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GRE > Math > Flashcards

Math Flashcards

1
Q

Add, Subtract, multiply and divide WHOLE NUMBERS

A

Check with oposite

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2
Q

Add Subtract, Multiply, and Divide FRACTIONS

A

Find a common demoninator before adding or subtracting

Multiplication - multiple numerators (top) then demoinators (bottom)

Divide - Multiply by the reciprocal

(Reduce across numerator for next demoinator)

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3
Q

Add, Subtract, Multiply, and Divide DECIMALS

A

Add/Subtract - Aline and compleate as normal

Multiply - Multiply numbers add number of decimal places

Divide - Make divisor whole then move divded decimal same amount

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4
Q

Convert FRACTIONS and DECIMALS

A

Fraction to Decimal - divide

Decimal to Fraction - Digits in the numerator - name in denominator

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5
Q

Add, Subtract, Multiply, and Divide POSITVE AND NEGATIVE NUMBERES

A

Do it as normal

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6
Q

How to plot points on the NUMBER LINE

A

Put on between numbers on line

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7
Q

How to plug a number into an ALGERBRAIC EXPRESSION

A

Plug into the corisponding numbers

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8
Q

How to SOLVE a simple LINEAR EQUATION

A

Isolate the variable

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9
Q

How to add and subtract LINE SEGMENTS

A

Add the segments

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10
Q

How to find the THIRD ANGLE of a TRIANGLE, given the other two angles

A

Add up to 180o

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11
Q

How to use PEMDAS

A

parentheses

Exponents

Multiplication/Division

Addition/Subtraction

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12
Q

How to use the PERCENT FORMULA

A

Part = Percent/100 x Whole

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13
Q

How to use the PERCENT INCREASE/DECREASE FROMULAS

A

Percent Change = amount change / original whole * 100%

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14
Q

How to perdict whether a sum. difference. or product will be ODD or EVEN

A

Take small numbers and see (2,3)

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15
Q

How to recognize MULTIPLES OF 2, 3, 4, 5, 6, 9, 10, and 12

A

2: Last digit is even
3: Sum of digits is a multiple of 3
4: Last two digits are a multiple of 4
5: Last digit is 5 or 0
6: 3 plus las digit is even
9: Sum is multiple of 9
10: Last digit is 0
12: 3 plus last two digits are a multiple of 4

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16
Q

How to find a COMMON FACTOR of two numbers

A

Find prime factors then multiple combiniations

(Smallest factor)

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17
Q

How to find a COMMON MULTIPLE of two numbers

A

Find prime factorization then multiple by the number of times each is seen

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18
Q

How to find the AVERAGE or ARITHMETIC MEAN

A

Average = Sum of terms / Number of terms

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19
Q

How to use the AVERAGE to find the SUM

A

Sum = Average x Number of terms

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20
Q

How to find the AVERAGE of CONSECUTIVE NUMBERS

A

Sum of smallest and largest / 2

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21
Q

How to COUNT CONSECUTIVE NUMBERS inclusively

A

B - A + 1

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22
Q

How to find the SUM OF CONSECUTIVE NUMBERS

A

Sum = Average x Number of terms

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23
Q

How to find the MEDIAN

A

Put in numerical order and take middle

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24
Q

HOW TO FIND THE MODE

A

The number that appears the most

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25
Q

How to find the RANGE

A

Difference between the greatest and least values

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26
Q

How to use acctual numbers to determine a RATIO

A

Ratio = of / to

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27
Q

How to use a ratio to determine an ACTUAL NUMBER

A

Cross product

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28
Q

How to use actual numbers to determine a RATE

A

Divided number by time

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29
Q

How to deal with TABLES, GRAPHS, AND CHARTS

A

Aproximate and choose closest read everything

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30
Q

How to count the NUMBER OF POSSIBILITIES

A

Multiple number of ways

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31
Q

How to calculate a simple PROBABILITY

A

Probability = Number of favorable outcomes / Total number of possible outcomes

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32
Q

How to work with new SYMBOLS

A

Read the problem

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33
Q

How to SIMPLIFY BINOMIALS

A

Multiply out

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34
Q

How to FACTOR certain POLYNOMIALS

A

ab + ac = a(b + c)

