Science Bowl Math Questions
Using an x-y coordinate axis, the figure represented by the equation [x2/36] + [y2/16] = 1 is centered about what x-y coordinate point?
ANSWER: (0,0)
Using an x-y coordinate axis, a parabola is represented by the equation x2 = 6y. The vertex of this parabola is at what coordinate point?
ANSWER: (0,0) or x = 0, y = 0
Using an x-y coordinate axis, a parabola is given by the equation y = x2. Give the x-y coordinates of the focal point for this parabola.
ANSWER: (0,1/4)
What is the volume of a sphere of radius "R"?
ANSWER: (4/3) pi R cubed
Name the famous mathematician/physicist who was born in the year Galileo died.
ANSWER: (ISAAC) NEWTON
Give the equation of one of the circles which satisfy the following criteria: a circle with a radius of 8 which is tangent to the y-axis and whose center lies on the x-axis.
ANSWER: (x - 8)2 + (y)2 = 82 or (x + 8)2 + (y)2 = 82
Two off-axis lines are perpendicular if and only if the product of their slopes is equal to what?
ANSWER: -1
What is the imaginary unit "i" when raised to the power 10?
ANSWER: -1
What is the log[base 5](1/25) equal to?
ANSWER: -2
What is the slope of the straight line whose x-intercept is +4 (read: plus 4) and whose yintercept is +8 (read: plus 8)?
ANSWER: -2 (read: minus 2)
The relationship between y and x is given by the equation, y = x2 + 7x + 14 (read: y equals x squared plus 7 x plus 14). For what values of x will y equal +2?
ANSWER: -4 AND -3
In calculus, what is the indefinite integral of the sin(U)dU equal to?
ANSWER: -cos(U) + CONSTANT
Given that the log[base 10](2) = .30 and that the log[base 10](3) =.48, what is the log[base 10](1.5) equal to?
ANSWER: .18
Given that the log[base 10](2) = .301, what is the log[base 10](8) equal to?
ANSWER: .903
An 8 meter length of rope is placed along the circumference of a circle whose diameter is 16 meters. At the circle's center, how many radians are subtended by the 8 meter length of rope?
ANSWER: 1
Exactly how many of the prime numbers are even?
ANSWER: 1
The relationship between y and x is given by the equation: y = x2 - 2x + 8. For what value of x is y a minimum?
ANSWER: 1
Find x if log[base 5](x) = -2.
ANSWER: 1/25 or .04
Two fair coins are tossed and at least one is a head. What is the probability that both coins are heads?
ANSWER: 1/3
The relation between y and x is given by the equation " y = ABS(4 -x) " (read: y equals the absolute value of the quantity 4 minus x). If y equals 6, give all possible values for X.
ANSWER: 10 AND -2
If an electronic circuit operates in 100 nanoseconds, how many operations can it perform in one second?
ANSWER: 10 MILLION or 10 to the seventh power
An ellipse is represented by the equation [x2/36] + [y2/16] = 1. What is the length of the major axis of this ellipse?
ANSWER: 12
If x = t4 (read: t raised to the fourth), what is the second derivative of x with respect to t equal to?
ANSWER: 12t2 (read: 12t squared)
The ratio of 2 positive numbers is 3 to 8 and their product is 864. What are the two numbers?
ANSWER: 18,48
How many degrees are there in pi radians?
ANSWER: 180 DEGREES
Given that the log[base 10](3) = .477, what is the log[base 10] of 300?
ANSWER: 2.477
What is the value of 125 to the two-thirds power?
ANSWER: 25
The scale on a blueprint of a bicycle says one half inch equals 1 foot. What will be the actual DIAMETER of the bicycle wheel if they are drawn with a RADIUS of ¾ inches.
ANSWER: 3 FEET (accept 36 inches)
What is the surface area of a sphere of radius "r"?
ANSWER: 4 pi R squared or 12.566 x R squared
For what value of the angle "A" is the cos(A) equal t the sin(A)?
ANSWER: 45o or p/4 RADIANS or (45o + n times 180o)
What is the sum of the first 100 positive integers?
ANSWER: 5050
Twelve socks are in a drawer; 4 are red, 7 are blue, and 1 is green. What is the maximum number of socks that you can pull out and only have 2 matching pairs?
ANSWER: 7
A "reunion of broken parts" is the meaning of the root of what word: A. algebra B. calculus C. mathematics D. none of the above
ANSWER: A - ALGEBRA
The sin2(A/2) (read: sine squared of angle A divided by 2) is equal to which of the following relationships? Is it: A. (1/2)[1 - cos(A)] B. (1/2)[1 - sin(A)] C. 2 sin(A) cos(A) D. none of the above
ANSWER: A or (1/2)[1 - cos(A)]
The tan(180o + A) (read: tangent of the quantity 18 degrees plus A) is equal to which of the following? A. tan(A) B. -tan(A) C. tan(-A) D. none of the above.
