To All You Mathletes... Trivia Quiz

Answer: none of these

Pi is a never-repeating never-ending number. Remember that now.

Answer: simple calculations involving the areas of squares and triangles

You can draw out a figure involving a square tilted on its side surrounded by four, equal-area right triangles, with height a, width b, and hypotenuse c. You can then write two equations stating that the area of the whole figure is equal to: (a+b)² = 4*(1/2*a*b)+c². Simplifying this yields a²+2ab+b²=2ab+c². Canceling the 2ab on both sides leaves a²+b²=c².

In case anyone is wondering, eigenvectors are vectors that are scaled but not rotated when a linear transformation is applied to them. These are used frequently in higher math.

Answer: zero

The key phrase is "with respect to x". There is no x term in the expression given, meaning that it is treated as a constant. The derivative of any constant is zero.

If the expression had been (pi*e)^x, its derivative would have been: ln(pi*e)*(pi*e)^x.

Answer: a series that derives its next term from the one preceding it

Not much else to say here. This was just a definition question.

Answer: linearize the data

Linearizing the data involves taking the logarithm of the equation so that the numbers end up being much easier to work with. If done correctly, your new data should look like a straight line instead of an exponential curve.

The Other Answers:
A linear regression is used only when your original data appears to fit the pattern of a line
A t-test is used to compare multiple different sets of data to test for differences
A hypothesis test is what it sounds like. You run one of a certain number of tests to see whether your hypothesis was right.

Answer: The tetrahedron has 1/6 the volume

To be honest, I'm not entirely sure how to prove this, but I do remember that the proof involved the triple scalar product: a·(b×c)

If anyone knows the full proof or can find it on the internet, send me a message.

Answer: Newton's Method

Newton's Method is a way to find the roots of complicated real equations such as sin²x+x²-ln(x)=0.

Integration involves finding the antiderivative of a function, Riemann Sums involves taking the limit of a sum (of slices of the function), and Simpson's Rule involves slicing the area into trapezoids and rectangles. All can be used to approximate area, but in most cases, integration is the easiest.

Answer: 15

Start in the innermost parentheses and work your way out.

3$2=3²-2³=9-8=1. Now the equation reads: 8#(3@1)
3@1=3+1+3*1=3+1+3=7. Now the equation reads: 8#7
8#7=8²-7²=64-49=15, which is your final answer.

Answer: sin²x-cos²x=tan²x

sin²x+cos²x=1 is the MOST fundamental trig identity off which much is based. 1+cot²x=csc²x can be found by dividing that equation by sin²x and tan²x+1=sec²x can be found by dividing that equation by cos²x.

I made up the other equation. (For a bonus point, for what values of x would that statement be true?

Answer to Bonus: Never. Simplifying the equation yields: 2sin²x=sec²x, which is never true.)

Answer: The Method of Lagrange Multipliers

The Method of Lagrange Multipliers is based on the idea that at the optimal point, the gradient (a vector consisting of the partial derivatives of each of the variables in the equation) of the function you are trying to optimize will be in the same direction as the gradient of the constraint, off by a constant scalar multiple. You can thus set up a number equations (the number of equations will be equal to the number of variables plus the number of constraints) and solve for the optimum point.

Stokes theorem is used to integrate over surfaces, Gauss-Jordan Elimination is used for row-reduction in matrices, and Green's Theorem is used for integration around a closed path in two dimensions.

I hope you did well.