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

a2 - b2 = (a - b)(a + b)

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35
Q

How to solve for one variable IN TERMS OF ANOTHER

A

isolate x on one side leaving y on the other

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36
Q

How to solve an INEQUALITY

A

Solve like an equation

Flip sing for negetaive quantity

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37
Q

How to handle ABSOLUTE VALUES

A

Solve for both negitive and positive

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38
Q

How to TRANSLATE ENGLISH INTO ALGEBRA

A

Addition - sum, plus, and

Subtraction - difference beteen, minus

Multiplicaiton - of, product, times

Division - quotient, per

Equals - is, was, will be

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39
Q

How to find and ANGLE formed by INTERSECTING LINES

A

Angles along a line add to 180o

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40
Q

How to find an angle formed by a TRANSVERSAL across PARALLEL LINES

A

All abtuse (>90) are equal

All acute (<90) are qual

acute + abtuse = 180

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41
Q

How to find the AREA of a TRIANGLE

A

Area = 1/2 bh

42
Q

How to work with ISOSCELES TRIANGLES

A

Two equal sides and angles

43
Q

How to work with EQUILATERAL TRIANGLES

A

Three queal sides and 60 angles

44
Q

How to work with SIMILAR TRIANGLES

A

Angles are equal and sides are proportional

45
Q

How to find the HYPOTENUSE or a LEG of a RIGHT TRIANGLE

A

a2+ b2 = c2

46
Q

How to spot SPECIAL RIGHT TRIANGLES

A

30 - 60 - 90 (3,4,5)(1,sq3,2)

45 - 45 - 90 (5,12,13) (1,1,sq2)

47
Q

How to find the PERIMETER of a RECTANGLE

A

Perimeter = 2(length + width)

48
Q

How to find the AREA of a RECTANGLE

A

Area = lw

49
Q

How to find the AREA of a SQUARE

A

Area = side2

50
Q

How to find the AREA of A PARALLELOGRAM

A

Area = (base)(height)

51
Q

How to find the AREA of a TRAPEZOID

A

Area = (average of parallel sides) x height

52
Q

How to find the CIRCUMFERENCE of a CIRCLE

A

C = 2πr

53
Q

How to find the AREA of a CIRCLE

A

A = πr2

54
Q

How to find the DISTANCE BETWEEN POINTS on the coordinate plane

A

Same x or y subtract (always positive)

If not use pythagorean theorem

55
Q

How to find the SLOPE of a LINE

A

Slope = Change in y / Change in x

56
Q

How to determince COMBINDED PERCENT INCREASE/DECREASE

A

Start with a 100 and work

57
Q

How to find the original WHOLE befre percent increase/decrease

A

Subtract or add percent to 1

58
Q

How to solve a SIMPLE INTEREST problem

A

interest = (principal) * (interest rate) * (time)

interest rate - decimal

time - years or fraction of a year

59
Q

How to solve a COMPOUND INTEREST problem

A

Final balance = (prinicpal) * ( 1 + interest rate/c)(time)(c)

c - number of times compounded annually

60
Q

How to solve a REMAINDERS problem

A

Pick a number and see what happens

61
Q

How to solve a DIGITS problem

A

Logic and trial/error

62
Q

How to find a WEIGHTED AVERAGE

A

Give each the weight then average

63
Q

How to find the NEW AVERAGE when a number is added or deleted

A

Find the original sum - number * average

Add new value and average

64
Q

How to use the ORIGINAL AVERAGE and NEW AVERAGE to figure out WHAT WAS ADDED OR DELETED

A

Number Added = new sum - original sum

Number deleded = original sum - new sum

65
Q

How to find an AVERAGE RATE

A

Average A per B = Total A / Total B

66
Q

How to solve a COMBINED WORK PROBLEM

A

inverse of time for each = inverse combinded

1/x + 1/y = 1/t

1 over fraction flips fraction

67
Q

How to determine a COMBINED RATIO

A

Multiply by the common then line up

68
Q

How to sovle a DILUTION or MIXTURE problem

A

Add then divide

or balance

69
Q

How to solve a GROUP problem involving BOTH/NEITHER

A

Group 1 + Group 2 + Neither - Both = Total

70
Q

How to solve a GROUP problem involving EITHER/OR CATEGORIES

A

Organize in a gride

71
Q

How to work with FACTORIALS

A

Product (x) of 1 to n

0! = 1

Division bring out till canceled

8! = 8 * 7!

