Science Bowl Questions (Math)
What is the angle formed, in degrees, between the hour and minute hand of an analog clock at 10:30 AM?
135
Find the sum of all interior angles, in degrees, in a regular polygon having 100 sides:
17,640
Convert the angle, 18º18'36" (read as: 18 degrees, 18 minutes, 36 seconds) to degrees, to the second decimal place:
18.31
Giving your answer in terms of π and in inches, what is the arc-length of a semi-circle whose diameter is 18 inches?
9π
Giving your answer in standard form, what is the last term in the binomial expansion of the following: (x + y)^6
y^6
Giving your answer as a proper fraction, what is the cube root of 125/343?
5/7
If $10,000 is placed in a savings account that pays 5% interest compounded annually, what is the total amount of money in the account at the end of 2 years, to the nearest dollar?
$11,025
What are the coordinates of the vertex in the graph of the following equation: y = 4x^2 + 8x - 5
(-1, -9)
If a point has polar coordinates (3, π), what are the rectangular coordinates?
(-3, 0)
The point (3, 2) is reflected across the graph of y = 6 and the resulting point is then reflected across the graph of y = x. What are the coordinates of the final point?
(10, 3)
Factor the following expression completely: 81x^2 + 180xy + 100y^2
(9x + 10y)^2
Simplify the following expression by combining like terms: 12.03A - 4.03B - 0.03(A - 40)
12A - 4.03B + 1.2
What is the determinant of a 2-by-2 square matrix whose rows are 4, 2 and -3, -4?
-10
Solve the following inequality for x: |3 - 2x| ≤ 7 (read as: the absolute value of, 3 minus 2x, close absolute value, is less than or equal to 7)
-2 ≤ x ≤ 5 (ACCEPT: 5 ≥ x ≥ -2)
What is the slope of a line perpendicular to the line given by the graph of the equation, -5x = -6y + 4
-6/5
Give the resulting vector for the cross product of vector 0,0,1 with vector 1,0,0
0,1,0
Assuming that the natural log of 5 = 1.6, find, to the first decimal place, the natural log of 5^13:
0.5
Solve the following equation for x over the integers: x^2 = 3x
0; 3
Solve the following equation for all real values of x: (x + 3)^2 = 16
1 AND -7
Cards numbered 1 through 10 lie on a table. If two cards are picked at random, without replacement, what is the probability, as a fraction in lowest terms, that the two cards will have values within one of each other?
1/5
Giving your answer in centimeters, what is the length of a side of a square whose diagonal measures 12sqrt2 centimeters?
12
If the shortest leg of a 30-60-90 right triangle is 6 inches, what is the measure, in inches, of the other 2 sides?
12 AND 6sqrt3
Factor the following expression completely: 12x^2 + 24x - 36
12(x + 3)(x - 1) (ACCEPT: 12(x - 1)(x + 3))
If y varies directly as x and z, and y = 12 when x = 4 and z = 5, find y when x = 10 and z = 20:
120
What is the area, in square feet, of a triangle whose perpendicular height is 20 feet with a base of 12 feet?
120
Find the prime factorization of 240:
2 × 2 × 2 × 2 × 3 × 5 (ACCEPT: 2^4 × 3 × 5)
Simplify the following, giving your answer in proper scientific notation: (6.0 × 10^12)(2.0 × 10^10)^2
2.4 × 10^33
Short Answer Multiply the following 4 numbers and give your answer in scientific notation: 30,000 × 3,000 × 30 × 0.1
2.7 × 10^8
Multiply the following complex numbers, giving your answer in standard a + bi form: (6 + 3i)(4 + i)
21 + 18i
What is the degree measure of the angle formed by 2 secants intersecting outside a circle if the measures of the intercepted arcs are 80º and 34º?
23
Find the area, in square centimeters, of a rhombus with a diagonal of 6 centimeters and a side of 5 centimeters:
24
Factor the following expression completely: 100x^2 - 25y^2
25(2x + y)(2x - y)
Find the sum of the first 10 terms of the arithmetic sequence whose first three terms are 7, 11, and 15:
250
An object is launched straight up from the ground with an initial velocity of 176 feet per second. What is the height of the object above the ground, in feet, 2 seconds into the flight?
