math wizard

7/28/2019 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+5y2-x+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

3n-2?


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ANSWER:

112


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3 minutes2. From the equation

12x3-8x2+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

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