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GRE-Math&Vocab > Math Formulas > Flashcards

Math Formulas Flashcards

1
Q

What are distinct prime factors?

A

prime factors that together multiply to the listed number but are not repeated

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2
Q

When would you use the picking number strategies?

A

Picking numbers do not use modular arithmatic on GRE (problem solving avoid -1, 0, 1). trying to pick different numbers that demonstrate thtat the information provided could produce different results (different relationships between two problems). Pciking numbers w/ special properties will often force there to be a difference (pos. vs. neg., odd vs. even, small vs. big, -1<0<1 1,0,1 only use these for quantitative comparison questions). if you are unable to produce different results for the comparison characteristiscs select the correct choice and move on
• pcik numbers for questions w/ variables in the question stem, choose numbers that follow rules and are easyto work with, choose numbers that follow rules and easy to work with. Multiple choice: if answer coices are numbers, any choice w/ right result sis correct, if answer choices are algebraic expressions, check every one; when picking numbers in quantittave comparison questions, force different results by choosing a variety of numbers

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3
Q

How do you back solve?

A

Backsolving: working “backward from an answer choice to determine whether it agrees w/ the information in the question stem.
• not work w/ quantitiative comparison, numeric entry questions, could work for data interpretation.
backsolving. have numbers in order. if manageable answer choice (B or D start point) likely answer.

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4
Q

What is the kaplan method?

A

Analyze the question (figure out the strategy), identify the task (what is the question asking exactly), choose a strategy (pick numbers, backsolve, do traditional math, take a strategic guess), confirm answer (check math and confirm answer to what questions ask).

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5
Q

What are reminders?

A

• reminders mean that goes into it once and what is left over

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6
Q

What is the kaplan method for problem solving?

A
  1. Analyze the question.
  2. Identify the task.
  3. Approach strategically.
    • Do the math
    • Pick numbers
    • Backsolve
    • Make a strategic guess
  4. Confirm your answer.
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7
Q

What is the kaplan method for quantitative comparison?

A
  1. Analyze the centered information and quantities.
  2. Approach strategically.
    • Compare, don’t calculate
    • Compare quantities piece by piece
    • Make one quantity look like the other
    • Do the same thing to both quantities
    • Pick numbers
    • Simplify the centered information
    • Suspect (D) is the answer
    •
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8
Q

What are the properties of a slope?

A

• slope=rise/run=change in y/change in x. going up is positive slope any line going down is negative slope. straight up is undefined slope. slope=y2-y1/x2-x1. y=mx+b

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9
Q

What are the volume and surface area of a cylinder?

A

• volume of a cylinder=(pi)r^2h; SA=2(pi)r^2+2(pi)rh

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10
Q

What is the volume and surface area of a rectangle?

A

• rectangles: surface area of uniform solids=sum of area of all sides. SA=2(lw)+2(lh)+2(wh). volume of uniform solids=area of base times height; volume=lxwxh

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11
Q

What is the circumference and area of a circle?

A

circumference=pid or 2pir. area=pir2. c=dpi

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12
Q

What are the angles and lengths of an isosceles triangle?

A

45:45:90 isosceles x: x: x square root of 2

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13
Q

What are the angles and lengths of a triangle?

A

30:60”90 x: x square root of three: 2x

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14
Q

What is the pythagreum theorem?

A

a2+b2=c2

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15
Q

What are the most common pythagreum theorem triangles?

A

. 3:4:5 ratios, 5:12:13.

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16
Q

What is the strategy of comparing two different shapes?

A

• doing shapes you subtract the area of the big shape from the area of the little shape

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17
Q

What is the radius and diameter?

A

radius is center to edge. diameter- directly through center and touches both edges.

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18
Q

How do you calculate the number of sides of a figure or the angles of a multi-sided angle?

A

• Interior angles or sum of interior angles. 180 (n-2) n=number of sides of figure

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19
Q

What are parallelograms and how do you find their area?