288
Find the following product, giving your answer in standard form: (4x^3 + x)(7x^3 + 4x^2)
28x^6 + 16x^5 + 7x^4 + 4x^3 (ACCEPT: x^3(28x^3 + 16x^2 + 7x + 4))
In what quadrant does θ (read as: theta) terminate if sine θ is positive and secant θ is negative?
2nd (ACCEPT: 2)
What is the smaller of two integers whose sum is 19 and whose product is 48?
3
It takes 20 minutes for Janis to prepare lunch. When Kristen helps, it only takes 12 minutes. How many minutes would it take Kristen to prepare the same lunch if she worked alone?
30
Find the numerical value of the geometric mean of the following 4 values: 2^1; 2^3; 2^8; 2^8
32 (DO NOT ACCEPT: 2^5)
Evaluate the following expression when a = 1/3, b = 4, c = -1, and d = -5: 2[3a - (b + c) - 4d]
36
Solve the following equation for x: -2|3 + (x/2)| = -10 (read as: negative 2 times the absolute value of 3 plus, open parenthesis, x divided by 2, close parenthesis, close absolute value, equals negative 10)
4 AND -16
Divide the following and give your answer in scientific notation: 8*10^7 ________ (4*10^4)^1/2
4 × 10^5
A jar of 100 marbles contains only 2 colors of marbles, red and blue. If there are 13 red marbles for every 12 blue marbles, how many blue marbles are in the jar?
48
There are 10 people on a bus who, when ranked from youngest to oldest, all differ from those on the bus closest in age to them by the same number of years. If the youngest is 6 and the oldest is 51, what is the common difference in their age?
5
Giving your answer in inches and in simplest radical form, if the hypotenuse of a 45-45-90º triangle is 10 inches, find the length of the other sides:
5sqrt2 (ACCEPT: BOTH 5sqrt2)
Find 2 mean proportionals between the numbers 3 and 24:
6 AND 12
In a circle with diameter AB, if the radius is 6 centimeters, find the length in centimeters, giving your answer in terms of π, of the arc AB:
6π
If the area of a regular pentagon is 280 square centimeters, what is the length, in centimeters, of each side if the apothem is 16 centimeters?
7
Giving your answer in millimeters squared, find the lateral surface area of a right pentagonal prism whose altitude is 12 millimeters and base has sides of length 8, 10, 12, 14, and 16 millimeters, respectively:
720
A flagpole casts a 100-foot long shadow. If a 6-foot tall person standing at the base of the pole casts an 8-foot shadow, how many feet tall is the flagpole?
75
One-fifth of 0.04% is equal to: W) 8 × 10^-2 X) 8 × 10^-3 Y) 8 × 10^-4 Z) 8 × 10^-5
8 × 10^-5
A circle has a diameter of 32 meters. Find the degree measure of the central angle of a sector of the circle if its arc length measures 8π meters:
90
Giving your answers in terms of π and in inches squared, find the total surface area of a closed right circular cone whose altitude is 8 inches and radius is 6 inches:
96π
The curve defined by the equation, Ax2 + Bx + Cy2 + Dy + E =0, can be an ellipse if which of the constants are positive?
A AND C
By words or number, name all of the following 3 statements that are TRUE for the function, f(x) = -3x^2 - 2x - 2 = 0: 1) there are no real zeros 2) the graph is a parabola opening downward 3) the graph has no x-intercepts
ALL
Consider triangle ABC, where the measure of angle A = 20º, B =117º, and C = 43º. Arrange the 3 sides in order of increasing length:
BC; AB; AC
What term BEST describes 2 angles with 90º as the sum of their measurements?
COMPLEMENTARY
Find the cotangent and cosecant, respectively, of a 90º angle:
COTAN = 0; COSECANT = 1
Identify the type of conic section represented by the equation, x^2 - 16y^2 = 64:
HYPERBOLA
The graph of the polar equation, r = 5 - 5 cosine θ, is a cardioid. In which two quadrants is most of the area of this cardioid?
II AND III (ACCEPT: 2 AND 3 or SECOND AND THIRD)
What is the specific name for a common tangent that intersects the segment joining the centers of 2 circles?
