Science Bowl Math
A customer purchased a candy bar costing $0.78 and was 3 cents short of having the exact amount without breaking a $1 bill. How much change did the customer have after the $1 bill was broken?
ANSWER: $0.97
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)
Find x if log[base 5](x) = -2.
ANSWER: 1/25 or .04
Using an x-y coordinate axis, a parabola is represented by the equation x2 = 6y. Thevertex 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-ycoordinates of the focal point for this parabola.
ANSWER: (0,1/4)
What is the volume of a right circular cone with radius r and height h?
ANSWER: (1/3)pr2h
What are the cartesian coordinates of the point of intersection of the two lines x - y = 5 and x + y = 1? (read: x minus y equals 5 and x plus y equals 1)
ANSWER: (3, -2) (accept x = 3 and y = -2 but not x = -2, y = 3)
What is the volume of a sphere of radius "R"?
ANSWER: (4/3) p R3
Name the famous mathematician/physicist who was born in the year Galileo died.
ANSWER: (ISAAC) NEWTON
Name the two discoverers of the fundamental theorem of calculus. Last names only are acceptable.
ANSWER: (SIR ISAAC) NEWTON AND (BARON VON) LEIBNITZ
Give the equation of one of the circles which satisfy the following criteria: a circle witha 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
A number minus its reciprocal is 14 larger than the original number. What was the number?
ANSWER: - 1/14
What is the slope of the line 2x + 3y = 7? (read: 2 x plus 3 y equals 7)
ANSWER: - 2/3 or -0.667
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 y interceptis +8 (read: plus 8)?
ANSWER: -2 (read: minus 2)
Express the product of the following complex numbers in the form a + bi (read: a plus bi) where a and b are real: 4 + 2i and 2 + 5i (read: 4 plus 2 i and 2 plus 5 i)
ANSWER: -2 + 24i (read: minus 2 plus 24 i)
In the complex plane, what are the roots of the equation x2 + 4x + 8 = 0? (read: xsquared plus 4 x plus 8 equals 0)
ANSWER: -2 - 2i and -2 + 2i
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
What is the slope of the curve y = x3 - 6x + 2 when it crosses the y axis?
ANSWER: -6
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 thelog[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
What is the limit of the fraction 1/x as x approaches infinity?
ANSWER: 0
A circle with a radius of 2 is defined by the equation x2 + y2 - 2y = 3. What are the coordinates in the cartesian coordinate system of the center of this circle?
ANSWER: 0,1 or x = 0, y = 1
The polar coordinates of a point are (3, p/2) (read: 3 comma p over 2). What are the cartesian coordinates of this point?
ANSWER: 0,3 or x = 0, y = 3
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
If q = 30°, what is csc2q - cot2q equal to? (read: If theta equals 30 degrees, what iscosecant squared theta minus cotangent squared theta equal to?)
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
What is the limit of the cos(X) (read: cosine of X) a X approaches zero?
ANSWER: 1
What is the limit of the fraction x/(x+1) as approaches infinity?
ANSWER: 1
What is the value of the integral from 1 to e of du/u (read: d u divided by u), where e is the base of the natural logarithm?
ANSWER: 1
What is the amplitude of the curve y = -1.5 sin x (read: y equals minus 1 point 5 sine x)?
ANSWER: 1.5 (do NOT accept -1.5)
To what value does the infinite series 1/4 + 1/8 + 1/16 + . . . ..converge? (read: onefourth plus one eighth plus one sixteenth, etc.)
ANSWER: 1/2
What is the slope of the curve y = ln x (read: y equals the natural logarithm of x) at x = 2?
ANSWER: 1/2
Two fair coins are tossed and at least one is a head. What is the probability that both coins are heads?
ANSWER: 1/3
y = 3x2 + 4x + 2 (read: y equals 3 x squared plus 4 x plus 2). What is the value of the derivative of y at x = 1?
ANSWER: 10
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
A biker goes EAST for 4 miles, NORTH for 12, EAST for another 4 and SOUTH for 6. What is the magnitude of the displacement?
ANSWER: 10 MILES
If an electronic circuit operates in 100 nanoseconds, how many operations can itperform in one second?
ANSWER: 10 MILLION or 107
The area bounded by the race track at your high school is a rectangle with semicircles at each end. The radius of the circular parts is 30 yards and the perimeter of the area bounded by the trackis 40 yards. Within ten yards, how long is each straight section of the track?
