www.YoYoBrain.com - Accelerators for Memory and Learning Questions for mathematics Category: Default - (161 questions) Define an inverse function reverses the result of the function operation and tells you what you started with or what what the input was to get the value What is the sin 0 Give sin 1 / 2 Give sin square root (2) / 2 Give: sin square root (3) / 2 Give: sin 1 What are the trigonometric (angle) sum sin (A + B) = sinA cosB + cosA sinB cos(A + identities (sin(A+B), cost(A+B),tan B) = cos A cos B - sin A sin B tan(A + B) = (tan A + tan B) / (1 - tan A tan B) cos 2a = ???? 1 - (2 sin^2 a) (2 cos^2 a) - 1 What is the Fibonacci series 0, 1, 1, 2, 3, 5, 8 .... after first 2 values each next value is generated by adding the preceding 2 What is the cos 1 Give: cos square root (3) / 2 Give: cos square root (2) / 2 Give: cos 1 / 2 Give: cos 0 Define: isosceles triangle 2 sides that are equal and angles opposite those sides are equal Define: sufficient condition A condition that must be satisfied for a statement to be true and without which the statement cannot be true. Define: abscissa and ordinate abscissa - independent variable (usually x) of a point on the Cartesian plane ordinate - dependent variable coordinate Define: inclusion theorem If limit of x approaching a for f(x) = limit of x approaching a for g(x) = A and f(x) = h(x) = g(x) for all x near a then limit of x approaching a h(x) = A Define: function mathematical relation in which every abscissa corresponds to at most one ordinate Define: minimal surface the shape of least area when bounded by a given closed space ex: shape of soap film between 2 empty circular rings Define: pi ratio of the diameter to the circumference 3.14.... Define: quaternion name given by W.R. Hamilton to ordered 4 set of real numbers used to represent hypercomplex numbers a + b i + c j + d k Define: one degree (of a circle) 1/360 of a full circle Who is J.W. Gibbs American mathematician (1839 - 1903) and physicists who developed much of vector analysis as we know it today Define: sin and cos in terms of unit circle on sin - is the y value of point cos - is the x cartesian system value of the point Define: Russell's paradox of sets If sets are subject only to some principle of free construction, then what of the set of all sets that are not members of themselves? The set of dogs, which is not a dog Define: tan a sin a / cos a Define: logistics equation correctly models a wide range of situations in which a growing population competes for limited supplies. A good example might be fish in a lake that has limited amount of food. X n+1 = kXn * ( 1 - Xn) The population at step n+1 = some constant * population at step n * ( 1 - population at step n) with population as a% of maximum carrying capacity Define: csc cosecant = 1 / sin Who is Edward Lorenz one of the early pioneers of choas theory - worked evolved out of trying to model weather Define: sec secant 1 / cos Define: geodesic (mathematics) the shortest line between two points on a mathematically defined surface (as a straight line on a plane or an arc of a great circle on a sphere) Define: cot 1 / tan or cos / sin Define: Thomsom lamp Suppose you have a reading lamp with a push-button that switches the light on and off. If the light is "off" when you press the button once, or any odd number of times, the lamp will be "on". Press it any number of even times and it will be "off". A little demon appears and decides he will press the button continually so as to leave the lamp 'on' for 1/2 a minute, then 'off' for 1/4 a minute, 'on' for 1/8 of a minute, 'off' for 1/16 of a minute and so on. He will have pressed the button an infinite number of times after 1 minute. So the big question is: Will the light be 'on' or 'off' after one minute. What does sinh, cosh, and tanh stand for hyperbolic sine hyperbolic cosine hyperbolic tangent Define: Goldbach's conjecture states: Every even integer greater than 2 can be written as the sum of two primes. Expressing a given even number as a sum of two primes is called a Goldbach partition of the number. \ For example, 4 = 2 + 2, 6 = 3 + 3 , 8 = 3 + 5,10 = 3 + 7 = 5 + 5, 12 = 5 + 7, 14 = 3 + 11 = 7 + 7, etc. Define: irrational number a number that can't be precisely represented as a ratio of 2 whole number ex: square root of 2 Who was Evariste Galois early 19th century French mathematician who laid the foundation for group theory Define: acute and obtuse angle acute