# Science / Advanced IJKL's of mathematics

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## Can you name the Advanced math terms beginning with I, J, K or L?

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1st letter/# wordsTermHint
I (2)f(x) = x
I (2)A method for finding the derivative of an implicitly defined function or relation.
I (2)A function with a graph that goes up as it is followed from left to right.
I (2)An undefined expression which can have a value if arrived at as a limit.
I (2)Proving a conjecture by assuming conjecture is false; if this leads to a contradiction, the original conjecture must have been true; employs the logical method modus tolens.
I (1)A method for proving a proposition that is valid for infinitely many different values of a variable.
I (1)A set that can be placed in one-to-one correspondence with a proper subset of itself.
I (1)A hypothetical number that is larger than zero but smaller than any positive real number.
I (2)A point at which a curve changes from concave up to concave down, or vice-versa.
I (3)A differential equation or partial differential equation accompanied by conditions for the value of the function and possibly its derivatives at one particular point in the domain.
I (1)The radius of a plane figure's inscribed circle.
I (2)A function for which the definite integral exists.
I (2)A convergence test used for positive series with decreasing terms.
I (3)A theorem verifying that the graph of a continuous function is connected.
I (1)A property of a class of mathematical objects that remains unchanged when transformations of a certain type are applied to the objects.
I (1)Negation of the hypothesis and conclusion of a conditional statement.
I (2)A square matrix which has an inverse.
I (1)A transformation that is invariant with respect to distance; the distance between any two points in the pre-image must be the same as the distance between the images of the two points.
1st letter/# wordsTermHint
I (2)An algorithm which involves repeated use of the same formula or steps.
J (2)Discontinuity for which the limits from the left and right both exist but are not equal to each other.
K (2)Topological figure that is closed and bottle shaped with only one surface area.
K (2)Figure - start with equilateral triangle, replace middle third of each segment with 2 sides of a new triangle, repeat process forever.
K (3)Topological problem: take a walk in a certain city & return to the starting point after crossing each of the city's 7 bridges just once.
L (2)Way to evaluate limits of fractions that evaluate to indeterminate expressions by finding limit of the derivatives of the numerator & denominator.
L (2)Line segment through a focus of a conic section, perpendicular to major axis, endpoints on curve.
L (3)The Ceiling Function.
L (4)The linear fit that matches the pattern of a set of paired data as closely as possible.
L (6)The smallest of all upper bounds of a set of numbers.
L (1)A helping theorem; proven, but not interesting enough to be a theorem; of interest only because it is a stepping stone in a formal proof.
L (1)r2 = a2 cos 2θ; A curve usually expressed in polar coordinates that resembles a figure eight.
L (1)r = b + a cos θ ; A famliy of related curves, of which the cardiod is a special kind.
L (1)The value a function approaches as the domain variable(s) approach a specific value.
L (2)Algorithm for finding largest or smallest possible values of a linear polynomial.
L (2)The appearance or properties of a function, graph, or geometric figure in the immediate neighborhood of a particular point.
L (1)A word for a set of points that forms a geometric figure or graph.
L (2)A model for a quantity that increases quickly at first and then more slowly as the quantity approaches an upper limit.

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