ANSWER: 106 YARDS (accept 96 to 116)
An ellipse is represented by the equation [x2/36] + [y2/16] = 1. What is the length of themajor axis of this ellipse?
ANSWER: 12
The population of a near-by town was 10,000 in January, 1990. It is estimated that the population will increase by 10% each year. What will be population of the town in January, 1992.
ANSWER: 12,100
If x = t4 (read: t raised to the fourth), what is the second derivative of x with respect to tequal to?
ANSWER: 12t2
Express the binary number 10010 as a decimal number.
ANSWER: 18
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 p radians?
ANSWER: 180 DEGREES
Express the decimal number 27 in Base 16 (Hexadecimal).
ANSWER: 1B
Solve this indefinite integral: [2/x] dx (read: the integral of 2 over x, dx).
ANSWER: 2 ln x + CONSTANT
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
What is 811/4 (read: 81 to the one-fourth power)?
ANSWER: 3
A student finds that the numerical values for the are and the volume of a sphere are equal. What is the radius for this sphere?
ANSWER: 3 (no units specified)
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)
If (sin(3x) + cos(3x))2 = 2 (read: the quantity sine x plus cosine 3 x squared equals 2)then what does 3sin(3x) cos(3x) (read 3 sine 3 x cosine 3 x) equal?
ANSWER: 3/2
A curve represented by the equation y = - 5 x2 intersects the line y = -20 at two points. What is the straight-line distance between the two intersections?
ANSWER: 4
What is the surface area of a sphere of radius "r"?
ANSWER: 4 p R2 or 12.566 x R2
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 distance between the points P and Q if their cartesian coordinates are (5, 5,1) and (1, 5, -2)? (read: 5 comma, 5 comma, 1 and 1 comma, 5 comma, minus 2)
ANSWER: 5
y = 4x + 3. What is the value of the integral of y from x = 0 to x = 1? (read: y equals 4 xplus 3)
ANSWER: 5
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
What is the area bounded by the curve y = x2 and the axis between x = 1 and x = 2?
ANSWER: 7/3 (or 2 and 1/3 or 2.333)
What is the name given to the radius of a circle that can be inscribed in any regular polygon?
ANSWER: APOTHEM
In what number base does 1 + 2 = 10?
ANSWER: BASE 3
How is the number 14 represented in the hexadecimal system?
ANSWER: E
How many vertices does a tetrahedron have?
ANSWER: FOUR
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
A woman is 22 years older than her daughter. Nine years ago she was twice as old as her daughter. What are their present ages?
ANSWER: THE WOMAN IS 53 YEARS OLD, THE DAUGHTER IS 31 YEARS OLD.
The sin2(A/2) (read: sine squared of angle A divided by 2) is equal to which of the following relationships? Is it: w) (1/2)[1 - cos(A)] (read: 1/2 times the quantity one minus the cosine of the angle A) x) (1/2)[1 - sin(A)] (read: 1/2 times the quantity one minus the sine of the angle A) y) 2 sin(A) cos(A) z) none of the above
ANSWER: W -- (1/2)[1 - cos(A)]
A "reunion of broken parts" is the meaning of the root of what word: w) algebra x) calculus y) mathematics z) none of the above
ANSWER: W -- ALGEBRA
The tan(180o + A) (read: tangent of the quantity 18 degrees plus A) is equal to which of the following? w) tan(A) x) -tan(A) y) tan(-A) z) none of the above.
