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DAT > Quantitative Reasoning > Flashcards

Quantitative Reasoning Flashcards

1
Q

How do you multiply fractions

A

Numerators x Numerators

Denominators x Denominators

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2
Q

How do you divide fractions

A

Flip the second Fraction

Then multiply

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3
Q

How do you add/subtract Fractions

A

get a common denominator and add/subtract the numerators (don’t change the denominator)

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4
Q

How do you go about comparing Fractions

A

get a common denominator and compare

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5
Q

How do you set up a ratio

A 
of = on top
to = on bottom
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6
Q

how do you solve a proportion

A

Cross multiply across the = sign

x/5 = 3/4
15/4

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7
Q

How do you do long division

A

see how many times the deominator can go into the numerator

15/400 = .037

400 goes into .03 times
15.00 - 12.00 = 3
How many times does 400 go into 3 (.007)

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8
Q

change .564 into a fraction

A

564/1000
282/500
141/250

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9
Q

how do you divide decimals

A

make them whole numbers and divide

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10
Q

what does percent =

A

part/whole

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11
Q

How do you find % increase

A

amount of increase/ Original whole

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12
Q

how do you find probability

A

of desired outcomes / # of possible outcomes

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13
Q

If we rolled 2 dice, what would be the probability of a total of 4

A

3 possible desired outcomes / 36 total outcomes (6x6)

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14
Q

how do you multiply powers with the same base

A

add the exponents

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15
Q

how do you divide powers with the same base

A

subtract the exponents

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16
Q

how do you raise the power to an exponent

A

multiply the exponents

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17
Q

how do you multiply powers with the same exponent

A

multiply the bases keep the exponent

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18
Q

how do you divide powers with the same exponent

A

divide the bases and keep the exponent

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19
Q

how do you divide polynomials

A

you just simply do long division with polynomials

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20
Q

What is finding a common factor in a polynomial

A

when you look at each part of the polynomial is there a common factor between all parts of the polynomial

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21
Q

How do you recognize differences of squares

A

when you have two identifiable squares with a minus sign between them

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22
Q

4x^2 - 9

A

(2x-3)(2x+3)

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23
Q

Learn to recognize squares of binomials

A

a^2 + 2ab + b^2 = (a+2)^2

a^2 - 2ab + b^2 = (a-b)^2

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24
Q

How can you factor out harder polynomials

A

plug in a 0 and see which answer equals the question. Then check all others to see if there are more. if there are more then plug in another number.

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25
Q

What are two ways to get an unknown out of a denominator

A
  1. multiply both sides by the unknown (if alone)

2. get one fraction on each side and cross multiply

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26
Q

how do get the unknown out of an exponent

A

You must get the bases to equal eachother. you do this by finding what they are both powers of (a common unpower)

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27
Q

8^x = 16 ^ (x-1)

A

both are unpowers of 2 (2^3 = 8) (2^4 = 16)
(2^3)^x = (2^4)^(x-1)
2^3x = 2^(4x-4)
since the bases are equal you can just set the exponents equal to each other and solve for x

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28
Q

How can you solve quadratic equations

A

1) get x^2 + x + # = 0 and try to factor the left side
2) quadratic formula
(negative b plus or minus the square root of b squared minus 4 a c. all over 2a)

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29
Q

How do you solve “in terms of” equations

A

get your variable all alone

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30
Q

What do you do here ax-x = something

A

divide by a-1

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31
Q

what do you do for aboslut values

A

think of it as two equations

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32
Q

What to remember when solving for an inequality

A

if you multiply or divide by a negative number you must flip the sign

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33
Q

When you have (absolute value) < X

or (absolute value) > X

A

you leave the sign the same

  • X < (absolute value) < X
  • X > (absolute value) > X
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34
Q

how do you find the area of a triangle

A

1/2 (base)(Height)

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35
Q

What is the triangle inequality theorum

A

the length of the third side is smaller than the two other sides added together, but larger than the larger side minus the smaller one

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36
Q

what does the sum of the interior angles of a triangle =

A

180

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37
Q

what does the sum of the exterior angles of a triangle =

A

360 (a polygons)

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38
Q

What to remember about similar triangles

A
  1. Figure out if they are indeed similar
  2. If so they have the same angles, and their sides are proportional
  3. The area of the triangles go as follows
    - proportional side ratio 2:1 area equals x^2
    - proportional side ratio 3:1 area equals 3^2
    (what ever the ratio is, that is raised to the power of two for area)
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39
Q

Isosceles triangle

A

when two sides, and two base angles are the same

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40
Q

How do you find the area of an equilateral triangle

A

S^2(Square root of 3)/4

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41
Q

What are some pythagorean triplets

A 
3,4,5 
5,12,13
7,24,25
8,15,17
9,40,41
11,60,61
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42
Q

What is the ratio of sides in a 45,45,90 triangle

A

1: 1:1(Square root of 2)
2: 2:2(square root of 2)

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43
Q

What is the ratio of sides in a 30,60,90 triangle

A

1:(Square root of 3):2
2:2(square root of 3):2
Hypoteneuse is twice the size of the shortest leg, and the other leg is the short leg times by the square root of three