A

• parallelogram- any quadrilateral where the sides across from each other are parallel. sides across from eachother angle. angles directly across are also the same. area is base times height so long as its perpendicular. rectangle and square are parallelograms.

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20
Q

What is the triangle inequality theorem?

A

• triangle inequality theorem if third side equaled the differene between the two sides third side has to be longer than the difference. third side has to be less than the sum bigger than the difference and smaller than the sum

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21
Q

What is the perimeter?

A

• perimeter length of all sides of shape

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22
Q

What is the area?

A

• area measurement of space inside shape measures two dimensional so squared. 1/2bh

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23
Q

What are the interior angles of a triangle?

A

• interior angles of triangle all add up to 180

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24
Q

What is special about an equilateral triangle?

A

• equilateral triangle all interior angles are the same, same as sides

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25
Q

What are the angles of different locations?

A
  • supplementary angles angles that add up to 180 degrees.

* angles in same position or are across from each other are the same degree

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26
Q

What are the multiplication principles?

A

ο Multiplication principles- combining multiple possibilities. Given the number of choices as the base and the number of possibilities as the power

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27
Q

What do you apply the slot strategy?

A

• apply the slot strategy to permutations questions to figure out how many ways things can be ordered. make a list of slots for the number of possibilities left for each from left to right? multiply all of the possibilities for each slot aka a factorial.

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28
Q

What is the permutation formula?

A

• nCk=n!/k!(n-k)! n=the total number of items how many items choosing from. k=subgroup how many are we trying to chose from that larger group. can do 6.4x5.3x4.2x3/1 set up permutation w/ slots then divide by the slots factorial.

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29
Q

What are overlapping sets?

A

• overlapping sets= group1+ group 2+neither-both

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30
Q

What is the average?

A

• average=sum of values/number of values

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31
Q

What is the teeter totter?

A

• balancing method draw teeter totter. Teeter Totter two numbers on one side w/ average in center and choice the number that would be holding it up on the other side away from the center number and compare w/out calculating looking at the numbers left that fill that.

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32
Q

What is frequency?

A

• frequency multiplying scores by their frequency and then divide by the total frequency or total number

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33
Q

What is the zeroing strategy?

A

• zeroing strategy- replace first number w/ a zero and increase up for each of the next options add all those to make it easier then add the average w/ the adjusted values to the first number seet and it is the new average

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34
Q

What is weighted average?

A

• weighted average multiple percent weighted w/ the amount and add each of those together.

35
Q

How do you determine the median?

A

• median=middle value. odd numbers of it just pick the middle one, if even numbers use average of two middle values

36
Q

How do you determine the mode?

A

mode-value that appears most frequently

37
Q

What is the probability?

A
  • probability=desired outcomes/total outcomes
  • probability of multiple events multiple the probabilities on whether they are independent (putting it back after pulling it out) or dependent not replacing it changing the total.
  • When doing probabilities if there are multiple ways of it add the two probabilities.
  • probability something wont work is 1- the probability
38
Q

What is range?

A

. range- greatest value-least value

39
Q

How do you calculate percent change?

A

• amount change change/original amount=percent change

40
Q

What do you want to happen when foiling fractions?

A
  • When foiling top and bottom most likely will cancel out

* isolating variables

41
Q

What is the protocol for quantitative comparison?

A

Analyze centered information and quanities (equation or role)
• Approach strategically. (if have to pick numbers have to pick two sets of numbers to prove yourself wrong and check the always relationships
• pick numbers, rule out or suspect d (if there does not seem to be enough information suspect d, if there is a possible relationship rule it out), do the math, simplify the centered information, compare piece by piece, do the same thing to both quantities, make the qunatities look alike

42
Q

What are some things to remember when picking number choices?

A

ο look at two largest numbers alone and if already more than it than it is automatically higher
ο don’t forget that not everything has to be whole numbers
ο don’t forget negatibe if possible, compare what the two things both have and then just see the difference between them

43
Q

When is back solving ideally used?