ANSWER: W -- TAN(A)
A square matrix which has all zeros below the main diagonal is called: w) upper triangular x) singular y) lower triangular z) invertable
ANSWER: W -- UPPER TRIANGULAR
The cotangent of the angle A is equal to which of the following? w) cot(-A) (pron: cotangent of the angle minus A) x) -cot(-A) (pron: minus the cotangent of the angle minus A) y) -cot(A) (pron: minus the cotangent of the angle A) z) none of the above
ANSWER: X -- -COT(-A)
Which of the following functions is NOT a transcendental function? Is it: w) trigonometric x) algebraic y) logarithmic z) exponential
ANSWER: X -- ALGEBRAIC
A fractal is a type of: w) fraction x) geometric shape y) geologic fault z) differential equation
ANSWER: X -- GEOMETRIC SHAPE
The equation: [(x - 2)2 /6] - [(y - 3)2 /5] = 2 defines which of the following? (read: the quantity x minus 2 squared divided by 6 MINUS the quantity y minus 3 squared divided by 5 equals 2) w) ellipse x) hyperbola y) spiral z) parabola
ANSWER: X -- HYPERBOLA
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: w) cardioid (pron: car-dee-oiz) x) three-leaved rose y) Archimedian-spiral z) limacon (pron: lee-ma-son)
ANSWER: X -- THREE-LEAVED ROSE
The trigonometric function cos(2A) (read: cosine of the angle 2A) is equal to which of the following relationships? w) 1 - [sin(A)]2 (read: one minus the sine squared of A) x) [cos(A)]2 - [sin(A)]2 (read: cosine squared of angle A minus the sine squared of angle A) y) 2[sin(A)][cos(A)] (read: 2 times the sine of A times the cosine of A)
ANSWER: X -- [cos(A)]2 - [sin(A)]2
For which values of X from the set of real numbers does the following inequality hold:8x - 6 < 2x + 6 (read: 8 x minus 6 is less than 2 x plus 6)
ANSWER: X < 2 (read: X less than 2)
The tan(-A) (read: tangent of the angle minus A) is equal to which of the following? w) tan(A) (read: tangent of the angle A) x) -tan(-A) (read: minus the tangent of the angle minus A) y) -tan(A) (read: minus the tangent of the angle A) z) none of the above
ANSWER: Y -- -TAN(A) (read: minus the tangent of the angle A)
The sin(2A) (read: the sine of angle 2A) is equal to which of the following relationships? w) sin(A) - cos(A) (read: sine of A minus the cosine of A) x) 3sin(A) / cos(A) (read: 3 times the sine of A divided by the cosine of A) y) 2 sin(A) cos(A) (read: 2 times the sine of A times the cosine of A) z) tan(A) - 1 (read: tangent of A minus 1)
ANSWER: Y -- 2 TIMES THE SIN(A) TIMES THE COS(A)
What type of numbers are included in the real number line that are not included in the rational number line? w) whole numbers x) integers y) irrational numbers z) fractional numbers
ANSWER: Y -- IRRATIONAL NUMBERS
Find the equation of the line that passes through the point (1,2) and is perpendicular tothe line y = 2x + 1.
ANSWER: Y = -(1/2)x + 2.5 or y - 2 = (-1/2)(x - 1)
If two sides of a quadrilateral are parallel and the other two sides are equal but NOT parallel, the quadrilateral is known as a: w) parallelogram x) triangle y) square z) trapezoid
ANSWER: Z - TRAPEZOID
If logx81 = 6 (read: the log base x of 81 equals 6), then x is equal to: w) 3 x) 9 y) 1/3 z) 91/3 (read: the cube root of 9)
ANSWER: Z -- 91/3 (read: the cube root of 9)
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: w) cardioid x) three-leaved rose y) Archimedian-spiral z) limacon (pron: lee-ma-son)
ANSWER: Z -- LIMACON
Matrix C is the product of matrix A times matrix B Which of the following must beTRUE. w) The number of rows of A equals the number of rows of B. x) The number of columns of A equals the number of columns of B. y) The number of rows of A equals the number of columns of B. z) The number of columns of A equals the number of rows of B.
ANSWER: Z -- THE NUMBER OF COLUMNS OF A EQUALS THE NUMBER OF ROWS
What is the period of the function t = cos 4s? (read: t equals the cosine of 4 s)
ANSWER: p /2 (or 1/2 p)
A wheel is rolling without slipping on a flat surface. If the diameter of the wheel is 1meter, how far does the hub of the wheel move when the wheel turns once?
ANSWER: p METERS or 3.14 METERS
For which values of x from the set of real numbers does the following inequality hold: 4x + 5 < x + 11 (read: 4 x plus 5 is less than x plus 11)
ANSWER: x < 2 (read: x LESS THAN 2)
Where does the graph of cotangent of x cross the x-axis?
ANSWER: x = p/2, 3p/2, 5p/2 ... or ODD INTEGERS OF p/2
If both x and y are functions of time, what is the derivative of the PRODUCT of x and ywith 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
