My District Competition is TOMORROW! FINAL Questions!

[chrishuff]

21. The geometric mean of 213 and 112 is what % of the arithmetic mean of 213 and 112?
Answer: 95%

27. Find the area of the circle (nearest tenth)
It's a picture with a triangle with side lengths of 4cm, 5cm, and 7cm.

It is NOT a right triangle, so 7cm as the diameter won't work
Answer: 40.1 cm^2

39. The I Scream 4 Ice Cream Shoppe has a special sale for triple scoop cones. The flavors available are vanilla, chocolate, strawberry, banana-nut, pecan praline, and peppermint. How many different triple scoops can they create from the available flavors?
A. 504
B. 168
C. 120
D. 56
E. 20

I tried Combinations and Permutations, getting answer choices C and E, but the correct answer according to the answer key is 56

41. A set of 5 integers has a mean of 22, a median of 23, and a mode of 27. What is the largest possible range of the set of integers?
Answer: 16

38. The directrix of the conic given by the equation y = 4x^2 - 4x + 1 is
Correct Answer: Y = -1/16

47. If a3 = 1, a4 = 8.25, and a5 = 15.5, than a1= ?
Answer: -13.5

49. The graph of 2x^2 + 4xy -y^2 - 2x + 3y = 6 is an
A. Circle
B. Ellipse
C. Hyperbola
D. Line
E. Parabola

Answer: C
I don't really need help with this question, but would like to know the secrets or the quickest way to identify what types of equation problems are.

53. Tyler Gehr drops a golf ball from a platform 12 feet above the ground. Each time it hits the ground it rebounds two-thirds of the distance it fell. Find the total distance the golf ball travels when it hits the ground the sixth time.
Correct Answer: 54 ft

54. The complex numbers w = 3 + i and z = i - 4 are graphed as vectors. What is the measure of the angle formed between them?
Correct Answer: 147.5 degrees

[nsguy1350]

21. Geometric mean is the nth root of the product of n elements. [unparseable or potentially dangerous latex formula] for these numbers, which apparently is 95% of their arithmetic mean.

27. It is circumscribed or inscribed (is the triangle inside or outside the triangle?)
I believe that if it's circumscribed, the radius of the circle is [unparseable or potentially dangerous latex formula], where a,b,c are the sides of the triangle, and K is the area, which can be found using Heron's formula, [unparseable or potentially dangerous latex formula], where s is the semiperimeter, so [unparseable or potentially dangerous latex formula].

39. You have 6 choices, and you can pick 3. However, you must "balls-and-pins" this one since you can pick two or more identical scoops (3 vanillas is valid, but regular 6C3 won't treat 3 vanillas as valid.) Therefore, you take [unparseable or potentially dangerous latex formula]

41. I'm not sure on how to do this efficiently.

47. Regular arithmetic sequence, with difference = 7.25. 1 - 14.5 = -13.5.

49. I believe you take the "discriminant", treating the coefficient [unparseable or potentially dangerous latex formula] term as the b term, and the [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] as having the a and c coefficients. You then take [unparseable or potentially dangerous latex formula], which is 24, which I believe gives you a hyperbola, since it's positive. Ellipse is negative, and circle is zero, I believe.

53. You have the first drop, the 12 feet, plus twice the sum of that distance times [unparseable or potentially dangerous latex formula], from n = 1 to n = 5 (the six drops include the first drop, so you sum from 1 to 5, not 1 to 6.)
[unparseable or potentially dangerous latex formula] should do it.

54. I know that on the complex plane, you have your real axis and complex axis. Thus, the vectors can be treated as <1,3> and <1,-4>. They start at the origin. Now, you have to find the angle between them, and I forgot how to do that. Hopefully someone else can fill that in for you.

[chrishuff]

MUCHOS GRACIAS!

Lol, I kind of forgot most of my Spanish. If I got it wrong, I meant to say "Thanks a lot!"

[FabensMath]

Close enough: "MUCHAS GRACIAS!"

[ohernandez]

To find the directrix of a parabola in this format y = Ax^2 + Bx + C :
directrix = -(discriminant+1)/(4A)
discriminant = B^2 - 4AC

[88bobcat]

[FabensMath]

[Salvadoramerican]

I agree with Fabenmath are there more shortcuts those would be very useful

[ohernandez]

[ohernandez]

Other useful shortcuts:

Finding angle between hour and minute hands:
[unparseable or potentially dangerous latex formula]

Angle between points: (A,B) (C,D)
cos^-1 [unparseable or potentially dangerous latex formula]