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Math Flashcards

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1
Q

sqrt(5)*sqrt(8)

A

sqrt (5*8)

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2
Q

Logb(M) - Logb(N)

A

Logb(M/N)

Log(10)-Log(5)= Log(2)

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3
Q

Logb(M^z)

A

zLogb(M)

Log(10^3)= 3Log(10)

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4
Q

Formula for combining options (where must pick one option per number of options)

Ie. there are 3 types of shells, 4 types of meat, 3 types of cheese, and 5 types of salsa. How many distinct tacos can be ordered assuming that any order contains exactly one of each of the above choices?

A

Total combinations = # of options x # of options etc…

Total combinations of tacos = 3 x 4 x 3 x 5 = 180

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5
Q

x^(a/b)

A

b-root(x^a)

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6
Q

Isosceles triangle

A

Two sides are equal

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7
Q

The reflection of y=2x+5

A

x=2y+5

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8
Q

Height of an equilateral triangle

A

(1/2)(length of sides)(√3)

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9
Q

Value of deposit using simple interest

A

V=P(1+(rt/100))

Assuming r is in decimal form (eg. 10% int= .10)

V= P (1+rt)

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10
Q 
Points on graph:
P
P'
P''
P'''
A

P: quadrant I (4,2)
P’: quadrant IV (4, -2)
P’’: quadrant II (-4, 2)
P’’’: quadrant III (-4, -2)

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11
Q

Formula for finding arc,angle, or area of sector when it is positioned at center of a circle

A

(sector angle/circle angle)=(sector arc/circle circumference)=(sector area/circle area)

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12
Q

Q3

A

Median of values above Q2 (median of data set)

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13
Q

Probability for all events happening together (“AND” question)

A

Multiply probabilities together

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14
Q

Rhombus

A
  • A parallelogram with equal sides
  • Area = bxh
  • If all the angles are right angles then it is a square
  • The rhombus with the largest possible area is a square
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15
Q

Sum in geometric sequence

A

(a[1-r^n])/[1-r]

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16
Q

Logb(M)+Logb(N)

A

Logb(MN)

Log(10)+Log(5)= Log(50)

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17
Q

Slopes of perpendicular lines

A

Inverse negatives of each other

Line A = 8
Line B = -1/8

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18
Q

Third side rule of triangles

A

Any side of a triangle must be greater than the difference of the other two sides, and less than their sum

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19
Q

Trapezoid

A
  • Quadrilateral with two sides parallel
  • Isosceles trapezoid: base angles are equal, so non-parallel sides are equal
  • Area of trapezoid: [(b1+b2)/2)] x height, where b1 and b2 are the lengths of the parallel sides
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20
Q

How to find vertex of parabola

A

Set equation = 0 to find x- intercepts
The x value of the vertex will be halfway between those intercepts.
Plug in x-value to find y-value of the vertex

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21
Q

Solving inequalities

A

Same as regular equations, except when both sides of the inequality are multiplied or divided by a negative number, the direction is reversed

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22
Q

5^2 x 2^2

A

10^2

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23
Q

Q1

A

Median of values below Q2 (median of data set)

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24
Q

What does it mean if the product of two numbers is odd?

A

Both numbers must be odd

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25
Q

Slope

A

Rise over run

Change in y/change in x

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26
Q

Sum in arithmetic sequence

A

Average of the first and last term multiplied by n

What is the sum of the first 20 terms? ([A20+A1]/2)*20

In an arithmetic sequence, the sum of the first and last term/2 = median = mean

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27
Q

a^m/a^n

A

a^(m-n)

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28
Q

What is the approx. percentile?

1) -2 SD
2) -1 SD
3) 0 SD
4) 1 SD
5) 2 SD
6) 3 SD

A

1) 2%
2) 16%
3) 50%
4) 84%
5) 98%
6) 99%

29
Q

Formula for combinations where order doesn’t matter

1) If picking select group: the number of possible pairings of 2 colors that can be selected from 5 possible options
2) If in subgroups, the order doesn’t matter: in how many ways can the word “MISSISSIPPI be rearranged?”

A

1) Everything!/(Picked!Notpicked!)
5!/(2!3!)

2) Everything!(Group1!Group2!Etc…)

For each individual subgroup (aka letter), the order does not matter
M=1 , I=4, S=4, P=2
11!/(1!4!4!2!)

