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GRE > Math > Flashcards

Math Flashcards

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1
Q

Rate equation

A
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2
Q

Range

A

Difference between the highest and lowest number in a list

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3
Q

Mean (average), median, mode, range

A

Median: middle value of a list

Mode: occurs most frequently in a list (the “most”)

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4
Q

Ratio box

A
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5
Q

Rules of exponents: MADSPM

A
  • When equal bases are Multiplied, Add the powers
  • When equal bases are Divided, Subtract the powers
  • When exponent is raised to a Power, Multiply the powers
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6
Q

Rules of exponents: negative exponents

A

Raise the reciprocal to the positive power

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7
Q

Rules of exponents: zero exponent

A

Always equal to zero

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8
Q

Rewriting exponents (beyond 5 rules)

A
  1. Rewrite using common bases
  2. Factor expression
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9
Q

Negative number raised to even power results in a positive or negative number?

A

positive

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10
Q

Negative number raised to odd power results in a positive or negative number?

A

Negative

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11
Q

Rules for adding and subtracting square roots

A
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12
Q

Rules for multiplying and dividing square roots

A
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13
Q

How to eliminate square roots

A

Raise to power of 2 (including rest of terms)

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14
Q

How to simplify square roots

A

Factor number under root that results in a perfect square

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15
Q

Expanded quadratic equations

A

Variable sqared; variable x coefficient; coefficient

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16
Q

How to factor a quadratic equation

A
  1. Separate x2 into: (x ) (x )
  2. Find factors of third term that, when added or subtracted, yield second term
  3. Determine operations that correspond to each term (+ or -)
  4. Solve for both roots (x=0)
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17
Q

What do fully factored quadratic equations look like?

A

Two sets of (x +/- number) = 0

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18
Q

How to expand a factored quadratic equation

A

Utilize FOIL: multiply First, Outside, Inside, Last

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19
Q

Common quadratic equations

A
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20
Q

Inequalities: When multiply or divide by negative number, must…

A

change direction of inequality symbol.

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21
Q

How to manipulate two equatuons with two variables

A

Add or subtract entire equation from another to cancel variable out (will most likely have to multiply one equation to get same number associated with variable)

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22
Q

Steps for plugging in numbers

A

Plug in when variables in problem and answer choices. Check ALL answer choices.

Selecting number:

  1. Use easy numbers that make sense in context
  2. Avoid numbers 1 and 0
  3. Avoid numbers that show up a lot in question or answers
  4. Avoid plugging in same number for multiple variables
  5. Avoid plugging in conversion numbers
  6. Fractions: choose number that works easily with fractions (e.g. product of demoninators)
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23
Q

Signs to plug in the answer (PITA)

A
  1. “How much” or “How many” type questions
  2. Inclination to write algebraic formula
  3. Answers are in ascending or descending order
  4. Variables are present
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24
Q

Steps for plugging in the answer (PITA)

A

Start with C, use “spreadsheet” to stay organized

25
Q

Plugging in on quantitative comparisons: FROZEN

A

When variables used, plug in twice using FROZEN:

  • Fractions - Repeats - One - Zero - Extremes - Negatives
  • (Repeats can be converstion numbers)
26
Q

Definition of prime number

A

Only factors are itself and 1

  • 0 and 1 are not prime; 2 is only even prime
  • Can only by positive integers
27
Q

Integer divisibility rules

A
  • Integer is divisible by 3 if sum of digits is divisible by 3
  • Integer is divisible by 4 if last two digits form number divisible by 4
  • Integer is divisible by 6 if divisible by both 2 and 3
  • Divisible by 8 if last 3 digits form number divisible by 8
  • Divisible by 9 if sum of digits is divisible by 9
28
Q

P | E | MD | AS

A
  1. Parenthesis
  2. Exponents
  3. Multiplication & division
  4. Addition & subtraction
29
Q

How to add/subtract fractions

A

Find lowest (or any) common demoninator.

Bowtie method:

30
Q

How to compare fractions

A

Bowtie method without multiplying bottom

31
Q

How to convert mixed numbers into fractions

A

Multiple denominator by integer and add to numerator

32
Q

Divisor, dividend, and quotient

A
33
Q

Definition of remainder

A

Leftover when one integer is not divisible by another

34
Q

Percentages in word problems

A
35
Q

Percent change equation

A

Note: For “difference”, always subtract lesser from greater

36
Q

Distributive law

A
37
Q

Types of triangles

A
38
Q

Triangle third side rule

A

Length of any one side of a triangle must be less than sum of other two sides and greater than difference between other two sides.

I.e. L = side length

(L1-L2) < L3 < (L1+L2)

39
Q

Area of a triangle

A
40
Q

Pythagorean theorum and super pythagorean theorum

A

Pythagorean: a2+b2=c2

Super pythagorean (diagonal in a rectangular solid): a2+b2+c2=d2

41
Q

30 : 60 : 90 right trangles

A
42
Q

45 : 45 : 90 right triangles

A
43
Q

Circumference of circle

A

circumference = 2πr or πd

44
Q

Circles: chords, arcs and central angles

A

Arcs and their central angles are always proportional

45
Q

Area of a circle

A

Area = πr2

46
Q

Sum of angles in a polygon

A

Sum of angles = 180(n-2)

47
Q

Quadrant numbering

A
48
Q

Equation of a line; slope

A

y = mx+b

slope = rise/run

49
Q

Surface area and volume of a cylinder

A

Surface area = 2πr(height)+2(πr2)

Volume = πr2(height)

50
Q

Surface area and volume of a rectangular solid

A

Surface area = 2(LW)+2(LH)+2(WH)

Volume = LWH

51
Q

How to find slope of a perpendicular line

A

Negative reciprocal

52
Q

Finding probability of: 1) one event AND another, 2) one event OR another

A

Probability of A and B = Probability of A x Probability of B

Probability of A or B = Probability of A + Probability of B

53
Q

Probability of A + Probability of not A =

A

1

54
Q

How to deal with factorials

A

Cancel or factor out, e.g.:

55
Q

Difference between permutations and combinations

A

With a combination, the order is irrelevant.

Permutations often ask for arrangements, orders, schedules or lists.

56
Q

To solve a permutation:

A

Similar to factorials

  • Figure out how many slots
  • Write down number of options for each slot
  • Multiply
57
Q

To solve a combination:

A

* Figure out how many slots

  • Fill in slots as you would a permutation
  • Divide by factorial of number of slots

E.g.:

58
Q

How to deal with strange symbols: #*µ⍛

A

Treat as a f(x) problem and use plug in strategies

59
Q

Group equation

A

T = G1 + G2 – B + N

T = total; G1 = first group; G2 = second group; B = members in both groups; N = members in either group

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