Math Wizard

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Transcript of Math Wizard

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NOVEMBER 24, 2011

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EASY ROUND
(5 questions)
1 point each

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5 seconds
1: The ratio of the circumference ofany circle to the diameter of the
circle is:
a. An integer
b. An irrational numberc. A rational number
d. A whole number

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ANSWER:
b. An irrational number

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2: In the non degenerate conic
3x2+6xy+5y2x+y=0, classify what kind:
a. Circle
b. Ellipse
c. Parabola
d. Hyperbola
5 seconds

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ANSWER:
b. Ellipse

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3. A golf ball of mass 50 grams was hitwith a velocity of 90 m/s. The head of
the golf club got contact with a ball for0.3 millisecond. What is the averageforce acting on the golf ball during
impact?
3 minutes

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ANSWER:
15 KN

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3 minutes4. At what speed does a gun recoil if
it weighs 44.5 N and fires a 1 gram
bullet at 2500 m/s.

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ANSWER:
0.55 m/s

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5 seconds5.Which of the following materials has
the highest thermal conductivity at
room temperature?
a. Diamond
b. Glassc. Porcelain
d. Graphite

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ANSWER:
a. Diamond

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AVERAGEROUND
(5 questions)
3 points each

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3 minutes1. What is the sum of the first terms of the
sequence whose general term is given by
3n2?

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ANSWER:
112

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3 minutes2. From the equation
12x38x2+kx+18=0, find the value of Kif one root is the negative of the
other.

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ANSWER:
27

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5 seconds3. A salt of weak bases when dissolved in
water and produces acidic solutions, is
said to have undergone what chemicalprocess?
a. Hydrolysis
b. Desalinationc. Hydrogeneratation
d. Neutralization

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ANSWER:
a. Hydrolysis

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5 minutes4.A man standing on the foot of a tower
throws a ball vertically upwards at a
certain velocity. On its way up, the timefor the ball to reach the top of the tower
is 1 second. On its way down, the time for
the ball to reach the top of the tower is 2seconds. How high is the tower in feet?

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ANSWER:
32.2 ft.

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5 minutes5. Two angles are adjacent and forman angle of 120. If the larger angle is
20 less than three times the smallerangle, find the larger angle.

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ANSWER:
85 degrees

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DIFFICULTROUND
(5 questions)
5 points each

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5 minutes1.After the price of petroleum oil went up
by 10%, a buyer reduced his oil
consumption by the same percent. Bywhat percent would his petroleum bill
be changed?

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ANSWER:
0.01 0r 1 %

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3 minutes2. The excess of the sum of the fourth
and fifth parts over the difference of
the half and the third parts of anumber is 119. Find the number.

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ANSWER:
420

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5 minutes3. Determine the radius of curvature
for the curve y= e raised to the
power x at point (0,1).

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ANSWER:
22 = 2 sq.root of 2

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3 minutes4.Assuming the earth to be a sphere of
radius 3960 miles, what is the distance of
point 36 N latitude from the equator?
a. 2844 miles
b. 2488 miles
c.2484 miles
d. 4288 miles

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ANSWER:
b. 2488 miles

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3 minutes5.A sphere is dropped in a can
partially filled with water. What is
the rise in height of water if theyhave equal diameters?

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ANSWER:
2/3 of diameter = 0.67 d

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TIE BREAKINGQUESTIONS

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3 minutes1. If thrice the smaller number
exceeds the larger by 12. Find the
larger number if the two numbersare consecutive odd integers.

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ANSWER:
9

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3 minutes2. A certain two digit number is 1 less
than five times the sum of its digits.
If 9 were added to the number, itsdigits would be reversed. Find thenumber.

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ANSWER:
34

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3 minutes3. Given an equilateral triangle, what
is the ratio of the area of a circle
inscribe to the area of a circlecircumscribed about the triangle?

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ANSWER:
1/4

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3 minutes
4. What is the of a power of adiverging lens whose focal length is
10 cm?

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ANSWER:
10 diopters

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5 seconds
5. What is the first derivative of ln(cos x)?

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ANSWER:
 tan x