Math Quiz

Answer: 79242972893648656

This may seem impossible to do, but three of these choices can be eliminated based on the digits. 2893467827688677 and 9134751098236810 can both be eliminated because a square number must end in a 1, 4, 5, 6, 9, or 00. Finally, 5916378240699596 is eliminated because a square number's digital root must be 1, 4, 7, or 9.

A digital root is calculated by adding the digits of the number and then adding the digits of the resulting number and repeating the process until we are left with a 1-digit number (e.g. to find the digital root of 89...8+9=17, 1+7=8).

This leaves us only one choice.

Answer: 2

The formula for finding an infinite sum is A/(1-R), where A is the first term and R is the common ratio, or the number by which you have to multiply the first term to get the second term. In this case, A = 1 and R = 0.5. A/(1-R) = 1/(1-0.5) = 1/0.5 = 2.

Answer: 279/2

It just takes some work to do this one. Start like this: f(2) = 3(2)/2 = 3. g(3) = 2(3) + 3 = 9, and so on.

Answer: (4/5, 2/5)

Take the coordinates separately. First, the x-coordinate. The x-coordinate of where the ant converges can be expressed as an infinite sum 1 - 1/4 + 1/16 - 1/64 + .... Using the formula given earlier, the sum is 1/(1-(-1/4)) = 4/5, so the x-coordinate is 4/5. Similarly solving for the y-coorindate of the point, we get 2/5.

Answer: Cannot be determined with the information given.

Yes, the North Pole is one possible place, but there are others. The "widest" part of the Earth is at the equator. However, if you go far enough north or south, the "circumference" of the earth will get smaller, eventually, near the poles, the circumference is only a mile. If you are one mile above such a place, then you can go one mile south and one mile east, circling the earth to end up right where you were, and then one mile north to end up back where you started.

This is sort of hard to explain without a diagram.

Answer: 1

Subtract 4x from both sides and you get 3x - 2 = 1. Then, add 2 to both sides to get 3x = 3. Finally, divide both sides by 3 and you get x = 1.

Answer: (x - y)(x^2 + xy + y^2)

If you do not already know how to factor the difference of two cubes, then just multiply all of the choices and you will get the right answer.

Answer: 4

To find the slope of the line tangent to a curve at x = a, you use limits. The expression is the limit as h approaches 0 of the expression (f(a + h) - f(h))/h. Evaluating the limit, we get 4.

Answer: 5050

There is a formula for the sum of 1 + 2 + 3 + 4 + 5 + ... + n. It is n(n+1)/2. Substituting 100 for n, we get 5050. If you don't know this formula, you can find the sum quickly by grouping the numbers like this:
1 + 2 + 3 + 4 + ... + 100 = 1 + 100 + 2 + 99 + ... + 50 + 51. This is equal to 101 + 101 + 101 + 101 + ... 50 times. Multiplying, 50 x 101 = 5050.

Answer: 5051

The formula for finding the number of regions that n lines can divide a plane into is (n(n+1)/2) + 1. Substituting 100 for n, we get 5051.