30
Q

Parallelogram

A
  • Quadrilateral with opposite sides parallel (and opposite angles equal)
  • Area = bxh
  • A parallelogram with equal sides = rhombus
  • A parallelogram whose angles are all right angles = rectangle
31
Q

Value of deposit compounded annually

A

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

32
Q

Quadratic formula

A

To find x-intercepts in equation ax^2+bx+c

x= {-b+/- root(b^2-4ac)}/2a

33
Q

Does Q1 or Q3 include the mean?

A

No. Median of the lower half or the upper half of the data (excluding the mean)

34
Q

Finding equation of circle

1) Circle with radius 3 and center at (6, -5)
2) Circle with radius 10 and center at origin

A

1) (x-6)^2+(y+5)^2 = 9

2) x^2 + y^2 = 100

35
Q

Establishing proportional trinagles

A

1) Side of one triangle is parallel to the corresponding side of another
2) All three angles are the same within the two triangles

36
Q

What happens to SD and range when

1) multiply all values in data set by x
2) divide all values in data set by x
3) Add x to all values in data set
4) Subtract x to all values in data set

**Check to see in study guides where SD changes due to addition and subtraction

A

1) SD= multiply by x, range= multiply by x
2) SD= divide by x, range= divide by x
3) SD= unchanged, range= unchanged
4) SD= unchanged, range= unchanged

37
Q

Value of deposit compounded n times per year

A

V= P(1+r/100n)^nt

38
Q

What are properties of 1 and 0?

A

Neither of them are prime numbers

0 is an even number
0 is an integer

39
Q

a^2 x b^2

A

(ab)^2

40
Q

Formula for combinations where order matters

1) If everything included: five students are lining up. How many different lines are possible?
2) Where only a select group from total is chosen: 10 student class is to choose a prez, VP, and secretary from the group. If no person can occupy more than one post, in how many ways can this be accomplished?

A

1) Everything!
5!= 5x4x3x2x1

2) Everything!/Not chosen!

10!/7!= 10x9x8
Another way of thinking about this is, how many options for first position (10), how many options for second position (9), how many options for third position (8)= 10x9x8

41
Q

sqrt(5)/sqrt(8)

A

sqrt (5/8)

42
Q

What do you need in order to say where a score falls (in what percentile?)

A

SD and mean

43
Q

x^(-a)

A

1/(x^a)

44
Q

Pythagoreum equation

A

leg^2+leg^2=H^2

  • If true, then the triangle must be a right triangle
  • If the sum of the squared legs is smaller than the square of the hypotenuse than the angle opposite the H is greater than 90
  • If the sum of the squared legs is greater than the H^2, then the angle opposite the H is smaller than 90
45
Q

Probability for “OR” question:

1) If both probabilities are independent (can happen at the same time)
2) If both probabilities can’t occur at the same time

A

1) 1-P(event never happening)

2) Add probabilities together

46
Q

30-60-90 rule

A

If triangle’s angles are 30-60-90 then the length of its sides are:

30: x
60: x√3
90: 2x

47
Q

Formula for finding arc,angle, or area of sector when it is positioned at the border of the circle (aka inscribed)

A

The central angle is 2x the inscribed angle; solve ratios from there

48
Q

45-45-90 rule

A

If triangle’s angles are 45-45-90, then the length of its sides are:

45: x
90: x√2

49
Q

Formula for sum of shape’s interior angles

A

180(n-2), where n is the number of sides

50
Q

Logb(N)

Eg. Log2(6)

A

Logx(N)/Logx(B)

Log2(6)= Log(6)/Log(2)

51
Q

If Number= base^power,

eg. 15=10^x

A

Logbase(number)=power

Log10(15)=x

52
Q

a^n * a^m

A

a^(n+m)

53
Q

If 15:x and x:100 are equivalent, what is x?

A

15/x = x/100

solve x from there

54
Q

Formula for overlapping sets, ie. students studying languages– 14 french, 12 Spanish, 10 Latin, 5 two languages

What about 14 french, 12 spanish, 10 latin, and 3 all three languages?

