Science Bowl Practice Questions - Math

Short Answer: In what number base does 1 + 2 = 10?

BASE 3

Short Answer: What is the period of the function t = cos 4s? (read: t equals the cosine of 4 s)

p /2 (or 1/2 p)

Short Answer: 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?

p METERS or 3.14 METERS

Short Answer: 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)

x < 2 (read: x LESS THAN 2)

Short Answer: Where does the graph of cotangent of x cross the x-axis?

x = p/2, 3p/2, 5p/2 ... or ODD INTEGERS OF p/2

Short Answer: 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?

$0.97

Short Answer: 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?

(0,0)

Short Answer: 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?

(0,0) or x = 0, y = 0

Short Answer: 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.

(0,1/4)

Short Answer: What is the volume of a right circular cone with radius r and height h?

(1/3)pr2h

Short Answer: 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)

(3, -2) (accept x = 3 and y = -2 but not x = -2, y = 3)

Short Answer: What is the volume of a sphere of radius "R"?

(4/3) p R3

Short Answer: If q = 30°, what is csc2 q - cot2 q equal to? (read: If theta equals 30 degrees, what is cosecant squared theta minus cotangent squared theta equal to?)

1

Short Answer: The relationship between y and x is given by the equation: y = x2 - 2x + 8. For what value of x is y a minimum?

1

Short Answer: What is the limit of the cos(X) (read: cosine of X) a X approaches zero?

1

Short Answer: What is the limit of the fraction x/(x+1) as approaches infinity?

1

Short Answer: 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?

1

Short Answer: What is the amplitude of the curve y = -1.5 sin x (read: y equals minus 1 point 5 sine x)?

1.5 (do NOT accept -1.5)

Short Answer: To what value does the infinite series 1/4 + 1/8 + 1/16 + . . . ..converge? (read: one fourth plus one eighth plus one sixteenth, etc.)

1/2

Short Answer: What is the slope of the curve y = ln x (read: y equals the natural logarithm of x) at x = 2?

1/2

Short Answer: Find x if log[base 5](x) = -2.

1/25 or .04

Short Answer: 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?

1

Short Answer: Exactly how many of the prime numbers are even?

1

Short Answer: Name the famous mathematician/physicist who was born in the year Galileo died.

(ISAAC) NEWTON

Short Answer: Name the two discoverers of the fundamental theorem of calculus. Last names only are acceptable.

(SIR ISAAC) NEWTON AND (BARON VON) LEIBNITZ

Short Answer: 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.

(x - 8)2 + (y)2 = 82 or (x + 8)2 + (y)2 = 82

Short Answer: A number minus its reciprocal is 14 larger than the original number. What was the number?

- 1/14

Short Answer: What is the slope of the line 2x + 3y = 7? (read: 2 x plus 3 y equals 7)

- 2/3 or -0.667

Short Answer: Two off-axis lines are perpendicular if and only if the product of their slopes is equal to what?

-1

Short Answer: What is the imaginary unit "i" when raised to the power 10?

-1

Short Answer: What is the log[base 5](1/25) equal to?

-2

Short Answer: What is the slope of the straight line whose x-intercept is +4 (read: plus 4) and whose y- intercept is +8 (read: plus 8)?

-2 (read: minus 2)

Short Answer: Express the product of the following complex numbers in the form a + bi (read: a plus b i) where a and b are real: 4 + 2i and 2 + 5i (read: 4 plus 2 i and 2 plus 5 i)

-2 + 24i (read: minus 2 plus 24 i)

Short Answer: In the complex plane, what are the roots of the equation x2 + 4x + 8 = 0? (read: x squared plus 4 x plus 8 equals 0)

-2 - 2i and -2 + 2i

Short Answer: 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?

-4 AND -3

Short Answer: What is the slope of the curve y = x3 - 6x + 2 when it crosses the y axis?

-6

Short Answer: In calculus, what is the indefinite integral of the sin(U)dU equal to?

-cos(U) + CONSTANT

Short Answer: 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?

.18

Short Answer: Given that the log[base 10](2) = .301, what is the log[base 10](8) equal to?

.903

Short Answer: What is the limit of the fraction 1/x as x approaches infinity?

0

Short Answer: 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?

0,1 or x = 0, y = 1

Short Answer: The polar coordinates of a point are (3, p/2) (read: 3 comma p over 2). What are the cartesian coordinates of this point?

0,3 or x = 0, y = 3

Short Answer: Two fair coins are tossed and at least one is a head. What is the probability that both coins are heads?

1/3

Short Answer: 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?

10

Short Answer: 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.

10 AND -2

Short Answer: 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?

10 MILES

Short Answer: If an electronic circuit operates in 100 nanoseconds, how many operations can it perform in one second?

10 MILLION or 107

Short Answer: 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 track is 40 yards. Within ten yards, how long is each straight section of the track?

