Algebra
The inverse of exponentiation
What is a logarithm?
sin2(θ)+cos2(θ) equals this
What is 1?
This rule is used when differentiating “a function within a function” like sin(x2)
What is the chain rule?
A data point that differs significantly from the other observations
What is an outlier?
This sequence begins with 0,1,1,2,3,5,8 where each number is the sum of the two preceding ones
What is the Fibonacci Sequence?
The sum of the solutions to the equation: 2x2-7x+5=0
What is 7/2 (or 3.5)?
The formula for the surface area of a sphere
What is 4πr2?
The point when a function changes from concave up to concave down (vise versa)
What is an inflection point?
This is the most common distribution curve in statistics and follows the Empirical Rule (68-95-99.7)
What is the Normal distribution?
This cipher shifts each letter in the alphabet by a set number of positions
What is the Caesar Cipher?
This value determines whether a quadratic equation has two distinct real solutions, one repeated real solution, or two non-real complex solutions.
What is the discriminant of a function (b2-4ac)?
The interior angles of a nonagon add to this value
What is 1260 degrees?
This is the derivative of tan-1(x)
What is 1/(1+x2)?
Events that can never occur simultaneously, and the occurrence of one guarantees that the other cannot happen
What are mutually exclusive (disjoint) events?
This irrational number is approximately 1.618 and represented by Φ
What is the Golden Ratio?
A point where a rational function is undefined but does not have a vertical asymptote; limit exists
What is a removable discontinuity (hole)?
On a sphere, the shortest path between two points is this type of circle
What is a great circle?
This elegant formula links five fundamental constants (e,i,π,1,0)
What is Euler’s Identity eiπ+1=0? (Proved using Taylor Series)
The inference procedure is used to estimate a population proportion with a confidence interval when certain conditions are met
What is a one-proportion z-interval?
These rare numbers are equal to the sum of their proper factors (the smaller numbers that divide them) (ex: 6 → 1 + 2 + 3 = 6)
What are perfect numbers?
This technique breaks down a complex fraction with polynomials into a sum of simpler fractions
What is partial fraction decomposition?
Formula for surface area of a regular octahedron (8 equilateral triangles) with edge length a
What is 2√3 a2?
Evaluate this integral from 0 to π/2: sin3(2x)*cos(x)
What is 16/35 (0.457)?
Statistical model that studies a sequence of random events where the probability of the next state depends solely on the current state; applications in LLMs and search engines
What is a Markov Chain?
Is ii an imaginary or real number? (include why/how to prove or an expression for ii)
What is a real number? (Proved using Euler's Identity/Formula; ii = e-π/2)