Algebra+number theory | Trigonometry and conics | Counting and Probability | Geometry | Potluck (harder questions, double points) |
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What is -b+-sqrt(b^2-4ac) all over 2a
It is the complete quadratic formula
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What is (sqrt(3)+1)/2
It is equal to cos60 + sin 60
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What is 33
It is the number of numbers two more than a multiple of three between 0 and 100
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What is 20
It is the area of a right triangle with legs 5 and 8
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Who are Isaac Newton and Gottfried Leibniz.
These two men both have claims to inventing calculus
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What is 288
If the gcd of two numbers is 6 and the lcm is 48, what i s the product of the two numbers?
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What is 7
It is the y coordinate of the apex of 2x^2+12x+25
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What is 5
It is the minimum number of socks I must blindly grab to be sure of a matching pair if I have 4 red socks, 2 blue socks, 1 green sock and 6 yellow socks
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What is a pythagorean triple
It is when two squares sum to another square
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What is
This proof writing technique is often compared to a line of dominos knocking each other over. It consists of two parts, a base case, and its namesake step.
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What is 59
If x=2(mod 3), 4 (mod 5) and 3 (mod 7) what is the minimum value of x
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What is e^(i*number)
Euler's identity states that this function is equivilant to cos(x)+i sine(x)
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What is 70
It is the number of ways to get from the bottom left corner of a 5x5 grid to the top right corner only moving up or right
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What is Stewarts theorem
A man and his dad put a bomb in a sink is a mneumonic for this theorem (Daily Double)
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What is a Klein bottle
It is what you get when you fold the edge of a Möbius strip back onto itself in the same way you make a tube from a sheet of paper. It does not have an inside, outside, or any edges. It also cannot exist in 3 dimensions
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What are Vieta's theorems
They state that the sum of the roots of a polynomial is equal to the second coefficient over the leading coeffcient times negative one.
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What is the law of cosines
It is a modified version of the Pythagorean theorem to work on all triangles.
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What is 20
It is the number of ways to distribute 3 pieces of candy to 4 children if the candies are identical
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What is Ptolemy's theorem.
It states that the sum the products of two opposite sides of a cyclic quadrilateral sum to the product of the diagonals
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What is the moving knife procedure
It is a way of doing I cut you chose for a unspecified number of people by having them shout mine when they are satisfied with the piece they will receive.
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What is (x-2)(2x-3)(x-5)
It is the factorized form of 2 x^3 - 17 x^2 + 41 x - 30
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What is a hyperbola
They have general form (x-q)^2/a^2-(y-p)^2/b^2=1
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What is 10
It is the number of ways to paint a cube with two colors, where two cubes are considered identical if they are rotations of each other.
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What is (AF*BD*CE)/(FB*DC*EA)
It is Ceva's theorem (state it using diagram)
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What is (accept any that work, eg. 1/2017(x-1)(x-2)(x-3)...(x-2017)+ constant)
It is a degree 2017 polynomial that gives integer results when you insert any integer between 0 and 2017 but has a leading coefficient of 1/2017 (give in factored form)
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