angle - less than 90 degreesobtuse angle - greater than 90 degrees Define: logarithm of N Every positive number N can be expressed as a power of 10; we can always find p such that: N = 10^p. We call p the logarithm of N to the base of 10 or the common logarithm of N Define: vertical and supplementary angles when two line intersect: vertical angles are opposite each other supplementary angles are side by side (their angles add to 180 degrees) Define: mantissa and characteristic of the decimal part in logarithm is the mantissa logarithms the part to the left of the decimal is the characteristic What is the irrational number Phi also known as the golden ratio ratio created when a line is divided in such a way that the relationship between the larger segment and the entire length is the same as the relationship between the smaller and larger segments. 1.6180339887..... How do you determine the characteristic of a 1.) for a number greater than 1, the logarithm of number N characteristic is positive and is one less than the number of digits before the decimal point 2.) for a number less than 1, the characteristic is negative and is one more than the number of zeros immediately following the decimal point. Define: the antilog of number p the number whose logarithm is p (reverse of logarithm) Define: log(M*N) log(M) + log(N) Define: log ( M / N) log(M) - log(N) Define: log (M^p) p * log(M) Define: manifold simple numbers in a particular order, removes the idea of actual physical space from coordinate analysis. Makes it simpler to analyze higher dimensions Who is responsible for creation of set theory Georg Cantor Define: cardinal number in set theory Each cardinal number corresponds to sets that have the same size. Cardinal number of 5 is assigned to all sets that have 5 members Define: chromatic number of a surface The number of colors that is sufficient so that regions with common boundary-line segments on a surface are distinguished by different colors Who is Authur Cayley invented matrix algebra Define: combinatorial geometry includes problems of covering, packing and symmetry Define: Latin square of the n-th order a permutation of n symbols arranged in n rows and n columns - used in design of experiments that will be subjected to statistical analysis Define: fractal curve when the estimated length of a curve becomes arbitrarily large as the measuring stick becomes smaller and smaller Define: fractal dimension a measure of the degree of irregularity considered at all scales ratio between the logarithms of the number of copies and the size of the seed relative to each copy (how much smaller is the next level of detail to the previous) Who coined the term fractals and developed Benoit Mandelbrot much of the base of math Define: mode locking in dynamic systems the tendency to fall back into a behavior pattern called an attractor, even when external pertubations knock the system off the attractor momentarily. Define: Sierpinski's Triangle You begin with a triangle. Then divide the triangle into 4 equal pieces. Then divide the outer three pieces in the same way as the initial, continuing into infinity. Define: Riemannian geometry geometries that are obtained by changing the way distance is measured in the plane one example would by hyperbolic geometry Who is Hippasus of Mepapontum Discovered irrational numbers and was reputadely drowned by Pythagoreans Who is Augustin Louis Cauchy French mathematician of 19th century who started a project of formulating and proving the theorems of calculus in a rigrous manner Cantor's definition of an infinite set a set that can be put into a one-to-one correspondence with a proper subset of itself Define: Bertrand Russel's barber paradox deals with classes. A class of books is not a book an so does not belong to itself, but a class of ideas is an idea and does belong to itself. A village barber advertises that he doesn't shave any people in the village who shave themselves, but he does shave all those who don't shave themselves. One does it occurred to him to ask whether he should shave himself. If he does shave himself then he can't shave himself because he only shaves people who don't shave themselves. Define: ordered set and well ordered set ordered - means, as in the case of the whole numbers, that if a and b are any 2 members of the set, either a precedes b or b precedes a.well ordered - Further, if a precedes b and b precedes c, then a precedes c.