A

Total = set + set - overlapping set

Total students = 14 + 12 + 10 - 5

If studying all three languages, subtract 3-1 = 2 for each student
For example, if there were 3 students studying all three the total would be = 14 + 12 + 10 - (2)(3)

55
Q

Tangent line to a circle

A

Perpendicular to the radius of the circle

56
Q

(a^m)^n

A

a^mn

57
Q

How to find n for
A) odd numbers from x to y (inclusive)
B) even numbers from x to y (inclusive)
C) consecutive numbers from x to y (inclusive)

A 
A) (y-x)/2 + 1
ex. what is n of odd integers from 1 to 199?
(199-1)/2 + 1 = 100
B) (y-x)/2 + 1
ex. what is n of even integers from 2 to 50?
(50-2) / 2 + 1 = 25
C) y-x + 1
ex. what is n of numbers from 4 to 50?
(50-4) + 1 = 47
58
Q

Factor out 2^99 - 2 ^96

A

2^96(2^3 - 1)

59
Q

Value in geometric sequence

A

a*r^(n-1)

60
Q

How can we know if the triangle that is inscribed in a circle is a right triangle?

A

-Right triangle if and only if the hypotenuse of the triangle is equal to the diameter of the circle (aka right triangle inscribed in a circle must be inscribed within a semi circle)

61
Q

Value in arithmetic sequence

A

v = a + d (n-1)

d= difference between each number
a= first number
62
Q

Group A’s average score is 90 and group B’s average score is 85. There are more than twice as many students in group A than group B. What is the mean?

A

Weighted mean.

2(90)+1(85)/(2+1)= 88.333
Since there are MORE than twice as many students in group A than group B, and group A’s average is higher than group B’s average then the mean is greater than 88.3333.

63
Q

Two similar triangles. The ratio of their sides is 1:9. What is the ratio of their area?

A

1:81

64
Q

Two coal carts, A and B, started simultaneously from opposite ends of a 400 yard track. Cart A traveled at a constant rate of 40 ft/s. Cart B traveled at a constant rate of 56 ft/s. After how many seconds of travel did the two carts collide? (1 yard=3ft)

A

Distance= 400 yd= 1200 ft

When doing a problem where objects are moving towards each other, add the rates together.

Rate of A and B= 40+56= 96 ft/s

Seconds until carts collide: 1200/96= 12.5 seconds

65
Q

In a probability experiment, G and H are independent events. The probability that G will occur is (1/2) and the probability that H will occur is (1/2).

What is the probability that either G will occur or H will occur, but not both?

A

What is the probability that either G will occur, H will occur, or both?
Since independent events can occur at the same time the probability is:
(1/2)+(1/2)-(1/4)= 3/4

This is the probability of G, H, or both.
Therefore the probability of G, H, but not both is
(3/4)-(1/4)= 2/4= (1/2)

66
Q

For a certain probability experiment, the probability that event A will occur is 1/2 and the probability that event B will occur is 1/3. What possible values could be the probability that the event AUB (that is, the event A or B, or both) will occur.

A

We do not know the relationship between the two events, so we can only find the minimum possible value and the maximum value for the event.

IF OVERLAPPING COMPLETELY
Minimum possible value: the larger value, eg. 1/2.
(A can’t be a subset of B since the probability of A occurring is greater than the probability of B occurring; if B is a subset of A, then the least probability is just the probability of A– this is if they intersect completely)

IF NOT OVERLAPPING AT ALL
Maximum possible value: if A and B do not intersect at all (aka if they are mutually exclusive and cannot happen at the same time), P(A)+P(B)= 1/2 + 1/3 = 5/6.

Therefore, the probability is between 1/2 and 5/6, inclusive.

67
Q

How many zeros does 10^5 have?

A

5

68
Q

The ratio of Kim’s time to paint a house to Jane’s time to paint a house is 3:5. If Kim and Jane work together at their respective constant rates, they can paint a house in 10 hours. How many hours does it take Kim to paint the house alone?

A
  • If it takes Kim and Jane 10 hours to paint a house then their combined rate is 1/10= .1 house/hr
  • ***so K+J= .1
  • If K:J time is 3:5 then K:J rate is 5:3 (less time means faster speed
  • ***in other words, Kim is 5/3 times faster than Jane
  • ***so K=5/3 J or J= 3/5K
  • Solving from here, you can find that K= .0625, aka .0625 house/hr
  • Dividing 1 by .0625, you can find that it takes Kim 16 hours to paint the house alone

GRE Math (1 decks)

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