ANSWER: A or TAN(A)
What is the name given to the radius of a circle that can be inscribed in any regular polygon?
ANSWER: APOTHEM
The polar equation, r = 3sin(3t), (read: r equals 3 times the sine of angle 3t) represents which of the following graphs? Is it the graph of a: A. cardioid B. three-leaved rose C. Archimedian-spiral D. limacon
ANSWER: B -- THREE-LEAVED ROSE
The cotangent of the angle A is equal to which of the following? A. cot(-A) B. -cot(-A) C. -cot(A) D. none of the above
ANSWER: B or -COT(-A)
The trigonometric function cos(2A) is equal to which of the following relationships? A. 1 - [sin(A)]2 B. [cos(A)]2 - [sin(A)]2 C. 2[sin(A)][cos(A)] D. none of the above
ANSWER: B or [cos(A)]2 - [sin(A)]2
In what number base does 1 + 2 = 10?
ANSWER: BASE 3
The tan(-A) (read: tangent of the angle minus A) is equal to which of the following? A. tan(A) B. -tan(-A) C. -tan(A) D. none of the above
ANSWER: C or -TAN(A)
The sin(2A) (read: the sine of angle 2A) is equal to which of the following relationships? A. sin(A) - cos(A) B. 3sin(A) / cos(A) C. 2 sin(A) cos(A) D. tan(A) - 1
ANSWER: C or 2 TIMES THE SIN(A) TIMES THE COS(A)
The polar equation, r = 3 - 2cos(t), (read: r equal 3 minus 2 times the cosine of the angle t) represents which of the following graphs? Is it the graph of a: A. cardioid B. three-leaved rose C. Archimedian-spiral D. limacon (pron: lee-ma-son)
ANSWER: D - LIMACON
How is the number 14 represented in the hexadecimal system?
ANSWER: E
How many vertices does a tetrahedron have?
ANSWER: FOUR
A wheel is rolling without slipping on a flat surface. If the diameter of the wheel is 1 meter, how far does the hub of the wheel move when the wheel turns once?
ANSWER: PI METERS or 3.14 METERS
What term is used to describe a triangle that has three UNEQUAL sides?
ANSWER: SCALENE
Give two trigonometric functions which are NEGATIVE in BOTH the third and fourth quadrants.
ANSWER: SINE and COSECANT
Find the equation of the line that passes through the point (1,2) and is perpendicular to the line y = 2x + 1.
ANSWER: Y = -(1/2)x + 2.5 or y - 2 = (-1/2)(x - 1)
If both x and y are functions of time, what is the derivative of the PRODUCT of x and y with respect to time equal to?
ANSWER: x[dy/dt] + y[dx/dt] or y[dx/dt] + x[dy/dt]
A straight line intersects a circle in the first and second quadrants for x values of +3 and -3. The equation of the circle is " x2 + y2 = 25 ". What is the EQUATION of the straight line?
ANSWER: y = 4
A straight line is plotted on an XY coordinate axis. The line intercepts the y axis at 3 and makes an angle of 45 degrees with respect to the x axis. Give the equation for this line.
ANSWER: y = x + 3 or y = -x + 3
The universal set U contains the elements {1,2,3,4,5}. Set A contains the elements {1,3}. What elements does the set A' (read: A prime) contain?
ANSWER: {2,4,5}
For a right triangle, the sin(A) is 3/5. To what value is the tan(A) (read: tangent of A) equal?
ANSWER: ¾
Give the rational numbers in the following set: -8, - 3 , 1/5, 0, π
Answer: -8, 1/5, 0
Farmer John grows corn, tomatoes, potatoes and squash. He has only 2 fields for growing these products and cannot grow more than one product per field. How many planting combinations can be done in one season?
Answer: 10
A farmer wishes to make a straight barbed wire fence 80 feet long. He wants to have a fence post every 8 feet. How many fence posts does he need?
Answer: 11
If perfect numbers, except 6, can be expressed by the sum of the cubes of an unbroken sequence of consecutive odd integers, what are the consecutive odd integers which, when cubed, give the perfect number 28?
Answer: 13 + 33
What 3 consecutive numbers add up to 45?
Answer: 14, 15, and 16
Convert 3/20 into a percentage:
Answer: 15%
What is the square root of 256?
Answer: 16
How many degrees are there in π radians:
Answer: 180o
Rounded off to the nearest whole year, how many years would it take for your money to double in an investment that was increasing with an annual compound rate of 3.5%?
Answer: 20 years
If the length of the cycloid is 4 times the diameter of a rotating circle, then the area under the arch traced out by that cycloid is how many times the area of the rotating circle?
Answer: 3 times
Give the range for the following six values 2, 7, 11, 19, 25, 33:
Answer: 31
If you start with 1 bacterium and double the number every 15 minutes, how many bacteria will you have at the end of 3 hours and 45 minutes?
