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GRE Math Flashcards

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1
Q

How many factors does 12 have?

A

12! (1,-1,2,-2,3,-3,4,-4,5,-5,6,-6,12,-12)

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2
Q

The product of an even integer and an odd integer is…

A

an even integer!

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3
Q

What digits can a prime number end in? How does this help to remember prime numbers below 100?

A

1,3,7 or 9 (expect for the only even prime 2). You then only need to double check if the number is divisible by 3 (if the number sum is divisible by 3) or by 7- if not, it’s prime!

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4
Q

Is 1 a prime number?

A

No! (It’s also not composite)

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5
Q

How many even prime numbers are there?

A

The only even prime number is 2!

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6
Q

What is a positive number that is not prime?

A

Composite!

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7
Q

What is the relationship between prime and composite numbers?

A

All composite numbers can be uniquely expressed as a product of factors that are prime numbers/divisors - this expression is called prime factorization

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8
Q

When is 1 a factor or multiple?

A

1 is a factor of every integer, 1 is only a multiple of 1 and -1

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9
Q

What is 6 divided by 24 in terms of quotient and remainder?

A

0 remainder 6

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10
Q

What is -32 divided by 3 in terms of quotient and remainder?

A

-11 remainder 1 (remainders can be negative but it’s not in this case)

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11
Q

For odd ordered roots (like cubed root) how many roots are there for positive and negative numbers?

A

One root!

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12
Q

For even ordered roots (like square root) how many roots are there for positive and negative numbers?

A

Two roots for every positive number and no roots for any negative number!

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13
Q

what is 7,532.418 written as exponents of 10?

A

7(10^3)+5(10^2)+3(10)+2(10^0)+4(10^-1)+1(10^-2)+8(10^-3)

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14
Q

Are (-3^2) and -3^2 the same?

A

No! The first is +9 and the second is -9!

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15
Q

What is a^0 and 0^0?

A

a^0=1 and 0^0 is undefined

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16
Q

What is the square root of a) 0 and b) 16? How about wit the square root symbol?

A

a) 0, b) 4 and -4! With the square root symbol the answer is only the positive root.

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17
Q

√3√10 equals?

A

√30

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18
Q

√5/√15 equals?

A

√5/15 = √1/3

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19
Q

What’s the difference in terminology between a repeating and non-repeating decimal?

A

repeating=rational and non-repeating= irrational

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20
Q

Is the entire real number line an interval?

A

Yes!

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21
Q

What is (7√2)√2?

A

7(√2√2) = (7)(2)= 14

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22
Q

What is the triangle inequality?

A

|r+s| is less than or equal to |r| + |s|

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23
Q

If s is between 0 and 1, how does s^2 compare to s?

A

s^2 is LESS than s!

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24
Q

What is the base when computing percent increase and decrease?

A

increase = base is smaller number, decrease = base is larger number!

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25
Q

How do you find all positive divisors?

A

Do prime factorization. Each prime to every exponent is a factor and then you need to multiply that prime to every exponent by the other prime(s) to every exponent.

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26
Q

Easy way to know if a number is divisible by 3?

A

If the sum of the numbers are divisible by 3 (ex. 192 -> 1+9+2=12 so is divisible by 3!)

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27
Q

Easy way to know if a number is divisible by 4?

A

If the last two digits of your number make a number that is divisible by 4, then the number itself is divisible by 4 (example: 144 - 44 is divisible by 4, so 144 will be divisible by 4)

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28
Q

Easy way to know if a number is divisible by 2^x?

A

If the last x digits of the number in question make a number that is divisible by 2^x, then said number is divisible by 2^x

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29
Q

Easy way to know if a number is divisible by 3^x?

A

If the sum of the digits of a number divisible by 3^x, then the number itself is divisible by 3^x

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30
Q

Easy way to know if a number is divisible by 5?

A

The number must end in 0 or 5

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31
Q

Easy way to find the number of positive divisors

A

Do prime factorization, then add 1 to both exponents and multiply them together (ex. 144 = 2^43^2->(4+1)(2+1)=53= 15!)

