo (maior que um)Número maior que um que não é primoDígito da unidadeDígito da dezenaDígito da centenaDígito do milhar0.X0.0X0.00X4*(8/8) + 3/8-(10*(2/2)+1/2)Zero fatorial é igual a 1

Composition of f with gTwo triangles that have the same shape but not necessarily the same sizeTwo triangles that have the same shape and sizeHipotenusaCatetosDe um lado da linha e do outro lado da linhaÂngulo retoThe insersection of a graph at the x-axis in a coordinate system{}

The median of an odd number of data is the middle number when the data are

listed in increasing order; the median of an even number of data is the arithmeticmean of the two middle numbers when the data are listed in increasing order.

Diferença entre o maior e menor número da lista

third quartile minus the first quartile (o que está entre o primeiro e terceiro quartis?)3 números que dividem uma lista em 4 partes iguais (baseado em medianas)99 números que dividem uma lista em 100 partes iguais (baseado em medianas)

For a list of data, where the arithmetic mean is denoted by m, the standarddeviation of the data refers to the nonnegative square root of the mean of the

squared differences between m and each of the data. This statistic is also known

If A and B have no elements in common, they are called disjoint sets or mutually exclusive sets.

Value that occurs more often (if there isn't repeated values, then there is no mode value. Also, there may be more than one mode)

as the population standard deviation and is not to be confused with the samplestandard deviation.

Result

The mean of a continuous random variable X is the point m on the x-axis at whichregion under the distribution curve would perfectly balance if a fulcrum wereplaced at x=m. The median of X is the point M on the x-axis at which the linex=M divides the region under the distribution curve into two regions of equalarea.Fulcro, eixoReceitaRevenue minus costMedida de volume: Aproximadamente 946,35mlDiagrama de Caixa (usa teoria da divisão por quartis)Gráfico de dispersãoResulta

Raio de um círculoNumber that do not terminate neither repeat.A/BFactors of a number that are only composed by prime numbersTerms in na equation that have the same variablesVariables are to a maximum power of two


V=P(1+r/100)^t

The same of the population standard deviation, but, as opposed to dividing by (n), divide by (n-1)


IMPORTANTE! VOCÊ JÁ CONFUNDIU ISSO E ERROU. ERA QUESTÃO DE ENTRADA NUMÉRICA, AÍ NÃO TEM NEM ITEM PRA CONFERIR A ORDEM DE GRANDEZA!

V=P(1+rt/100); sendo r o juros em percentagem

V=P(1+r/(100*n))^(n*t); sendo r o juros em um período e n o número de vezes neste período que o juros é contabilizado

Trocar o x por y e o y por x na equação. The graph of h(x)+c is the graph of h(x) shifted upward by c units. The graph of h(x)−c is the graph of h(x) shifted downward by c units. The graph of h(x+c) is the graph of h(x) shifted to the left by c units. The graph of h(x−c) is the graph of h(x) shifted to the right by c units.

(a+b)² = a² + 2ab + b²; (a-b)² = a² - 2ab + b²; a² - b² = (a+b)(a-b)

If a polygon has n sides, it can be divided into n−2 trianglesthe sum of the measures of the interior angles of an n-sided polygon is (n−2)(180 )

All the internal angles are equal

Paralelogramo: quadrilátero cujos lados opostos são paralelos.

A=(raiz(3)*L^2)/4

height of triangleRAÍZ(p*(p-a)*(p-b)*(p.c)) em que p=(a+b+c)/2

Exemplo

the integer 4 has six factors: −4, −2, −1, 1, 2, and 4-17/4 resulta -3 com resto +42,3,5,7,11, etc2,4,6,7,9,10, etc

585=(3^2)*(5)*(13)In w3z+5z2−z2+6; the terms 5z2 and −z2 are like terms


Se é dado o juros anual "r", para saber o mensal, utilizamos n=12, ou seja, dividimos os juros por 12, e contabilizamos a cada mês (por isso multiplicada o expoente por 12)

y=x^2 e y=raiz(x) são simétricas em relação a x=y, assim y=raiz(x) é uma parábola na origem com a abertura para o lado direito.

excel de resumo de estudo para teste de matemática do gre (2014)

Documents