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FE Prep > Math > Flashcards

Math Flashcards

1
Q

What is the Unites States unit system called?

A

US Customary System (USCS)

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2
Q

What is the gravitational acceleration in ft/s^2?

A

32.174 ft/s^2

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3
Q

What is the gravitational acceleration in m/s^2?

A

9.807 m/s^2

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4
Q

What multiple of 10 does the prefix “deka” represent?

A

10^1

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5
Q

What multiple of 10 does the prefix “hecto” represent?

A

10^2

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6
Q

What multiple of 10 does the prefix “kilo” represent?

A

10^3

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7
Q

What multiple of 10 does the prefix “mega” represent?

A

10^6

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8
Q

What multiple of 10 does the prefix “giga” represent?

A

10^9

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9
Q

What multiple of 10 does the prefix “tera” represent?

A

10^12

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10
Q

What multiple of 10 does the prefix “peta” represent?

A

10^15

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11
Q

What multiple of 10 does the prefix “exa” represent?

A

10^18

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12
Q

What multiple of 10 does the prefix “deci” represent?

A

10^-1

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13
Q

What multiple of 10 does the prefix “centi” represent?

A

10^-2

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14
Q

What multiple of 10 does the prefix “milli” represent?

A

10^-3

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15
Q

What multiple of 10 does the prefix “micro” represent?

A

10^-6

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16
Q

What multiple of 10 does the prefix “nano” represent?

A

10^-9

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17
Q

What multiple of 10 does the prefix “pico” represent?

A

10^-12

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18
Q

What multiple of 10 does the prefix “femto” represent?

A

10^-15

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19
Q

What multiple of 10 does the prefix “atto” represent?

A

10^-18

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20
Q

What is the conversion factor of F to C?

A

1.8C + 32

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21
Q

What is the conversion factor of F to R?

A

F + 459.69

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22
Q

What is the conversion factor of C to K?

A

C + 273.15

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23
Q

In addition or subtraction between 2 numbers with a different number of significant figures after the decimal point, how many significant figures are after the decimal point in the sum or difference?

A

The same as the number with the least significant figures after the decimal point.

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24
Q

In addition or subtraction between 2 numbers with a different number of significant figures before the decimal point, how many significant figures are before the decimal point in the sum or difference?

A

The same as the number with the most significant figures before the decimal point.

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25
Q

How many significant figures are in a product or dividend?

A

The same as the number with the least amount of significant figures.

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26
Q

What does a∈A mean?

A

a is a member or element of A.

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27
Q

What does { } or Φ represent?

A

The empty or null set.

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28
Q

What does A ⊆ B mean?

A

A is a subset of B.

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29
Q

What does A ⊂ B mean?

A

A is a proper subset of B.

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30
Q

What is a proper subset?

A

A proper subset is a subset that is not equal to the set it is a subset to.

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31
Q

What is (a,b)?

A

An ordered pair.

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32
Q

What is an ordered pair?

A

A collection of 2 elements in which the order matters.

33
Q

What does the symbol P(s) mean?

A

The power set of s.

34
Q

What is a power set?

A

The set of all subsets.

35
Q

What does A ∪ B mean?

A

The union of sets A and B.

36
Q

What is a mathematical union?

A

The combination of all elements in both sets to form a single set containing all elements in both.

37
Q

What does A ∩ B mean?

A

The intersection of sets A and B.

38
Q

What is an intersection of 2 sets?

A

The set of elements shared by both sets.

39
Q

What does A×B mean in set theory?

A

The Cartesian Product of A and B.

40
Q

What is the Cartesian product of 2 sets?

A

The set of all variations of ordered pairs between the 2 sets.

41
Q

What is the Cartesian product of 2 sets?

A

A set containing all possible combinations of ordered pairs between the elements of both sets.

42
Q

What does ∀x mean?

A

“For every” x. Or that whatever follows the symbol applies to all x.

43
Q

What does ∃x mean?

A

“There exists” within x, or there is exactly one element in x where the statement following the symbol holds true.

44
Q

What is the general form of the straight line equation?

A

Ax + By + C = 0

45
Q

What is the standard form of the line equation?

A

y = mx + b

46
Q

What is the point slope form of the line equation?

A

y - y1 = m(x -x1)

47
Q

What is the equation to solve for the roots to the quadratic equation?

A

X = (-b ± (b^2 - 4ac)^(1/2)) / (2a)

48
Q

What is the equation to a sphere?

A

(x - h)^2 + (y - k)^2 + (z - m)^2 = r^2 with center at (h, k, m)

49
Q

What is the algebraic manipulation of logb(x) = c?

A

b^c = x

50
Q

How do you change from one logarithm base to another?

A

logb(x) = (loga(x)) / (loga(b))

51
Q

What is logb(b^n)?

A

n

52
Q

What is an algebraic manipulation of log(x^c)?

A

clog(x)

53
Q

What is an algebraic manipulation of log(xy)?

A

log(x) + log(y)

54
Q

What is an algebraic manipulation of log(x / y)?

A

log(x) - log(y)

55
Q

Where a complex number in polar form is z = c ∠ θ, how does c relate to a and b where z = a + bi?

A

c = (a^2 + b^2)^(1/2)

56
Q

Where a complex number in polar form is z = c ∠ θ, how does θ relate to a and b where z = a + bi.

A

θ = tan^-1(b/a)

57
Q

How does a in the complex form z = a + bi relate to the complex form z = c ∠ θ?

A

a = c cos(θ)

58
Q

How does b in the complex form z = a + bi relate to the complex form z = c ∠ θ?

A

b = c sin(θ)

59
Q

How do you add complex numbers?

A

Algebraically in rectangular form.

60
Q

How do you multiply complex numbers?

A

Multiply c components and add angles.

61
Q

What is the mathematical definition of a complex conjugate?

A

Where z = a + bi, z* = a - bi.

62
Q

What is eulers formula?

A

e^(ix) = cosx + isinx

63
Q

What is the law of sines?

A

a/(sinA) = b/(sinB) where a and b are sides on the same triangle and A and B are the opposite angles on that same triangle.

64
Q

What is the law of cosines?

A

a^2 = b^2 + c^2 - 2bccos(A)

65
Q

What is the volume of a sphere?

A

V = 4πr^3/3

66
Q

What is the surface area of a sphere?

A

4πr^2

67
Q

What is the volume of a right circular cone?

A

V = πr^2h/3

68
Q

What is the surface area of a right circular cone?

A

πr(r + (r^2 + h^2)^(1/2))

69
Q

How is csc defined?

A

1/sin

70
Q

How do you define cos θ using eulers identity?

A

(e^(jθ) + e^(-jθ))/2

71
Q

How do you define sin θ using eulers identity?

A

e^(jθ) - e^(-jθ)/(2j)

72
Q

What is the definition of dy/dx?

A

The limit as x approaches 0 of delta y/delta x.

73
Q

How do you check for local maxima?

A

f’(a)=0 and f”(a)<0

74
Q

How do you check for local minima?

A

f’(a)=0 and f”(a)>0

75
Q

What is an inflection point?

A

Where curvature changes from convex to concave or vice versa.

76
Q

How do you verify an inflection point?

A

f”(a)=0 and signs are flipped in f”(a) on either side of a.

77
Q

How do you determine a partial derivative?

A

Treat all other variables as constants.

78
Q

What is the chain rule?

A

dy/dx=dy/du * du/dx

FE Prep (2 decks)

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