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44
Q

What is the area of a trapezoid

A

(Base1 + base2)/2 *height

The bases are the two parallel sides

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45
Q

What is the area of a parallelagram

A

base * height

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46
Q

What is the area of a hexagon

A

3s^2(square root of three)/2

47
Q

How do you find the circumference of a circle

A

2(pie)r

(pie)d

48
Q

How do you find the length of an ARC

A

(n/360)(2”pie”r)

49
Q

how do you find The area of a circle

A

“pie”r^2

50
Q

How do you find the area of a sector

A

(n/360)(“Pie”r^2)

51
Q

how do you find the lateral area of a cone

A

1/2cl
c = base circumference
l = slant height

52
Q

How do you find the volume of a cone

A

1/3”pie”r^2*h

53
Q

how do you find the surface area of a sphere

A

4”pie”r^2

54
Q

How do you find the volume of a sphere

A

4/3”pie”r^3

55
Q

How do you find the volume of a pyramid

A

1/3Bh

56
Q

how do you find the surface area of the rectangular solid

A

2lw + 2wh + 2 lh

57
Q

how do you find the volume of an uniform solid

A

area of the base * height

58
Q

how do you find the area of a rectangular solid

A

lwh

59
Q

How do you find the volume of a cube

A

side^3

60
Q

How do you find the volume of a cylinder

A

“pie”r^2 * h

61
Q

How do you find distance between points on a grid

A

Distance = Square root of (x1-x2)^2 + (y1-y2)^2

62
Q

What are the slopes of two perpendicular lines

A

one and it’s opposite reciprocal

2 and -1/2

63
Q

how do you find the turning point on a graph with an absolute value

A

Not sure yet, maybe whatever value makes the absolute value thing = 0

64
Q

What is the reciprocal of sine, cosine, and tangent

A

cosecant, secant, cotangent

65
Q

What does sin^2 x + cos^2 x = ?

A

sin^2 x +cos^2 x = 1

66
Q

What does tan^2 x + 1 =

A

tan ^2 x + 1 = sec ^2 x

67
Q

What does 1 + cot^2x = ?

A

1 + cot^2x = csc^2 x

68
Q

what does 2 pie radians =

A

360 degrees

69
Q

What does 1 Radian =

A

180/pie (57.3 degrees)

70
Q

what does 3 radians =

A

360/2pie

71
Q

what does sin 0 =

A

0

72
Q

What does sin 30 =

A

1/2

73
Q

what does sin 45 =

A

1/ square root of 2

74
Q

what does sin 60 =

A

3/2

75
Q

what does sin 90 =

A

1

76
Q

What does cos 0 =

A

1

77
Q

what does cos 30 =

A

3/2

78
Q

what does cos 45=

A

1/ square root of 2

79
Q

what does cos 60 =

A

1/2

80
Q

what does cos 90 =

A

0

81
Q

what does tan 0 =

A

0

82
Q

what does tan 30 =

A

1/ square root of 3

83
Q

what is tan 45

A

1

84
Q

what is tan 60

A

square root of 3

85
Q

what is tan 90

A

not defined

86
Q

what is cot 0

A

not defined

87
Q

what is cot 30

A

square root of 3

88
Q

what is cot 45

A

1

89
Q

what is cot 60

A

1/ square root of 3

90
Q

what is cot 90

A

0

91
Q

what is sec 0

A

1

92
Q

what is sec 30

A

2/ square root of 3

93
Q

what is sec 45

A

square root of 2

94
Q

what is sec 60

A

2

95
Q

what is sec 90

A

not defined

96
Q

what is cosec 0

A

not defined

97
Q

what is cosec 30

A

2

98
Q

what is cosec 45

A

square root of 2

99
Q

what is cosec 60

A

2/ square root of 3

100
Q

what is cosec 90

A

1

101
Q

What happens to the sins cos as you pass 90 degrees

A

you just begin to go back,
so sin 60 = sin 120
cos 15 = cos 105

102
Q

What happens to the sins and cos as you pass 180 degrees

A

you just make the normal one negative

sin -30 = -1/2

103
Q

What does the sin -1 of 7/74

A

sin Angle = 7/74

104
Q

How do you get the volume of a prism

A

V = base area x h

105
Q

What is the area of an equilateral triangle

A

Area = [S^2 (square root of 3)]/4

106
Q

how do you find the center of a circle (X-2)^2 + (Y-5)^2

A

x= 2, y= 5

(2,5) is the center of the circle

107
Q

What does tan (theta) =

A

sin (theta)/cos (theta)

108
Q

what does Sec =

A

1/cos

109
Q

what does sin^2 + cos^2 =

A

1

110
Q

what does sin =

A

Cos x Tan

111
Q

what are the sin/cos/tan values for Quadrant 1,2,3,4

A

Quadrant 1 +sin, +cos, +tan
Quadrant 2 +sin, -cos, -tan
Quadrant 3 -sin, -cos, + tan
Quadrant 4 -sin, +cos, -tan

112
Q

what does pie/6 =

A

30 degrees

113
Q

what is the equation for annual interest

A 
A = P(1 + (r/n)^nt
A = amount in the account
P = starting amount
r = interest rate (decimal)
n = number of times compounded anually
t = time in years

DAT (14 decks)

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