To All You Mathletes...Part II

15 Points Per Correct Answer - No time limit  

1. To begin with, let's try some arithmetic probability. If you're playing a game where you have two tries to guess a number between 1 and 10 (inclusive), what are the odds that you guess the number correctly in one of those two tries (assuming you don't guess the same number twice)? 1/5 19/90 1/10 21/90

2. Let's continue with some Algebra I. If you have a rectangular swimming pool of volume 105 m³ whose length is 2 meters longer than its width and whose depth is 2 meters shorter than its width, what is the perimeter (around the top) of the rectangular pool? 12 meters 5 meters 18 meters 24 meters

3. Let's move on to a little geometry. If you connect the midpoints of all four sides of a quadrilateral to create a new quadrilateral, that new quadrilateral will always be a parallelogram. True False

4. Next up, Algebra II: What would the set of all points satisfying the equation: √(y²) = √(x²) (In the answers, abs(x) denotes the absolute value of x.) y=x y=abs(x) y=-x y=±abs(x)

5. Let's do some Precalculus. You've traveled in a motorboat 8 miles away from the dock (the origin) at a 30° angle above the shoreline (the x-axis). You then make a turn back toward the shore and travel exactly 5 miles so that your boat stops exactly on the shoreline. Given the above information, you could be at exactly two different points on the shore (the x-axis) right now: (A,0) and (B,0). What's the difference (in miles) between these two points? 3 miles 6 miles -3 + 4√3 miles 3 + 4√3 miles

6. Differential Calculus: You are blowing up a perfectly spherical balloon. The radius (in centimeters) of the balloon after t seconds is given by r(t)=2√t. At what rate is the volume of the balloon changing at time t=4? (Remember that the volume of a sphere is (4/3)πr3.) 16π cm³/s 8π cm³/s 64π cm³/s 32π cm³/s

7. On to Integral Calculus now. Of the following, which would you want to integrate the least? (Hint: It's the only one that you can't integrate.) x/ln(x) ln(x)/x x*ln(x) 1/(x*ln(x))

8. Uh-oh. It's going to get worse from here. Next up is...gulp...Multivariable Calculus. Let's say that m is the number of movies you see each month and s is the number of songs you buy on iTunes (you'd never illegally download, of course). Your happiness H is represented by the function H = 10m0.8s0.2. Each movie costs $8 and each song costs $1. You have a $50 budget. Assuming you're spending all of your money, how many movies should you watch and how many songs should you buy to maximize your happiness? 3 movies, 26 songs 4 movies, 18 songs 5 movies, 10 songs 6 movies, 2 songs

9. A little different: Linear Algebra. (I'll make this conceptual to give you a break.) If you know that an nxn matrix A is invertible, what can you NOT also say about it? There is at least one non-zero vector in the kernel of A. The determinant of A does not equal 0. The image of A spans Rn. The rank of A is n.

10. Let's get Complex to end this quiz... This isn't really practical at all, but it's pretty cool. What is the principal value of ii? The letter i denotes the square root of -1. -1 e-π e e-π/2