106 YARDS (accept 96 to 116)

Short Answer: An ellipse is represented by the equation [x2 /36] + [y2 /16] = 1. What is the length of the major axis of this ellipse?

12

Short Answer: 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.

12,100

Short Answer: If x = t4 (read: t raised to the fourth), what is the second derivative of x with respect to t equal to?

12t2 (read: 12t squared)

Short Answer: Express the binary number 10010 as a decimal number.

18

Short Answer: The ratio of 2 positive numbers is 3 to 8 and their product is 864. What are the two numbers?

18,48

Short Answer: How many degrees are there in p radians?

180 DEGREES

Short Answer: Express the decimal number 27 in Base 16 (Hexadecimal).

1B

Short Answer: Solve this indefinite integral: [2/x] dx (read: the integral of 2 over x, dx).

2 ln x + CONSTANT

Short Answer: Given that the log[base 10](3) = .477, what is the log[base 10] of 300?

2.477

Short Answer: What is the value of 125 to the two-thirds power?

25

Short Answer: What is 81^1/4 (read: 81 to the one-fourth power)?

3

Short Answer: 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?

3 (no units specified)

Short Answer: 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 3⁄4 inches.

3 FEET (accept 36 inches)

Short Answer: 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?

3/2

Short Answer: For a right triangle, the sin(A) is 3/5. To what value is the tan(A) (read: tangent of A) equal?

3⁄4

Short Answer: 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?

4

Short Answer: What is the surface area of a sphere of radius "r"?

4 p R2 or 12.566 x R2

Short Answer: For what value of the angle "A" is the cos(A) equal t the sin(A)?

45o or p/4 RADIANS or (45o + n times 180o)

Short Answer: 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)

5

Short Answer: y = 4x + 3. What is the value of the integral of y from x = 0 to x = 1? (read: y equals 4 x plus 3)

5

Short Answer: What is the sum of the first 100 positive integers?

5050

Short Answer: 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?

7

Short Answer: What is the area bounded by the curve y = x2 and the axis between x = 1 and x = 2?

7/3 (or 2 and 1/3 or 2.333)

Short Answer: What is the name given to the radius of a circle that can be inscribed in any regular polygon?

APOTHEM

Short Answer: How is the number 14 represented in the hexadecimal system?

E

Short Answer: How many vertices does a tetrahedron have?

FOUR

Short Answer: What term is used to describe a triangle that has three UNEQUAL sides?

SCALENE

Short Answer: Give two trigonometric functions which are NEGATIVE in BOTH the third and fourth quadrants.

SINE and COSECANT

Short Answer: 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?

THE WOMAN IS 53 YEARS OLD, THE DAUGHTER IS 31 YEARS OLD.

Multiple Choice: 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

W -- (1/2)[1 - cos(A)]

Multiple Choice: 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

W -- ALGEBRA

Multiple Choice: 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.

W -- TAN(A)

Multiple Choice: A square matrix which has all zeros below the main diagonal is called: w) upper triangular x) singular y) lower triangular z) invertable

W -- UPPER TRIANGULAR

Multiple Choice: 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

X -- -COT(-A)

Multiple Choice: Which of the following functions is NOT a transcendental function? Is it: w) trigonometric x) algebraic y) logarithmic z) exponential

X -- ALGEBRAIC

Multiple Choice: A fractal is a type of: w) fraction x) geometric shape y) geologic fault z) differential equation

X -- GEOMETRIC SHAPE

Multiple Choice: 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

X -- HYPERBOLA

Multiple Choice: 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)

X -- THREE-LEAVED ROSE

Multiple Choice: 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) z) none of the above

X -- [cos(A)]2 - [sin(A)]2

Short Answer: 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)

X < 2 (read: X less than 2)

Multiple Choice: 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

Y -- -TAN(A) (read: minus the tangent of the angle A)

Multiple Choice: 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)

Y -- 2 TIMES THE SIN(A) TIMES THE COS(A)

Multiple Choice: 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

Y -- IRRATIONAL NUMBERS

Short Answer: Find the equation of the line that passes through the point (1,2) and is perpendicular to the line y = 2x + 1.

Y = -(1/2)x + 2.5 or y - 2 = (-1/2)(x - 1)

Short Answer: 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

Z - TRAPEZOID

Multiple Choice: 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)

Z -- 91/3 (read: the cube root of 9)

Multiple Choice: 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)

Z -- LIMACON

Multiple Choice; Matrix C is the product of matrix A times matrix B Which of the following must be TRUE. 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.

Z -- THE NUMBER OF COLUMNS OF A EQUALS THE NUMBER OF ROWS

Short Answer: 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?

x[dy/dt] + y[dx/dt] or y[dx/dt] + x[dy/dt]

Short Answer: 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?

y = 4

Short Answer: 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.

y = x + 3 or y = -x + 3

Short Answer: 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?

{2,4,5}