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32
Q

How many primes between 0-100?

A

25!

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33
Q

How many terms is 8/n+p?

A

One!!

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34
Q

What is the degree of a polynomial?

A

Greatest degree (exponent) of its terms (degree 2 is quadratic and degree 3 is cubic)

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35
Q

What is the degree of a constant term?

A

Zero! (x^0=1)

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36
Q

What is the degree of -7xy^3?

A

Four! (x^1, y^3 -> 1+3=4)

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37
Q

When is 7x(x+2)/2(x+2) undefined?

A

When x=-2 (denominator is zero)

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38
Q

Identity of a^2-b^2?

A

=(a+b)(a-b)

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39
Q

Identity of (a+b)^3?

A

=a^3 + 3a^2b + 3ab^2 + b^3

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40
Q

Identity of (a-b)^3?

A

=a^3 - 3a^2b + 3ab^2 - b^3

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41
Q

What is true if x^a=x^b (and x is positive and not 1)

A

a=b!

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42
Q

What is 2^a in fraction form?

A

1/(2^-a)

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43
Q

(y^3)(y^-1)

A

y^2

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44
Q

Two fractions that equal x^a-b?

A

x^a/x^b = 1/(x^b-a)

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45
Q

What is 0^0?

A

Undefined

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46
Q

(x^a)(y^a) versus (x^a)(y^b)

A

(xy)^a and (xy)^a+b

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47
Q

(10z)^3=

A

(10^3)(z^3)=1,000z^3

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48
Q

What are equivalent equations?

A

Equations that have the same solutions (ex. for both x+1=2 and 2x+2=4, x=1)

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49
Q

Which one is a linear equation: 1) 2x+1=7x, 2) x+y^2=0, 3) xz=3

A

Only 1! (2x+1=7x)

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50
Q

What is an identity?

A

Two equations that are equal for all values

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51
Q

QUADRATIC FORMULA?!

A

negative b plus or minus the square root of b squared minus 4ac over 2a

52
Q

What is the square root of zero?

A

Zero!

53
Q

The slide method of factoring

A

Move a to a*c and then remember to divide a from each answer at the end!!

54
Q

When does an inequality sign flip?

A

When both sides are multiplied or divided by a negative number

55
Q

What is the decimal version of increasing x by 14%?

A

1.14x

56
Q

PRACTICE SOME RATE QUESTIONS ;)

A

PRACTICE SOME RATE QUESTIONS ;)

57
Q

Equation for simple interest

A

value = initial investment * (1 + (percent * time in years/100))

58
Q

Equation for compound interest

A

value = initial investment * (1 + (percent/100))^(number of times compounded * time in years)

59
Q

What are the order of the four quadrants?

A

From top right counter clockwise (ex in points- Q1: (4,2); Q2: (-4,2); Q3: (-4,-2); Q4: (4,-2))

60
Q

What is the point (4,2) reflected about the x-axis?

A

(4,-2)!

61
Q

What is the point (4,2) reflected about the y-axis?

A

(-4,2)!

62
Q

What is the point (4,2) reflected about the origin?

A

(-4,-2)!

63
Q

What are the variables in the equation for a line?

A

y=mx+b, m is the slope and b is the y-intercept

64
Q

What is the equation for finding the slope?

A

(y2-y1)/(x2-x1) (rise over run)

65
Q

What is the slope and equation for a horizontal line?

A

Slope is zero and equation is y=b

66
Q

What is the slope and equation for a vertical line?

A

Slope is undefined and equation is x=a (where a is the x-intercept)

67
Q

If the slope of a line is 2 what are is the slope of the perpendicular line?

A

-1/2 (Negative reciprocal)

68
Q

How do you solve for the y-intercept? the x-intercept?

A

Find y-intercept by picking any point, putting it in line equation and solving for b. Find x-intercept by solving for when y=0.