72
Q

How to sovle a PERMUTATION problem

A

Factorial ways if using all

P = n! / (n-k)!

n - # in the larger group

k - # arranging

73
Q

How to solve a COMBINATION problem

A

When order does not matter

C = n!/k!(n-k)!

n - # in the larger group

k - # you’re choosing

74
Q

How to sovle PROBABILITY problems where probabilities must be multiplied

A

Probability = Number of favorable outcomes / Number of possible outcomes

Probability of the first * probability of the second

Coing is multiple ways of getting heads or tails

75
Q

How to deal with STANDARD DEVIATION

A

Find the average of the set

find the differences between the mean and each value

square each of the differences

find the average of the squared differences

Take the positive square root of the average

76
Q

How to MULTIPLY/DIVIDE VALUES WITH EXPONENTS POWERS

A

Multiply - Add exponents

Divide - Subtract exponents

77
Q

How to handle a value with an EXPONENT RASTED TO AND EXPONENT

A

Multiply exponents

78
Q

How to handle POWERS with a base of ZERO and POWERS with an EXPONENT of ZERO

A

0 to anything = 0

Anything raised to 0 = 1

0 raised to 0 is undefined

79
Q

How to handle NEGATIVE POWERS

A

The reciprocal of the number rasied to the exponent

80
Q

How to handle FRACTIONAL POWERS

A

Relate to roots

81
Q

How to handle CUBE ROOTS

A

Only one cube root

same sign as number

82
Q

How to ADD, SUBTRACT, MULTIPLY, AND DIVIDE ROOTS

A

Add and subtract only when the parts inside are the same

Multiple and devide deal with both parts separately

83
Q

How to SIMPLIFY A RADICAL

A

Find perfect squares (4,9,16,25,36)

Bring out and siplify

84
Q

to solve certain QUADRATIC EQUATIONS

A

Manipulate to = 0

Factor the left side into two sets

85
Q

How to solve MULTIPLE EQUATIONS

A

Align terms and add

86
Q

How to solve a SEQUENCE problem

A

Plug the nth into the formula

87
Q

How to solve a FUNCTION problem

A

Plug numbers in

1 to 1

88
Q

How to handle GRAPHS of FUNCTIONS

A

Pick obvious points and plug into the problem

89
Q

How to handle LINEAR EQUATIONS

A

y - mx + b

m = slope = rise/run

b = y intercept

plug in if necisary

90
Q

How to find the x- and y-INTERCEPTS of a line

A

x - y = 0

y - x = 0

91
Q

How to find the MAXIMU and MINIMUM lengths for a SIDE of a TRIANGLE

A

Third side is greater then the difference (-) and less than the sum (+)

92
Q

How to find one angle or the sum of all the ANGLES of a REGULAR POLYGON

A

Sum = (n-2) * 180

Degree = ((n-2)*180)/n

93
Q

How to find the LENGTH of an ARC

A

Length = (n/360) * 2πr

94
Q

How to find the AREA of a SECTOR

A

Area of sector = (no/360) x πr2

95
Q

How to find the dimensions or area of an INSCRIBED or CIRCUMSCRIBED FIGURE

A

Find a corilation

96
Q

How to find the VOLUME or a RECTANGULAR SOLID

A

Volume = length x width x height

97
Q

How to find the SURACE AREA of a RECTANGULAR SOLID

A

Surface Area = 2(lw) + 2(wh) + 2(lh)

98
Q

How to find the DIAGONAL of a RECTANGULAR SOLID

A

Use Pythagorean theorem twice

Once for the top face

Then once for the diaganal

99
Q

How to find the VOLUME of a CYLINDER

A

Volume = πr2h

100
Q

How to find the SURFACE AREA of a CYLINDER

A

Surface area = 2πr2 + 2πrh

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