A

• “ideal”s for backsolving: numbers in answer choices in ascending or descending orders that are manageable, choices that correspond to just one unknown in the question, incorrect choices that can be seen as greater or less than the correct choice. check b or d to check the fewest number of choices possible

44
Q

When do you use back solving?

A

• backsolving use when answer choices are numbers and question has a single variable, B,D technique requires that answer choices arranged in ascending and descending order and able to readily determine wehther an incorrect choice is too large or small. backsolving when you can logically reduce number of potentially correct answers

45
Q

What do you do when presented w/ quantities that have multiple parts expressed?

A

• evaluating piece by piece when presented w/ quantities that have multiple parts expressed in a similar manner, making quantities look alike if they are expressed in completely different terms , do same thing to both quantities treat as if an inequality,

46
Q

What are the steps to this?

A
  • analyze the centered information and quantities
  • centerd information above the quantities applies to both
  • simplify centerd information if applicable
  • determine how the centered information affects the quantities
  • approach strategically
  • select a strategy to use in comparing quantities
  • other strategies minimize or eliminate calculations that can cause problems.
47
Q

What is PEMDAS?

A
  • Apply order of operations when solving equaitons or simplying expressions (please[parentheses] excuse[exponents] my dear[division] aunt[addition] sally[subtraction]) work from inside out.
  • For multiple layers of parentheses work from the innermost to the outermost.
  • exponents also includes radicals
  • multiplaction and division have equal weight in equations, as do addition and subtraction solve from left to right.
  • perform mathematical operation using fractions
  • simplify expressions and equantions by applying the rules for exponents and radical
48
Q

What are fractions?

A

• Fractions are made up of two numbers: the numerator and denominator. Fractions represent divisions and can be rewritten as division expressions.

49
Q

How do you add or subtract fractions?

A

o To add or subtract fractions, first find a common denominatory. Multiply the numerators and denominators by the same constant

50
Q

How do you multiple fractions?

A

o When multiplying fractions, multiply a numerator by a numerator and a denominator by a denominator. When possible, reduce first to simply the calculation.

51
Q

How do you divide fractions?

A

o When dividing fractions, multiply the number in the numerator b the repiprocal of the number in the denominator. Reduce to simplify the calculation. you can reduce either within each fraction or by cross cancelling. Apply the same steps when dividing an integer by a fraction or a fraction by an integer.

52
Q

What is a mixed number?

A

o A mixed number is a number that includes both an integer and a fraction. An improper fraction is a fraction in which the numerator is greater than or equal to the denominator. Its value is either 1 or greater than 1.

53
Q

What are the common fractions?

A

o Fractions can be converted to decimals using division. Memorizing common fraction/decimal equivalents can save you time on test day. ½=.5, 1/3=.333, ¼=.25, 1/5=.2, 1/6=.16666, 1/8=0.125, 1/9=0.1111, 1/10=0.1

54
Q

What are exponents?

A

• Exponents. an exponent indicated the number of times a base is multiplied by itself.

55
Q

What do you when multiplying exponents with the same base?

A

add the two expnoents

56
Q

What do you do when dividing exponents w/ the same base?

A

subtract the exponents

57
Q

When raising a power to another power?

A

multiple those exponents c

58
Q

What are special about negative exponents?

A

can be expressed as a reciprocal over 1

59
Q

What happens when a number is raised to the zero power

A

. Any number (except )) raised to the zero power equals 1

60
Q

What happens when a negative number is raised to an odd exponent?

A

answer will always be negative

61
Q

What happens when a negative number is raised to an even exponent?

A

always positive

62
Q

What happens w/ fractions and exponents?

A

For fractions that fall between 0 and 1 on the number line, the higher the exponent, the smaller the number actually gets. For fractions that fall between -1 and 0, raising the fraction to increasing exponents will result in alternative negative and positive fractions whose values get closer to 0. 10^5

63
Q

What happens when ten is raised to a power?