Answer: 32,768
What is the total angular distance in degrees over a sphere?
Answer: 360 Degrees
Every even integer greater than 2 can be written as the sum of two primes. Give the respective two pairs of prime numbers that when added give 8 and 12:
Answer: 5 and 3 for the number 8; and 7 and 5 for the number 12
What is the mean for the following data set of 5 numbers: 84, 50, 73, 27, 16
Answer: 50
π radians encompass what percent of a circle?
Answer: 50%
What is the sum of the internal angles of a pentagon:
Answer: 540°
The product of 6 factorial is how many times larger than the product of 5 factorial?
Answer: 6
What is the greatest common divisor for the numbers 102 and 30?
Answer: 6
Six factorial equals what number?
Answer: 720
What is the cube root of 729?
Answer: 9
A person with lung cancer is given an MRI. Four radiologists examine each MRI independently. If each specialist can detect lung cancer with 80% accuracy, what is the probability that at least one of them will detect cancer in this patient: A. 0.998 B. 0.01 C. 0.25 D. 0.8
Answer: A
In the hexadecimal counting system, the letter c stands for what base-10 number: A. 12 B. 3 C. 16 D. 11
Answer: A
Using an x- y coordinate axis, a parabola is represented by the equation x2 = 6y. The vertex of this parabola is at what coordinate point: A. (0, 0) B. (1, 1) C. (1, 2) D. (2, 2)
Answer: A
Which of the following is the surface area of a perfect sphere with a radius of 10 meters? A. 1256.7 m2 B. 1200.5 m2 C. 628 m2 D. 125.7 m2
Answer: A
Assuming a year in a dog's life is equivalent to 7 years of a human's life, what is 1 hour of a dog's life approximately equivalent to in a human's life? A. 3 ½ hours B. 7 hours C. 5 hours D. 4 ½ days
Answer: B
In a normal distribution, approximately what percentage of the cases, to the nearest whole number, falls within 4 standard deviations of the mean: A. 68% B. 100% C. 99% D. 75%
Answer: B
Systematic random samp ling is to be used to select 5 addresses from an ordered list containing 500 addresses. A 1- in-100 systematic sample is used to select the 5 addresses. What is the chance that any specific address will be chosen: A. 1/5 B. 1/100 C. 5/100 D. 5
Answer: B
Which of the following mathematicians is responsible for the Cartesian plane that is also known as the rectangular coordinate system: A. Pythagoroas B. Rene Descartes C. Kirk Godel D. Fredric Gauss
Answer: B
Continuing up the number sequence of natural numbers, prime numbers become which of the following: A. non-existent at a certain point B. all even after a certain point C. less and less frequent D. more frequent
Answer: C
In a simple random sample: A. response bias will be small B. non-response bias will be small C. any two samples of the same size will have the same cha nce of being drawn D. each subject is asked every question and random responses are allowed
Answer: C
The surface of a sphere subtends a solid angle of what amount at its center: A. π B. 2π C. 4π D. ½ π
Answer: C
The Babylonian number system is base 60, which makes it: A. vigesimal B. quinary C. binary D. sexagesimal
Answer: D
Which of the following does NOT yield a periodic non-terminating decimal: A. 5/6 B. 1/27 C. 1/18 D. 7/8
Answer: D
Which of the following is the mathematical term for a radical that expresses an irrational number: A. turk B. radicand C. finical D. surd
Answer: D
Which of the following properties would you use to compute the chances of rolling either a 7 or an 11 with a pair of dice: A. multiplicative B. conditional C. independent D. additive
Answer: D
In 1700 AD, this person showed that a series of 0's and 1's could be used to denote a number:
Answer: Gottfried Liebniz
When a quadratic function is plotted on a typical graph, it assumes what shape?
Answer: Parabola
The converse of this theorem is: if the sum of the squares of two sides of a triangle equal the square of the third side then the triangle is a right triangle. What is the name of the theorem?
Answer: Pythagorean Theorem
A country adopted a policy requiring all couples to continue having children until they had a girl, after which they must stop having children. How many children will the average family have and what will the sex distribution be?
Answer: Two Children - One Boy And One Girl
What form of geometry is one in which the parallel postulate of Euclidean Geometry does NOT hold:
Answer: non-euclidean geometry
According to "Set Theory", sets that do NOT contain themselves are typically referred to as:
Answer: normal sets
If in a sequence of natural numbers, starting with 2, you begin eliminating every second number after 2, then every third number after 3, then every fourth number after 4, and so on, what type of numbers will be left?
Answer: prime numbers
In statistics, what is the common term for the square root of the variance?
Answer: standard deviation
The imaginary unit "i" is numerically defined as what?
Answer: the square root of negative 1
Where is the y intercept for y = sin x?
Answer: zero