69
Q

What is the point (4,2) reflected about the line y=x?

A

(2,4)!

70
Q

How do you find the the reflection over y=x of a line?

A

Interchange the x and y and then solve for y.

71
Q

When is a parabola upwards?

A

When a (the constant for x^2) is positive!

72
Q

When is a parabola downwards?

A

When a (the constant for x^2) is negative!

73
Q

How do you solve for the vertex of a parabola?

A

x= NEGATIVE b/2a

74
Q

What is the equation for a circle?

A

(x-a)^2 + (y-b)^2 = r^2 The center is point (a,b) and r is the radius

75
Q

What is the equation for absolute value?

A

piecewise-defined function, y=x when x is greater than zero, y=-x is less than zero

76
Q

How does y=x^2 relate to y=sqrt or x?

A

The are reflections over the line y=x

77
Q

What is the equation of a parabola opening up to the right (vertex at origin)?

A

For x≥0, the top half is y=sqrt of x and the bottom half is y= -sqrt of x

78
Q

How is y=|x|+2 different than y=|x|?

A

y=|x| is shifted UP by 2 units!

79
Q

How is y=(x+1)^2 different than y=x^2?

A

y=x^2 is shifted LEFT by 1 unit!

80
Q

How is y=(x-4)^2 different than y=x^2?

A

y=x^2 is shifted RIGHT by 4 units!

81
Q

How is y=2|x-1| different than y=|x|?

A

y=|x| is shifted RIGHT by 1 unit and stretched upward (away from x-axis) by a factor of 2

82
Q

How is y= - x^2/4 different than y=x^2?

A

The parabola is facing downward and is squished toward the x-axis by a factor of 1/4

83
Q

(s^7)(t^7)=

A

(st)^7

84
Q

(x^10)(y^-1) / (x^-5)(y^5)

A

x^15 / y^6

85
Q

Two lines intersect, making 4 angles. A=60,B=120,C=60,D=120. Which are opposite angles?

A

A&C (both 60) and B&D (both 120)

86
Q

All polygons in GRE are what kind? What is true of each interior angle?

A

Convex polygon where each interior angle is less than 180.

87
Q

How many triangles can you fit in a polygon? What does this mean about the sum of all interior angles?

A

triangles = Number of sides minus 2. Sum of angles = number of triangles * 180 aka (n-2)*180

88
Q

What is a regular polygon?

A

All sides and angles are congruent

89
Q

What is true of the sides of any triangle?

A

The length of one side must be less than the sum of the other two

90
Q

What are the angles and side ratio for an isosceles right triangle?

A

angles are 45,45,90; side ratio is 1:1:sqrt2

91
Q

What are the angles and side ratio for half an equilateral triangle?

A

angles are 30,60,90; side ratio is 1 (base), sqrt of 3 (height), 2 (hypotenuse) (*Note: the hypotenuse is 2 times the base)

92
Q

What are the three propositions to prove congruent triangles?

A

SSS (side,side,side are = in both triangles); ASA (angle, side, angle); SAS (side, angle, side)

93
Q

What is true about side ratios with similar triangles?

A

1) The ratios of corresponding sides from both triangles are the same between all 3 pairs of sides. 2) The ratios between one side with another in the same triangle is the same for the other triangle.

94
Q

What is true of angles in a parallelogram?

A

Opposite angles are congruent.

95
Q

What is the formula for the area of all parallelograms? Is a trapezoid a parallelogram?

A

A=bh; NO a trapezoid is not a parallelogram (only one pair of sides are parallel instead of both)

96
Q

What is the formula for the area of a trapezoid?

A

A=1/2 (b1+b2)(h)

97
Q

What is the best fractional approximation of pi?

A

22/7

98
Q

How is the measure of an arc and it’s central angle related?

A

They are equal!

99
Q

The ratio of the length of the arc to the (a)______ is equal to the ratio of the degree measure of the arc/central angle to (b)______.