A

the exponent tells you the number of zeroes that follow the 1

64
Q

What are radicals?

A

• Radicals: when squaring something remember -3 and 3, when given square route it is always positive. a radical symbol respresents the positive square root. When simplifying an equation or expression, complete the operations outside the radicals, then the operations inside the radicals. Only like radicals can be added or subtracted. A fractional exponent indicates a square (etc.) root. When multiplying or dividing inside the radical sign, radicals can be “split” into multiple square routes. Radicals cannot be “split” when adding or subtracting inside the radical sign.

65
Q

When questions include exponents and/or radicals

A

look for opportunities to simplify or re-express the values in order to find strategic shortcuts in the calculations.

66
Q

What are the simplified subtractions and additions of odds and evens?

A

• Odd +/- odd=even. even +/- even=even, odd +/- even=odd. odd x odd =odd, even x even=even, odd x even=even. • Two signs of the same are a positive. Multiplying numbers w/ different signs are a negative. Subtracting from a negative is adding a positive.

67
Q

What is a special integer?

A

0 is an even integer

68
Q

What are the 7 prime numbers up to 20?

A

: 2,3,5, 7, 11, 13, 17

69
Q

What are the prime factors of an integer?

A

• Prime factors of integer are tree of multiples to get to a number. Prime factors of 48 are 2^4 and 3. Distinct prime factors of 48 are 2 &3. Multiple of 48 is 48 multiplies by something. Divisble by using the primer tree and the simplest numbers answer choices divisible by those things.

70
Q

What is a linear equation?

A
  • equation w/ no exponnents involved one equation at a time. more than one equation at a time is a system of equations. however many variables you have means the number of distinct equations.
71
Q

How do you solve a system of two linear equations?

A

substitution. make a variable go by itself by subtracting the other one.
by combination. add or subtract one equation from the other to cancel out variables.

72
Q

What is an inequality?

A

• inequality- if multiplying or dividing by a negative sign you must flip the inequality sign

73
Q

What is an absolute value?

A

• absolute value is the positive distance of a number away from 0. Absolute value of x=4 x equals + or – 4 so solve equations w/ both + and – ways.

74
Q

What does must be true mean in a question?

A

• Must be true-means that it includes both of those answers.

75
Q

What is the quadratic equation?

A

• quadratic equation w/ a variable of an exponent of two with foil and reverse foil (First outside inside and last).

76
Q

What do you do when faced w/ a symbol question?

A

• manipulate expressions and equations that use function notation. symbols work the same way as functions just different way to show it

77
Q

What are nested functions?

A

• nested functions start with innermost and work way out subsitues symbols for functions for less confusion.

78
Q

What do you do for ratios that are extrapolating?

A

• For ratios of trying to extrapolate to actual values set the values equal. 6/7=18/x if want the total have the denominator be the total of both or all of the different groups then set that equal. 6/13=18/x

79
Q

What is a percentage?

A

• Percentage: part of a whole. 12/60. 30% of 20 is 20% of 30 always equivalent. amount of change or difference between new numbers percent of original starting numbers.

80
Q

What is the percent change?

A

• percent change=(amount of change/original amount)x100

81
Q

What are the 3 formulas for a speed and average speed problem?

A

• 3-part speed and average speed problem. Distance=rate X time. rate=distance/time. time=distance/rate. distance is king of the hill.

82
Q

What do you do when there are multiple legs of a trip?

A

• when there are multiple legs of a trip, find the average speed by determining the total distance and time. Rate=total distance/total time. 180+120

83
Q

How do you solve combined work problems?

A

• solve combined work problems by applying the combined work formula just add the two rates together. T(amount of time to complete one job)=A(times it takes first person to do the job) X B(times it taks second person to do the job)/A+B

GRE-Math&Vocab (2 decks)

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