INTERNAL COMMON TANGENT (ACCEPT: INTERNAL or INTERNAL TANGENT)
What are the leading coefficient and degree, respectively, of the following polynomial: 3x^2 - 6x^5 + 7
LEADING COEFFICIENT = -6; DEGREE = 5
Giving your answer as up, down, left, or right, the graph of the equation x = 5y - 8y^2 - 1 opens in what direction?
LEFT
Of the following 5 functions identify all that are NOT differentiable for all real numbers: | x | (read as: absolute value of x); cosine(x); tangent(x); ex; the greatest integer function
TAN(x); THE GREATEST INTEGER FUNCTION
What is the name for the test that can be used to visually determine whether or not a relation defined by a graph represents a function?
VERTICAL LINE TEST (ACCEPT: VERTICAL LINE)
Which of the following is a second quadrant angle in standard position: W) 500º X) -180º Y) -680º Z) 930º
W) 500º
A data set has a mean of 10 and variance of 10. If every set element is multiplied by 2, which of the following is TRUE of the new mean and variance: W) mean is 20, variance is 40 X) mean is 20, variance is 10 Y) mean is 20, variance is 20 Z) mean is 10, variance is 20
W) MEAN IS 20, VARIANCE IS 40
If triangle ABD is congruent with triangle EFG, which of the following MUST be true: W) side AB is congruent to side EF X) side AD is congruent to side FG Y) measure of angle B = measure of angle G Z) measure of angle A = measure of angle G
W) SIDE AB IS CONGRUENT TO SIDE EF
Which of the following is the equation for the tangent line for y = x4 at the point (1, 1): W) y = 4x - 3 X) y = 4x - 1 Y) y = 4x + 1 Z) y = 4x + 3
W) y = 4x - 3
Which of the following is NOT true of matrices: W) a square matrix that has an inverse is called invertible X) a matrix does not have to have an inverse Y) a matrix that does not have an inverse is called non-singular Z) a matrix must be square in order to have an inverse
Y) A MATRIX THAT DOES NOT HAVE AN INVERSE IS CALLED NON-SINGULAR
Giving your answer in standard form, give the equation of the circle with center at (0, 0) and diameter of 6:
x^2 + y^2 = 9
Find the x and y intercepts of the line passing through the point (4, 8) that is perpendicular to the line 3x - 6y - 12 = 0:
X-INTERCEPT = (8, 0) (ACCEPT: 8); Y-INTERCEPT = (0, 16) (ACCEPT: 16)
Which of the following points is closest to the point (1, -2): W) (3, -5) X) (0, 3) Y) (3, 0) Z) (-5, -5)
Y) (3, 0)
Which of the following is NOT a Pythagorean triple: W) 15, 20, 25 X) 10, 24, 26 Y) 16, 24, 30 Z) 33, 44, 55
Y) 16, 24, 30
If e^x/5 = 30, which of the following is the value of x, assuming that the natural log of 2 = 0.7, and the natural log of 15 = 2.7: W) 15 X) 16 Y) 17 Z) 18
Y) 17
Which of the following numbers is evenly divisible by both 11 and 3: W) 7791 X) 7553 Y) 5181 Z) 8769
Y) 5181
What is the product of the following 2 values: (1) the greatest common divisor of 7 and 14; and (2) the least common multiple of 7 and 14: W) 21 X) 49 Y) 98 Z) 196
Y) 98
Which of the following is NOT true: W) all central angles in a regular polygon are equal X) irregular polygons are not considered to have centers and have no central angles Y) the circumcircle of a regular polygon is the circle that passes through at least one vertex Z) all regular polygons are convex
Y) THE CIRCUMCIRCLE OF A REGULAR POLYGON IS THE CIRCLE THAT PASSES THROUGH AT LEAST ONE VERTEX
Which of the following is TRUE about any two successive terms in the Fibonacci sequence: W) their product is a Fibonacci number X) they are either both odd or both even Y) they are relatively prime Z) their quotient is the golden ratio
Y) THEY ARE RELATIVELY PRIME
The graph of r = 3 secant (θ) (read as: r = 3 secant theta) is a: W) parabola X) circle Y) hyperbola Z) line
Z) LINE
Simplify the following expression:x^1/2x^2/5
x^9/10 (ACCEPT: 10sqrtx^9)
Short Answer Simplify the following expression, where a is not equal to zero if b = 0 or if b = -1: (a^b^2)(a^b)
a^b^2+2