A

(a) Circumference; (b) 360 degrees

100
Q

The ratio of the area of a sector (slice) to the (a)______ is equal to the ratio of the degree measure of the arc/central angle to (b)______.

A

(a) Full circle area; (b) 360 degrees

101
Q

If a circle radius intersects a line at a point on the circle at 90 degrees, what is true of the line?

A

It is a tangent!

102
Q

If a line intersects a circle at one point, what is true of it’s relation to the radius that intersects that same point?

A

The lines are perpendicular!

103
Q

If the center of a circle is on one of the sides of an inscribed triangle, is is a (1)________. This means that the triangle is a (2)________ triangle.

A

(1) Diameter of the circle; (2) right triangle!

104
Q

Two or more circles with the same center are called

A

Concentric circles

105
Q

How many edges and vertices does a rectangular solid have?

A

12 edges and 8 vertices

106
Q

What is the formula for the volume and surface area of a rectangular solid?

A

V=lwh; SA= 2(lw+lh+wh)

107
Q

What is formula for the volume of a cylinder?

A

Area of the base times the height (i.e. V=pir^2h)

108
Q

What is formula for the surface area of a cylinder?

A

Area of both bases plus area of the wrap around rectangle (i.e. 2pir^2 + 2pir*h)

109
Q

What is a relative frequency?

A

frequency divided by the total number of data

110
Q

How do histograms directly relate to probability?

A

The sum of the areas under the bars equal 100% and the area under one bar over 100% is the probability that that item or group of items will show up.

111
Q

How would you find the degree of the angle/arc for a slice of a pie chart that represents 7% of the whole?

A

360*.07 = 25.2 degrees

112
Q

Can a list of number have more than one mode?

A

Yes! (If more than one number appear the most time)

113
Q

How do you find Q1 and Q3 of a number list?

A

Write the numbers in order, spit it into 2 (removing the median if there is an odd # of #s), find the median of the two smaller groups (**Q2 always = median)

114
Q

What is Q1-3 in terms of 99 Percentiles?

A

Q1=P25; Q2=P50; Q3=P75

115
Q

What is the interquartile range?

A

Q3-Q1

116
Q

What is the equation for the weighted mean of the list 2,4,4,5,5,5? What is special about the weights?

A

1(2)+2(4)+3(5)/(1+2+3) = 25/6; The weights add up to the total # of #s

117
Q

Which is affected by a very high or low outlier? (a)mean (b)median

A

A! (the median doesn’t change if you change one number to a very high or low number as long as it’s order in the list stays the same)

118
Q

HOW DO YOU COMPUTE STANDARD DEVIATION?

A
  1. Find the mean; 2. Find difference between mean and each value; 3. Square the differences; 4. Find avg of squared differences; 5. Find the positive square root
119
Q

How does the ‘sample standard deviation’ differ from ‘(population) standard deviation’? When do you use the former?

A

Sample means dividing the sum of the square differences by n-1 instead of n. This is preferred for a sample of data taken from a larger populations of data.

120
Q

What is the process of standardization? Why is it useful?

A

Subtract the mean from each value in a list and divide by the standard deviation. This provides a measure of position relative to the rest of the data independent of the units or absolute values (i.e. how many standard deviations a value is away from the mean in either direction)

121
Q

How does an empty set { } relate to all other sets?

A

An empty set is a subset of every set

122
Q

What is the difference between a list and a set?

A

In a set repetition isn’t counted and order doesn’t matter! So the set {1,2,3,2} and set {3,1,2} are the SAME!

123
Q

What does |S| for the set {1,2,3,2}

A

|S|=3, which is the number of unique elements in the set

124
Q

A ∩ B? What is it called when there is none?

A

The INTERSECTION of sets A & B, the set of all elements that are in BOTH (i.e. the overlap). Sets with no overlap are called disjoint or mutually exclusive.

125
Q

A ∪ B?

A

the UNION of sets A & B, the set of all elements that are in EITHER A, B or both.

GRE Math (1 decks)

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