Math

Question 1

What is the Unites States unit system called?

Answer 1

US Customary System (USCS)

Question 2

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

Answer 2

32.174 ft/s^2

Question 3

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

Answer 3

9.807 m/s^2

Question 4

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

Answer 4

10^1

Question 5

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

Answer 5

10^2

Question 6

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

Answer 6

10^3

Question 7

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

Answer 7

10^6

Question 8

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

Answer 8

10^9

Question 9

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

Answer 9

10^12

Question 10

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

Answer 10

10^15

Question 11

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

Answer 11

10^18

Question 12

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

Answer 12

10^-1

Question 13

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

Answer 13

10^-2

Question 14

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

Answer 14

10^-3

Question 15

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

Answer 15

10^-6

Question 16

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

Answer 16

10^-9

Question 17

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

Answer 17

10^-12

Question 18

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

Answer 18

10^-15

Question 19

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

Answer 19

10^-18

Question 20

What is the conversion factor of F to C?

Answer 20

1.8C + 32

Question 21

What is the conversion factor of F to R?

Answer 21

F + 459.69

Question 22

What is the conversion factor of C to K?

Answer 22

C + 273.15

Question 23

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?

Answer 23

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

Question 24

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?

Answer 24

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

Question 25

How many significant figures are in a product or dividend?

Answer 25

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

Question 26

What does a∈A mean?

Answer 26

a is a member or element of A.

Question 27

What does { } or Φ represent?

Answer 27

The empty or null set.

Question 28

What does A ⊆ B mean?

Answer 28

A is a subset of B.

Question 29

What does A ⊂ B mean?

Answer 29

A is a proper subset of B.

Question 30

What is a proper subset?

Answer 30

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

Question 31

What is (a,b)?

Answer 31

An ordered pair.

Question 32

What is an ordered pair?

Answer 32

A collection of 2 elements in which the order matters.

Question 33

What does the symbol P(s) mean?

Answer 33

The power set of s.

Question 34

What is a power set?

Answer 34

The set of all subsets.

Question 35

What does A ∪ B mean?

Answer 35

The union of sets A and B.

Question 36

What is a mathematical union?

Answer 36

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

Question 37

What does A ∩ B mean?

Answer 37

The intersection of sets A and B.

Question 38

What is an intersection of 2 sets?

Answer 38

The set of elements shared by both sets.

Question 39

What does A×B mean in set theory?

Answer 39

The Cartesian Product of A and B.

Question 40

What is the Cartesian product of 2 sets?

Answer 40

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

Question 41

What is the Cartesian product of 2 sets?

Answer 41

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

Question 42

What does ∀x mean?

Answer 42

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

Question 43

What does ∃x mean?

Answer 43

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

Question 44

What is the general form of the straight line equation?

Answer 44

Ax + By + C = 0

Question 45

What is the standard form of the line equation?

Answer 45

y = mx + b

Question 46

What is the point slope form of the line equation?

Answer 46

y - y1 = m(x -x1)

Question 47

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

Answer 47

X = (-b ± (b^2 - 4ac)^(1/2)) / (2a)

Question 48

What is the equation to a sphere?

Answer 48

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

Question 49

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

Answer 49

b^c = x

Question 50

How do you change from one logarithm base to another?

Answer 50

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

Question 51

What is logb(b^n)?

Answer 51

n

Question 52

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

Answer 52

clog(x)

Question 53

What is an algebraic manipulation of log(xy)?

Answer 53

log(x) + log(y)

Question 54

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

Answer 54

log(x) - log(y)

Question 55

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

Answer 55

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

Question 56

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

Answer 56

θ = tan^-1(b/a)

Question 57

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

Answer 57

a = c cos(θ)

Question 58

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

Answer 58

b = c sin(θ)

Question 59

How do you add complex numbers?

Answer 59

Algebraically in rectangular form.

Question 60

How do you multiply complex numbers?

Answer 60

Multiply c components and add angles.

Question 61

What is the mathematical definition of a complex conjugate?

Answer 61

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

Question 62

What is eulers formula?

Answer 62

e^(ix) = cosx + isinx

Question 63

What is the law of sines?

Answer 63

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.

Question 64

What is the law of cosines?

Answer 64

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

Question 65

What is the volume of a sphere?

Answer 65

V = 4πr^3/3

Question 66

What is the surface area of a sphere?

Answer 66

4πr^2

Question 67

What is the volume of a right circular cone?

Answer 67

V = πr^2h/3

Question 68

What is the surface area of a right circular cone?

Answer 68

πr(r + (r^2 + h^2)^(1/2))

Question 69

How is csc defined?

Answer 69

1/sin

Question 70

How do you define cos θ using eulers identity?

Answer 70

(e^(jθ) + e^(-jθ))/2

Question 71

How do you define sin θ using eulers identity?

Answer 71

e^(jθ) - e^(-jθ)/(2j)

Question 72

What is the definition of dy/dx?

Answer 72

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

Question 73

How do you check for local maxima?

Answer 73

f’(a)=0 and f”(a)<0

Question 74

How do you check for local minima?

Answer 74

f’(a)=0 and f”(a)>0

Question 75

What is an inflection point?

Answer 75

Where curvature changes from convex to concave or vice versa.

Question 76

How do you verify an inflection point?

Answer 76

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

Question 77

How do you determine a partial derivative?

Answer 77

Treat all other variables as constants.

Question 78

What is the chain rule?

Answer 78

dy/dx=dy/du * du/dx