Math Flashcards
What is the Unites States unit system called?
US Customary System (USCS)
What is the gravitational acceleration in ft/s^2?
32.174 ft/s^2
What is the gravitational acceleration in m/s^2?
9.807 m/s^2
What multiple of 10 does the prefix “deka” represent?
10^1
What multiple of 10 does the prefix “hecto” represent?
10^2
What multiple of 10 does the prefix “kilo” represent?
10^3
What multiple of 10 does the prefix “mega” represent?
10^6
What multiple of 10 does the prefix “giga” represent?
10^9
What multiple of 10 does the prefix “tera” represent?
10^12
What multiple of 10 does the prefix “peta” represent?
10^15
What multiple of 10 does the prefix “exa” represent?
10^18
What multiple of 10 does the prefix “deci” represent?
10^-1
What multiple of 10 does the prefix “centi” represent?
10^-2
What multiple of 10 does the prefix “milli” represent?
10^-3
What multiple of 10 does the prefix “micro” represent?
10^-6
What multiple of 10 does the prefix “nano” represent?
10^-9
What multiple of 10 does the prefix “pico” represent?
10^-12
What multiple of 10 does the prefix “femto” represent?
10^-15
What multiple of 10 does the prefix “atto” represent?
10^-18
What is the conversion factor of F to C?
1.8C + 32
What is the conversion factor of F to R?
F + 459.69
What is the conversion factor of C to K?
C + 273.15
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?
The same as the number with the least significant figures after the decimal point.
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?
The same as the number with the most significant figures before the decimal point.
How many significant figures are in a product or dividend?
The same as the number with the least amount of significant figures.
What does a∈A mean?
a is a member or element of A.
What does { } or Φ represent?
The empty or null set.
What does A ⊆ B mean?
A is a subset of B.
What does A ⊂ B mean?
A is a proper subset of B.
What is a proper subset?
A proper subset is a subset that is not equal to the set it is a subset to.
What is (a,b)?
An ordered pair.
What is an ordered pair?
A collection of 2 elements in which the order matters.
What does the symbol P(s) mean?
The power set of s.
What is a power set?
The set of all subsets.
What does A ∪ B mean?
The union of sets A and B.
What is a mathematical union?
The combination of all elements in both sets to form a single set containing all elements in both.
What does A ∩ B mean?
The intersection of sets A and B.
What is an intersection of 2 sets?
The set of elements shared by both sets.
What does A×B mean in set theory?
The Cartesian Product of A and B.
What is the Cartesian product of 2 sets?
The set of all variations of ordered pairs between the 2 sets.
What is the Cartesian product of 2 sets?
A set containing all possible combinations of ordered pairs between the elements of both sets.
What does ∀x mean?
“For every” x. Or that whatever follows the symbol applies to all x.
What does ∃x mean?
“There exists” within x, or there is exactly one element in x where the statement following the symbol holds true.
What is the general form of the straight line equation?
Ax + By + C = 0
What is the standard form of the line equation?
y = mx + b
What is the point slope form of the line equation?
y - y1 = m(x -x1)
What is the equation to solve for the roots to the quadratic equation?
X = (-b ± (b^2 - 4ac)^(1/2)) / (2a)
What is the equation to a sphere?
(x - h)^2 + (y - k)^2 + (z - m)^2 = r^2 with center at (h, k, m)
What is the algebraic manipulation of logb(x) = c?
b^c = x
How do you change from one logarithm base to another?
logb(x) = (loga(x)) / (loga(b))
What is logb(b^n)?
n
What is an algebraic manipulation of log(x^c)?
clog(x)
What is an algebraic manipulation of log(xy)?
log(x) + log(y)
What is an algebraic manipulation of log(x / y)?
log(x) - log(y)
Where a complex number in polar form is z = c ∠ θ, how does c relate to a and b where z = a + bi?
c = (a^2 + b^2)^(1/2)
Where a complex number in polar form is z = c ∠ θ, how does θ relate to a and b where z = a + bi.
θ = tan^-1(b/a)
How does a in the complex form z = a + bi relate to the complex form z = c ∠ θ?
a = c cos(θ)
How does b in the complex form z = a + bi relate to the complex form z = c ∠ θ?
b = c sin(θ)
How do you add complex numbers?
Algebraically in rectangular form.
How do you multiply complex numbers?
Multiply c components and add angles.
What is the mathematical definition of a complex conjugate?
Where z = a + bi, z* = a - bi.
What is eulers formula?
e^(ix) = cosx + isinx
What is the law of sines?
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.
What is the law of cosines?
a^2 = b^2 + c^2 - 2bccos(A)
What is the volume of a sphere?
V = 4πr^3/3
What is the surface area of a sphere?
4πr^2
What is the volume of a right circular cone?
V = πr^2h/3
What is the surface area of a right circular cone?
πr(r + (r^2 + h^2)^(1/2))
How is csc defined?
1/sin
How do you define cos θ using eulers identity?
(e^(jθ) + e^(-jθ))/2
How do you define sin θ using eulers identity?
e^(jθ) - e^(-jθ)/(2j)
What is the definition of dy/dx?
The limit as x approaches 0 of delta y/delta x.
How do you check for local maxima?
f’(a)=0 and f”(a)<0
How do you check for local minima?
f’(a)=0 and f”(a)>0
What is an inflection point?
Where curvature changes from convex to concave or vice versa.
How do you verify an inflection point?
f”(a)=0 and signs are flipped in f”(a) on either side of a.
How do you determine a partial derivative?
Treat all other variables as constants.
What is the chain rule?
dy/dx=dy/du * du/dx
